GRADE XII

NAME:

CLASS:
 INDEX

Chapter
TITLE Page No
No.

9 Ray Optics and Optical Instruments 3

10 Wave Optics 18

11 Dual Nature of Radiation and Matter 28

12 Atoms 37

13 Nuclei 44

14 Semiconductor Electronics: Materials, Devices and Simple Circuits 50

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CHAPTER 09: RAY OPTICS AND OPTICAL INSTRUMENTS

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IMPORTANT FORMULAE
1 1 1
1. Mirror formula 𝑓 = 𝑢 + 𝑣; where f is the focal length, u is the object distance and v is the
image distance.
ℎ 𝑣
2. Magnification produced by a spherical mirror 𝑚 = ℎ 𝑖 = − (𝑢)
𝑜
sin 𝑖 𝑛
3. Snell’s law sin 𝑟 = 𝑛2 ; where n2 is the refractive index of the output medium and n1 is the
1
refractive index of input medium.
𝑛
4. Critical angle sin 𝑖𝑐 = 𝑛𝑅 ; where nR is the refractive index of rarer medium and nD is the
𝐷
refractive index of denser medium.
𝑛 𝑛 𝑛 −𝑛
5. Refraction through a spherical surface 𝑣2 − 𝑢1 = 2 𝑅 1; where n2 is the refractive index of
the output medium and n1 is the refractive index of input medium and R is the radius of
curvature of the spherical surface.
1 𝑛 1 1
6. Lens maker formula 𝑓 = (𝑛2 − 1) (𝑅 − 𝑅 ); where n2 is the refractive index of the
1 1 2
output medium and n1 is the refractive index of input medium and R1 and R2 are the
refractive indices of the spherical lens.

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 1 1 1
7. Thin lens formula 𝑓 = 𝑣 − 𝑢; where f is the focal length, u is the object distance and v is
the image distance.
1 1 1
8. Thin lenses in contact (coaxially) 𝑓 = 𝑓 + 𝑓
1 2
1
9. Power of a lens 𝑃 = 𝑓(𝑖𝑛 𝑚𝑒𝑡𝑟𝑒𝑠)
𝑅
10. Focal length of equi – convex lens 𝑓 = 2(𝑛−1); n is the refractive index of the material of
the lens.
𝑅
11. Focal length of plano – convex lens 𝑓 = 𝑛−1; n is the refractive index of the material of
the lens.
𝑅
12. Focal length of equi – concave lesn 𝑓 = − 2(𝑛−1); n is the refractive index of the material
of the lens.
𝑅
13. Focal length of plano – convex lens 𝑓 = − 𝑛−1; n is the refractive index of the material of
the lens.
14. Power of combination of thin lenses 𝑃 = 𝑃1 + 𝑃2 + 𝑃3 + ⋯
1 𝑛 1 1
15. Lens immersed in liquid 𝑓′ = (𝑛 𝑙𝑒𝑛𝑠 − 1) (𝑅 − 𝑅 )
𝑙𝑖𝑞𝑢𝑖𝑑 1 2
𝐴+𝐷𝑚
sin( )
2
16. Refractive index of material of prism 𝑛 = 𝐴 ; where A is the angle of the prism
sin( )
2
and Dm is the minimum deviation.
17. For a thin prism 𝑑 = (𝑛 − 1)𝐴
18. Magnification produced by simple microscope
𝐷
a. Strained vision 𝑚 = 𝑓
𝐷
b. Relaxed vision 𝑚 = 1 + 𝑓
D = 25 cm is the least distance of distinct vision for a healthy human eye
19. Magnification produced by a compound microscope
a. 𝑚 = 𝑚𝑜 𝑚𝑒
𝑣
b. Magnification of objective 𝑚𝑜 = 𝑢𝑜
𝑜
𝐷
c. Magnification of eye piece 𝑚𝑒 = (1 + 𝑓 ) 𝑓𝑜𝑟 𝑟𝑒𝑙𝑎𝑥𝑒𝑑 𝑣𝑖𝑠𝑖𝑜𝑛; 𝑚𝑒 =
𝑒
𝐷
𝑓𝑜𝑟 𝑠𝑡𝑟𝑎𝑖𝑛𝑒𝑑 𝑣𝑖𝑠𝑖𝑜𝑛.
𝑓𝑒
𝐿 𝐷
d. For image formed at infinity 𝑚 = 𝑓
𝑜 𝑓𝑒
𝑓𝑜
20. Magnifying power of telescope 𝑚 = 𝑓
𝑒
21. Optical tube length of telescope 𝐿 = 𝑓𝑜 + 𝑓𝑒

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Classwork questions:
Reflection
1. Describe the size nature and position of the image formed when an object is placed at a
distance of 15 cm from a concave mirror of focal length 10 cm.
2. An object is placed in front of a convex mirror at a distance of 52 cm. A plane mirror is
introduced covering the lower half of the convex mirror. Distance between the object and
the plane mirror is 30 cm. It is found that there is no parallax between the images formed
by the two mirrors. What is the radius of curvature of the convex mirror?
3. A rod of length 10 cm lies along the principal axis of a concave mirror of focal length 10
cm in such a way that the end closer to the pole is 20 cm away from it. Calculate the
length of the image.
4. A square wire of side 3.0 cm is placed 25 cm away from a concave mirror of focal length
10 cm. What is the area enclosed by the image of the wire? The centre of the wire is on
the axis of the mirror with its two sides normal to the axis.
Refraction (Snell’s law, lateral shift, normal shift and TIR)
5. The wavelength of light in air is 630 nm. (a) What is its frequency? (b) What is its
wavelength in glass of refractive index 1.5? (c) What is its speed in glass?
6. A transparent cube of side 210 mm contains a small air bubble. Its apparent distance
when viewed through one face of the cube is 100 mm and when viewed through the
opposite face is 40 mm. (a) What is the actual distance of the bubble from the second
face? (b) What is the refractive index of the material of the cube?
7. A fish inside water sees the outside world as if it is contained in a cone, which subtends a
circle at the surface of the water. Calculate the radius of the circle if the fish is at a depth
of 2 m and refractive index of water is 1.33.
8. A tank is filled with water to a height of 12.5 cm. The apparent depth of a needle lying at
the bottom of the tank is measured by a microscope to be 9.4 cm. What is the refractive
index of water? If water is replaced by a liquid of refractive index 1.63 up to the same
height, by what distance would the microscope have to be moved to focus on the needle
again?
Refraction (through spherical surface and lens)
9. A plano – convex lens of thickness 6 mm is placed on a table with its plane surface
upwards. Its thickness appears to be 4 mm. On reversing the lens, its thickness appears to
be 30/7 mm. Calculate the refractive index of the material of the lens and its focal length.
10. A lens has a focal length 0.2 m when kept in air. On immersing it in water, its focal
length increases by 0.6 m, calculate the refractive index of water if the refractive index of
glass is 1.5.
11. The convex surface of a thin concavo – convex lens of glass of refractive index 1.5 has a
radius of curvature of 0.2 m. The concave surface has a radius of curvature of 0.6 m. If
the concave part is filled with water of refractive index 1.33, find the focal length of lens
with glass combination.

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 12. An equi – convex lens of focal length 0.1 m has an object at a distance of 0.4 m from it. If
the lens is sliced into two identical plano – convex lenses and one of them is retained in
the original position of the lens, calculate the distance through which the screen has to be
moved and the direction of motion to get the image on the screen. Refractive index of the
material of the lens is 1.5.
13. Wavelength of monochromatic light on passing from air to glass reduces to 2/3 times its
value in air. An object held at 1.25 m from an equi – convex lens made of the above glass
has its image at a distance of 5 m from the lens. Calculate the radius of curvature of the
lens surface.
Combination of thin lenses and Power of a lens
14. What is the focal length of a convex lens of focal length 30 cm kept in contact with a
concave lens of focal length 20 cm? Is the system a converging or a diverging lens?
Ignore the thickness of the lenses.
15. Two lenses of focal lengths 0.20 m and 0.30 m are kept in contact. Find the focal length
of the combination. Calculate the power of the lenses and the combination.
Refraction through Prism
16. A prism of angle 60° produces an angle of minimum deviation of 40°. Calculate (a)
refractive index of the material of the prism (b) angle of incidence.
17. A certain prism is found to produce a minimum deviation of 38°. It produces a deviation
of 44° when the angle of incidence is either 42° 𝑜𝑟 62°. Determine the refracting angle of
the prism, the angle of incidence for minimum deviation and the refractive index of the
material of the prism.
18. At what angle should a ray of light be incident on the face of an equilateral prism, so that
it just suffers total internal reflection at the other face? Refractive index of the material of
the prism is 1.5.
19. A ray of monochromatic light is incident normally on one face of a triangular prism of
refracting angle 30° and refractive index 1.5. Find the angle of emergence and the
deviation produced.
Optical instruments
20. A compound microscope consists of an objective lens of focal length 2.0 cm and an eye –
piece of focal length 6.25 separated by a distance of 15 cm. How far from the objective
should an object be placed in order to obtain the final image at the least distance of
distinct vision? What is the magnifying power of the microscope?
21. A telescope is used to observe the Moon 3.8 × 108 𝑚 away. The objective has a focal
length of 17 m and the eye – piece has a focal length of 17 cm. Find the minimum
distance between object points on the Moon that are just barely resolved by an eye
looking through the telescope. Assume that the resolution is limited by the eye’s acuity
and that the minimum angle of resolution is 5.0 × 10−4 𝑟𝑎𝑑.
22. A man with normal near point (25 cm) reads a book with small print using a magnifying
glass (a thin convex lens of focal length 5 cm).

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 a. What is the closest and the farthest distance at which he should keep the lens from
the page so that he can read the book when viewing through the magnifying
glass?
b. What is the maximum and minimum angular magnification possible using the
above simple microscope?
23. A person with a normal near point using a compound microscope with objective of focal
length 8.0 mm and an eye – piece of focal length 2.5 cm can bring an object placed at 9.0
mm from the objective in sharp focus. What is the separation between the two lenses?
Calculate the magnifying power of the microscope?
Homework questions:
Reflection
1. The image of an object due to a convex mirror is 4 cm from the mirror. If the mirror has a
radius of curvature of 24 cm, find (i) object position and (ii) the magnification.
2. A small candle, 2.5 cm in size is placed at 27 cm in front of a concave mirror of radius of
curvature 36 cm. At what distance from the mirror should a screen be placed in order to
obtain a sharp image? Describe the nature and size of the image.
3. An erect image three times the size of the object is obtained with a concave mirror of
radius of curvature 36 cm. What is the position of the object?
Refraction (Snell’s law, lateral shift, normal shift and TIR)
4. Monochromatic light of wavelength 589 nm is incident on air – water interface. Calculate
the wavelength, frequency and velocity of (a) reflected ray (b) refracted ray of light.
Refractive index of water is 1.33.
5. A small pin fixed on a table top is viewed from above from a distance of 50 cm. By what
distance would the pin appear to be raised if it is viewed from the same point through a
15 cm thick glass slab held parallel to the table? Refractive index of the glass = 1.5. Does
the answer depend on the location of the slab?
6. A small air bubble is trapped in a glass cube of edge 0.24 m. When viewed from one
face, it appears to be 0.1 m from the surface and when viewed through the opposite face
it appears to be 0.06 m from the surface. What is the refractive index of the glass cube?
7. A small bulb is placed at the bottom of a tank containing water to a depth of 80 cm. What
is the area of the surface of water through which light from the bulb can emerge out?
Refractive index of water is 1.33. (Consider the bulb to be a point source).
Refraction (through spherical surface and lens)
8. An object 3.0 cm in size is placed 14 cm in front of a concave lens of focal length 21 cm.
Describe the features of the image produced by the lens.
9. Double convex lenses are to be manufactured from a glass of refractive index 1.55 with
both faces of the same radius of curvature. What is the radius of curvature required if the
focal length is to be 20 cm?
10. A convex lens has 20 cm focal length in air.

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 a. What is its focal length when immersed in water?
b. What is its focal length when immersed in a liquid of refractive index 1.6?
Combination of thin lenses and Power of a lens
11. A convex and concave lens of focal lengths 10 and 20 cm are kept coaxially in contact. A
point object is placed at a distance of 50 cm from this combination. Find the position of
the final image due to the combination (assume that the lenses are of negligible
thickness).
12. If f = 0.5 m for a glass lens, what is the power of the lens?
Refraction through Prism
13. Calculate the angle of a prism made of material of refractive index 1.618 producing a
minimum deviation of 48°.
14. At what angle should a ray of light be incident on the face of a prism of refracting angle
60° so that it just suffers total internal reflection at the other face? The refractive index of
the material of the prism is 1.524.
15. A prism is made of glass of unknown refractive index. A parallel beam of light is incident
on a face of the prism. The angle of minimum deviation is measured to be 40°. What is
the refractive index of the material of the prism? The refracting angle of the prism is 60°.
Optical instruments
16. An angular magnification of 30 X is desired using an objective of focal length 1.25 cm
and an eye – piece of focal length 5 cm. How will you set up the compound microscope?
17. The optical tube length of a compound microscope is 20 cm. The focal lengths of the
objective and the eye – piece are 1 cm and 2 cm respectively. The final image is viewed
at infinity. Calculate the magnification.
WORKSHEET 01

1. A ray of light is incident at 30° on a boundary separating a denser medium (𝑛𝑑 = √3)
and a rarer medium (𝑛𝑟 = 1). The angle of deviation is
(A) 60° (B) 30° (C) 90° (D) 45°
2. A ray of light falls on a glass plate of refractive index n. If the angle between the
reflected and refracted rays is 90°, then the angle of incidence is
1 1
(A) sin−1 𝑛 (B) sin−1 (C) tan−1 (D) tan−1 𝑛
𝑛 𝑛
3. A ray of light 500 nm takes time t1 to traverse 20 m in air. It takes time t2 to traverse the
same distance in a liquid of refractive index 1.6. The difference between the time taken in
the two cases is
(A) 4 x 10-8 s (B) 6 x 10-8 s (C) 2 x 10-8 s (D) 8 x 10-8 s
4. When a ray of light enters a medium of refractive index n, it is observed that the angle of
refraction is equal to half of the angle of incidence. The angle of incidence is
𝑛 𝑛 𝑛
(A) 2 cos −1 2 (B) cos −1 2 (C) 2 cos −1 𝑛 (D) 2 sin−1 2

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5. A ray of light passes through four transparent media of refractive indices n1, n2, n3 and n4
as shown in the figure. The surfaces of the media are parallel. If the emergent ray CD is
parallel to the incident ray AB, we must have
(A) n1 = n2
(B) n3 = n2
(C) n3 = n4
(D) n1 = n4
6. A small object is placed at a distance of 20cm from a glass slab of thickness 10 cm. The
farther side of the glass slab is silvered. An image appears to be at 23.2cm behind the
silvered face of the block. The refractive index of the glass is
(A) 1.49 (B) 1.51 (C) 1.59 (D) 1.48
7. A ray of light passing from glass to water is incident on the glass-water interface at 65°.
If the critical angle for the pair of media is 63°, then the ray will
(A) Emerge into water with a deviation of 2° from the normal
(B) Be refracted into water with a deviation of 2°
(C) Be totally internally reflected back into glass with a deviation of 50°
(D) Be totally internally reflected back into glass with a deviation of 65°
8. A source of light is kept at the bottom of a tank in which water is present to a depth of 5
m. An opaque disc has to be floated on the surface of water so that the source is not seen
from above. If the refractive index of water is (4/3), then the minimum radius of the disc
should be
3 15 √7
(A) 15√17 𝑚 (B) 𝑚 (C) 𝑚 (D) 15 𝑚
√7 √7
9. A ray of light incident normally on one of the refracting faces of a prism just emerges
from the other face, if the angle of the prism is
(A) Equal to the critical angle (B) Equal to twice the critical angle
(C) Equal to half the critical angle (D) Less than critical angle
10. A ray of light is incident normally on one face of a right angled isosceles prism. It
emerges parallel to that face. The refractive index of the material of the prism is
(A) 1.33 (B) 1.414 (C) 1.5 (D) 1.732
11. Composite light consisting of blue, green, and red rays is incident on a right angled
isosceles prism as shown in the figure. The critical angles for the material of the prism for
blue, green, and red rays are 43°, 44°, 47° respectively.
The prism will separate
(A) Blue colour from red and green
(B) Red colour from blue and green
(C) Green colour from red and blue
(D) All the colours

12. It is found that the angle of refraction is half the angle of incidence when a ray passes
symmetrically through a prism of refractive index √2. The angle of the prism is
(A) 60° (B) 45° (C) 75° (D) 90°

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13. The refractive index of glass is 1.520 for red light and it is 1.525 for blue light. D1 and D2
are the angles of minimum deviation of red light and blue light respectively, due to a thin
prism. Then,
(A) D1 > D2 (B) D1 < D2 (C) D1 = D2 (D) None of these
14. If n1 and n2 are the refractive indices of two media separated by a spherical refracting
surface as shown, the relation between n1 and n2

(A) n1 > n2 (B) n1 < n2 (C) n1 = n2 (D) None of these

15. A point object is placed at the centre of a glass sphere of diameter 12cm and refractive
index 1.5. The distance of the image from the surface of the sphere appears to be at
(A) 1.2 cm (B) 6 cm (C) 9 cm (D) 12 cm
16. A beam of light is incident on a convex spherical surface of radius of curvature 20 cm
and refractive index n = 1.5. After refraction from the spherical surface, the rays
(A) Actually meet at some point on the principal axis
(B) Meet or appear to meet at a distance of 60 cm from the spherical surface
(C) Meet at a distance of 60 cm from the spherical surface
(D) Both (A) and (C)
17. If lower half of a concave mirror is blackened
(A) Image distance increases (B) Image distance decreases
(C) Image intensity decreases (D) Image intensity increases
18. A parallel beam of rays in a medium of refractive index n1 is incident on a biconcave lens
made of a material of refractive index n. After refraction from the first surface the rays
converge to a point in a medium of refractive index n2, on the other side. If refraction
does not take place at the second surface, the relation between n1, n2 and n is
(A) n1 = n < n2 (B) n1 < n = n2 (C) n1 > n = n2 (D) n1 = n > n2
19. The radius of curvature of the convex face of a plano-convex lens is 15cm. The refractive
index of the material is 1.4. Then the power of the lens is
(A) 1.6 D (B) 1.66 D (C) 2.6 D (D) 2.66 D
20. The principal focus of an equiconvex lens (ng = 1.5) is at a distance of 10cm from the
lens in air. When the lens is inside a liquid of refractive index 1.25, the focal length will
be
(A) 20 cm (B) 25 cm (C) 15 cm (D) 30 cm
21. Two thin lenses are in contact. Their focal lengths are 2 m and 0.25 m. The power of the
combination is
(A) 4.5 D (B) 2.25 D (C) 1.75 D (D) 9 D
22. If a parallel beam of light is incident on a combination of a convex lens of focal length f
and a concave lens of focal length 0.5 f in contact, the image will be
(A) Real and at a distance v = 0.5 f (B) Real and at a distance v = f
(C) Virtual and at a distance v = f (D) Virtual and at a distance v = 0.5 f

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23. When the image is at least distance of distinct vision, the magnification due to a simple
microscope of focal length 5cm is
(A) 2 (B) 4 (C) 5 (D) 6
24. An equiconvex lens of focal length 60 cm is cut into two equal parts A and
B as shown so as to obtain two plano – convex lenses. The focal length of
each part is
(A) 30 cm
(B) 60 cm
(C) 120 cm
(D) 240 cm
25. A simple telescope, consisting of an objective of focal length 60 cm and a single eye lens
of focal length 5 cm is focused on a distant object in such a way that parallel rays emerge
from the eye lens. If the object subtends an angle of 2° at the objective, the angular width
of the image is
(A) 10° (B) 24° (C) 50° (D) 12°
26. The magnifying power of the objective of a compound microscope is 5. If the magnifying
power of the microscope is 30, then the magnifying power of eye piece will be
(A) 150 (B) 6 (C) 0.667 (D) 24
27. An astronomical telescope gives an angular magnification of magnitude 5 for distant
objects. The separation between the objective and the eye piece is 36 cm. The final image
is formed at infinity. Then the focal lengths fo of the objective and fe of the eyepiece
respectively are
(A) 45 cm and – 9 cm (B) 50 cm and 10 cm
(B) 7.2 cm and 5 cm (D) 30 cm and 6 cm
28. The focal length of the objective lens of a telescope is 30cm and that of its eye lens is 3
cm. It is focused on a scale 2 m distant from it. The distance of the objective lens from
the eye lens to see with relaxed eye is
(A) 33 cm (B) 65.3 cm (C) 38.3 cm (D) 40.3 cm
29. A telescope has an objective lens of focal length 200 cm and an eye piece of focal length
2 cm. If this telescope is used to see a 50 m tall building at a distance of 2 km, the height
of image of the building formed by the objective lens will be
(A) 5 cm (B) 10 cm (C) 1 cm (D) 2 cm
30. In an astronomical telescope, the objective lens of focal length fo and eye piece of focal
length fe are separated by a distance L. Then L is
(A) fo + fe (B) fo – fe
(C) Much greater than fo or fe (D) Much less than fo or fe
WORKSHEET 02
Assertion and Reason based questions
Directions: These questions consist of two statements, each printed as Assertion and
Reason. While answering these questions, you are required to choose any one of the
following four responses.

12
 (a) Both Assertion and Reason are correct and the Reason is a correct explanation of the
Assertion.
(b) Both Assertion and Reason are correct but Reason is not a correct explanation of the
Assertion.
(c) Assertion is correct, Reason is incorrect
(d) Both Assertion and Reason are incorrect
1. Assertion: An object is placed at a distance of f from a convex mirror of focal length f its
image will form at infinity.
Reason: The distance of image in convex mirror is always negative
2. Assertion: The focal length of convex mirror will increase if the mirror is placed in
water.
Reason: The focal length of convex mirror of radius R is, R = f/2.
3. Assertion: The image of a point object situated at the centre of hemispherical lens is also
at the centre.
Reason: For hemisphere Snell’s law is not valid.
4. Assertion: The images formed by total internal reflections are much brighter than those
formed by mirrors or lenses.
Reason: There is no loss of intensity in total internal reflection.
5. Assertion: Critical angle of light passing from glass to air is least for light of violet
colour.
Reason: Refractive index of glass is maximum for violet light.
6. Assertion: Ray of light passing through optical centre of a lens goes undeviated.
Reason: Ray falls normally at the optical centre and in normal incidence, there is no
deviation of light produced.
7. Assertion: A convex mirror cannot form real images.
Reason: Convex mirror converges the parallel rays that are incident on it.
8. Assertion: The mirror formula is valid for mirrors of small apertures.
Reason: Laws of reflection is valid for only plane mirrors.
9. Assertion: Air bubbles shine in water.
Reason: Air bubbles shine in water due to refraction of light.
10. Assertion: A convex lens of focal length 30 cm can't be used as a simple microscope in
normal setting.
𝐷
Reason: For normal setting, the angular magnification of simple microscope is 𝑀 = 𝑓

WORKSHEET 03
2 and 3 mark questions
1. Draw a ray diagram to show image formation when the concave mirror produces a real,
inverted and magnified image of the object.
2. When monochromatic light travels from one medium to another, its wavelength changes
but frequency remains same. Explain.
3. Find the radius of curvature of the convex surface of a plano-convex lens, whose focal
length is 0.3 m and the refractive index of the material of the lens is 1.5.

13
4. What is the focal length of a focal convex lens of length 30 cm in contact with a lens of
focal length 20 cm? Is the system a converging lens or diverging lens? Ignore thickness
of the lens.
5. Two lenses of focal lengths 6 cm and 50 cm are to be used for making a telescope. Which
will you see for the objective and why?
6. A ray of light is incident at an angle of 60° on one face of a rectangular glass slab of
thickness 0.1 m and refractive index 1.5. Calculate the lateral shift produced.
7. The radii of curvature of the surfaces of a double convex lens are 20 cm and 40 cm,
respectively and its focal length is 20 cm. What is refractive index of the material of the
lens?
8. A telescope consists of two lenses of focal lengths 20 cm and 5 cm. Obtain its
magnifying power when the final image is (i) at infinity (ii) at 25 cm from the lenses of
eye.
9. A convex lens of focal length 5 cm is used as a simple microscope. What will be the
magnifying power when the image is formed at the least distance of distinct vision?
10. (a) Draw a ray diagram to show image formation when the concave mirror produces a
real, inverted and magnified image of the object.
(b) Obtain the mirror formula and write the expression for the linear magnification.
11. Derive the expression for the refractive index of the material of a prism in terms of the
angle of deviation (Dm) and the angle of the prism (A).
12. (a) Draw a labeled ray diagram of a refracting telescope. Define its magnifying power
and write the expression for it. Write 2 important limitations of a refracting telescope
over a reflecting type telescope.
(b) Draw a neat labeled ray diagram of a compound microscope. Define its magnifying
power and write an expression for it for (i) normal adjustment and (ii) strained vision.
13. Use the mirror equation to show that an object placed between f and 2f of a concave
mirror produces a real image beyond 2f. [HOTS]
14. The figure shows a ray of light falling normally on the face AB of an equilateral glass
prism having refractive index 3/2, placed in water of refractive index 4/3. Will this ray
suffer total internal reflection on striking the face AC? Justify your answer. [HOTS]

15. A biconvex lens made of a transparent material of refractive index 1.25 is immersed in
water of refractive index 1.33. Will the lens behave as a converging or a diverging lens?
Give reason. [HOTS]
16. A lens shown in figure is made of two different materials. A point object is placed on the
principal axis of the lens. How many images will be obtained? [HOTS]

14
 17. You are given three lenses having powers P1 = 6 D, P2 = 3 D and P3 = 12 D. Which two
of these lenses will you choose to construct a microscope? [HOTS]
18. A ray of light incident at an angle θ on a refracting face of a prism emerges from the
other face normally. If the angle of the prism is 50 and the prism is made of a material of
refractive index 1.5. Find the angle of incidence. [HOTS]
19. You are given four sources of light each one providing a light of a single colour-red, blue,
green and yellow. Suppose the angle of refraction for a beam of yellow light
corresponding to a particular angle of incidence at the interface of two media is 900.
Which of the following statements is correct it the source of yellow light is replaced with
that of other lights without changing the angle of incidence? [HOTS]
(A) The beam of red light would undergo total internal reflection.
(B) The beam of red light would bend toward normal while it gets refracted through the
second medium.
(C) The beam of blue light would undergo total internal reflection.
(D) The beam of green light would bend away from the normal as it gets refracted
through the second medium.
20. The radius of curvature of the curved surface of a plano – convex lens is 20 cm. If the
refractive index of the material of the prism is 1.5, it will [HOTS]
(A) Behave as a convex lens only for the objects that lie on its curved side.
(B) Behave as a concave lens for the objects that lie on its curved side.
(C) Behave as a convex lens irrespective of the side on which the object lies.
(D) Behave as a concave lens irrespective of the side on which the object lies.
TEST YOURSELF
1 Two lenses are in contact having powers of 5D and -3D. The focal length of 1
this combination will be
(A) 50 cm (B) 75 cm (C) 25 cm (D) 20 cm
2 An object 2 cm high is placed at a distance of 16 cm from a concave mirror, 1
which produces a real image 3 cm high. What is the focal length of the mirror?
(A) – 9.6 cm (B) – 3.6 cm (C) – 6.3 cm (D) – 8.3 cm

15
3 A plot of angle of deviation D versus angle of incidence for a triangular prism 1
is shown below. The angle of incidence for which the light ray travels parallel
to the base is
(A) 30o
(B) 60o
(C) 45o
(D) Data insufficient.

4 You are given following three lenses. Which two lenses will you see as an 1
eyepiece and as an objective to construct an astronomical telescope?
(A) L1− Objective lens, L3− Eyepiece
(B) L3− Objective lens, L1− Eyepiece
(C) L1− Objective lens, L2− Eyepiece
(D) L2− Objective lens, L3− Eyepiece

5 A: The optical instruments are used to increase the size of the image of the 1
object.
R: The optical instruments are used to increase the visual angle
6 A: The image formed by a concave mirror is certainly real if the object is 1
virtual.
R: The image formed by a concave mirror is certainly virtual if the object is
real.
7 An object is placed in front of a convex mirror of focal length 30 cm. If the 2
image is a quarter of the size of the object, find the position of the image.
8 An object AB is kept in front of a concave 3
mirror as shown in the figure.
(a) Complete the ray diagram showing e
image formation of the object.
(b) How will the position and intensity or
image be affected, if the lower half of the
mirror's reflecting surface is painted black?
9 (a) Write the necessary conditions for the phenomenon of total internal 5
reflection to occur.
(b) Write the relation between refractive index and critical angle for a given
pair of optical media.
(c) Using a neatly labeled ray diagram and appropriate sign conventions, derive
the thin lens formula for a concave lens.
10 Consider two lenses A and B of focal length f1 and f 2 placed in contact with 4
each other. Let the object be placed at a point O beyond the focus of the first
lens A. The first lens produces an image at I1. Since image I1 is real, it serves as
a virtual object for the second lens B, producing the final image at I. It must,
however, be borne in mind that formation of image by the first lens is presumed
16
only to facilitate determination of the position of the final image. In fact, the
direction of rays emerging from the first lens gets modified in accordance with
the angle at which they strike the second lens. Since the lenses are thin, we
assume the optical centres of the lenses to be coincident. Let this central point
be denoted by P. If the two lens-system is regarded as equivalent to a single
lens of focal length f, we have
(i) Two lenses of power +10D and –5D are placed in contact. Where the object
should be held from the lens so as to obtain a virtual image of magnification 2?
(A) 5 cm (B) – 5 cm (C) 10 cm (D) – 10 cm
(ii) The plane faces of two identical plano-convex lenses, each having focal
length of 40 cm, are placed against each other to form a usual convex lens. The
distance from this lens at which an object must be placed to obtain a real,
inverted image with magnification '–1' is
(A) 80 cm (B) 40 cm (C) 20 cm (D) 160 cm
(iii) Two thin lenses of focal lengths 20 cm and –20 cm are placed in contact
with each other. The combination has a focal length equal to
(A) Infinity (B) 50 cm (C) 60 cm (D) 10 cm
(iv) If a convex lens of focal length 80 cm and a concave lens of focal length 50
cm are combined together, what will be their resulting power
(A) + 6.5 D (B) – 6.5 D (C) +7.5 D (D) – 0.75 D

17
CHAPTER 10: WAVE OPTICS

18
IMPORTANT FORMULAE
sin 𝑖 𝑛 𝑣 𝜆
1. Snell’s law sin 𝑟 = 𝑛2 = 𝑣1 = 𝜆1
1 2 2
2. Interference of light
a. 𝐼 = 𝐼1 + 𝐼2 + 2√𝐼1 𝐼2 𝑐𝑜𝑠𝜑
b. Condition for maxima ∆𝜑 = 2𝑛𝜋; 𝑛 = 0, 1, 2, 3 … ….
c. Condition for minima ∆𝜑 = (2𝑛 ± 1)𝜋; 𝑛 = 0, 1, 2, 3 … … …
2
𝐼𝑚𝑎𝑥 (√𝐼1 +√𝐼2 )
d. = 2
𝐼𝑚𝑖𝑛 (√𝐼1 −√𝐼2 )
e. 𝐼𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 ∝ 𝑤𝑖𝑑𝑡ℎ 𝑜𝑓 𝑠𝑙𝑖𝑡 ∝ 𝑠𝑞𝑢𝑎𝑟𝑒 𝑜𝑓 𝑎𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒
3. Young’s Double Slit Experiment
𝜆𝐷
a. Fringe width 𝛽 = 𝑑
𝑛𝜆𝐷
b. Constructive interference (bright fringes) 𝑥𝑛 = 𝑑
(2𝑛−1)𝜆𝐷
c. Destructive interference (dark fringes) 𝑥𝑛 = 2𝑑
4. Diffraction of light at a single slit
𝑛𝜆
a. Path difference sin 𝜃𝑛 = 𝑎
2𝐷𝜆
b. Width of central maximum 𝛽 = 2𝑦 = 𝑎
2𝜆
c. Angular width of central maximum 2𝜃 = 𝑎
5. Intensity of any point on the screen 𝐼 = 4𝐼𝑜 𝑐𝑜𝑠 2 𝜑2

Classwork questions
Interference of Light
1. Two coherent sources of intensities Io and 16 Io give rise to an interference pattern.
Calculate the intensities on a screen corresponding to the points of path difference (a)
zero, (b) λ/4 and (c) λ/2
2. In YDSE two narrow parallel slits 0.2 mm apart are illuminated with monochromatic
light of wavelength 600 nm to get fringe pattern on a screen 0.8 m away from the slits.
Calculate the distance of
a. Third dark fringe from the central bright fringe and
b. Second bright fringe from the central bright fringe.
3. What should be the minimum distance at which an observation screen of width 7.8 mm
be held to get 25 bright fringes in YDSE, using light of wavelength 540 nm? Given: the
slit separation is 2 mm.
4. Two slits in YDSE have widths in the ration 4:1. Calculate the ratio of maximum
intensity to the minimum intensity.

19
 5. The path difference between two beams of light reaching a point in a Young’s experiment
is 1.2 × 10−6 𝑚. Find the nature of interference at the point for light of wavelength (a)
600 nm (b) 480 nm and (c) 540 nm.
6. The distance between two coherent sources is 3 mm and the screen is 0.9 m from the
sources. The 16th dark fringe is at a distance of 2 mm from the central bright fringe. Find
the
a. Wavelength of light used
b. Distance of the 10th bright fringe from the central bright fringe
c. Distance of the 10th bright fringe from the central bright fringe when the
separation between the screen and the slits is increased by 0,1 m
7. A beam of light consisting of two wavelengths 4200 𝐴° 𝑎𝑛𝑑 5600 𝐴° is used to obtain
interference fringes in YDSE. The distance between the sits is 0.3 mm and the distance
between the slits and the screen is 1.5 m. Compute the least distance of the point from the
central maximum, where the bright fringes due to both the wavelengths coincide.
Diffraction
8. A convex lens of focal length 20 cm forms a single slit diffraction pattern of a slit of
width 0.1 mm. Find the distance of the first dark band from the central maximum, if the
wavelength of light used is 400 nm.
9. A beam of parallel rays of light of wavelength 600 nm is incident normally on a slit. Due
to diffraction, each first order minimum lies at a distance of 0.6 mm from the central
maximum on either side of it. The distance of the screen from the slit is 1 m. Calculate
the width of the slit.
10. Light of wavelength 560 nm falls normally on a slit of width 0.05 mm. Find the angular
positions of third secondary maximum and third minimum in the diffraction pattern.
Homework questions
Interference of light
1. Two narrow parallel slits 1 mm apart are illuminated with monochromatic light of
wavelength 590 nm. Calculate the fringe width obtained on a screen 1 m away from the
slits.
2. Calculate the angular fringe width of a dark band in a YDSE using light of wavelength 00
nm and a slit separation of 3 mm.
3. In a YDSE, the distance between slits is 1 mm. The fringe width is found to be 0.6 mm.
When the screen is moved through a distance of 0.25 m, away from the plane of the slits
the fringe width becomes 0.75 mm. Find the wavelength of light used.
4. Calculate the angular positions of (a) 3rd bright fringe and (b) 5th dark fringe in an
interference pattern produced by a light of wavelength 480 nm, if the separation is 0.16
mm.
5. In a YDSE, the wavelength of light used is 500 nm, slit separation is 1 mm and the
distance between the slits and the screen is 1.2 m. Calculate the distance between the 5th
and the 10th bright fringes.

20
Diffraction
6. A convex lens of focal length 0.4 m forms a single diffraction pattern of a slit 0.02 mm
wide. Calculate the distance of the third bright band from the central maximum, if the
wavelength of light used is 690 nm.
7. In a single slit diffraction experiment when light of wavelength 589.3nm is used, the
distance between the two first order minima on both the sides of the central maximum is
0.028 m. The distance of the screen is 1 m from the plane of the slit. Calculate the width
of the slit.
8. A parallel beam of light of wavelength 500 nm falls on a narrow slit and the resulting
diffraction pattern is observed on a screen 1 m away. It is observed that the first
minimum is at a distance of 2.5 mm from the centre of the screen. Find the width of the
slit.
WORKSHEET 01
1. Huygen’s principle of secondary wavelets may be used to
(A) Find the velocity of light in vacuum
(B) Explain the particle behavior of light
(C) Find the new position of wavefront
(D) Explain photoelectric effect
2. Ray diverging from a point source on a wavefront are
(A) Cylindrical (B) Spherical (C) Plane (D) Cubical
3. The phase difference between the two light waves reaching at a point P is 100π.Their
path difference is equal to
(A) 10 λ (B) 25 λ (C) 50 λ (D) 100 λ
4. Two points P and Q are situated at the same distance from a point source of light on
opposite sides as shown in figure. The phase difference between the light waves arriving
at these points is
𝜋
(A) 2 (B) 𝜋
𝜋
(C) 4 (D) zero

5. In an experiment to study interference, two slits act as coherent sources of equal

amplitude ‘a’ and of same wavelength λ. In another set up, two sources are of equal
amplitude ‘a’ and of same wavelength λ, but are incoherent. The ratio of the intensities in
the two cases is (which respect to a point equidistant from the two slits)
(A) 2:1 (B) 1:2 (C) 3:4 (D) 4:3
6. In an experiment to study interference, a fringe pattern is seen on a screen placed at a
distance D. The slits are separated by a distance d and are illuminated by light of
wavelength λ. The distance from the central point to the nearest point where the intensity
falls to half of the maximum is
𝜆𝐷 𝜆𝐷 𝜆𝐷 𝜆𝐷
(A) 3𝑑 (B) 2𝑑 (C) (D) 4𝑑
𝑑

21
 𝜋
7. If two waves represented by 𝑦1 = 4 𝑠𝑖𝑛(𝜔𝑡) and 𝑦2 = 3 𝑠𝑖𝑛 (𝜔𝑡 + 3 ) interfere at a
point, the amplitude of the resultant wave will be
(A) 7 units (B) 6 units (C) 5 units (D) 3.5 units
8. Two coherent waves of intensities I and 4 I undergo interference. Then the maximum and
minimum intensities in the interference pattern are
(A) 5I, I (B) 5I, 3I (C) 9I, I (D) 9I, 3I
9. The graph depicting fringe width β against distance d between the slits in a Young’s
double slit experiment is

10. In a YDS setup, the slit separation is d = 0.5 mm. Interference pattern is observed on a
screen placed at a distance of 1 m. It is found that 9th bright fringe is at a distance of 9.0
mm from the second dark fringe. The wavelength of light used is (in 𝐴° units)
(A) 5600 (B) 6000 (C) 7500 (D) 7000
11. Two sources of light of wavelengths 4000 𝐴° and 5600 𝐴° are used in a YDSE
simultaneously. The order of the fringes of the two patterns which will be coinciding are
(A) 3rd order due to 1st source and 5th order due to the 2nd source.
(B) 7th order due to the 1st source and 5th order due to the 2nd source.
(C) 5th order due to the 1st source and 3rd order due to the 2nd source.
(D) 5th order due to 1st source and 7th order due to 2nd source.
12. In a Young’s double slit experiment, 60 fringes are visible in the field of view, due to a
sodium lamp of wavelength 5893 𝐴°. If another source of light of wavelength 4200 𝐴° is
used in place of the first source, the number of fringes visible in the field of view will be
about
(A) 60 (B) 72 (C) 84 (D) 56
13. In a YDSE the percentage change in the fringe width, when slits-screen distance is
increased by 20 % and slit separation is increased by 50 % will be
(A) 50 % (B) 20 % (C) 40 % (D) 30 %
14. In a Young’s double slit experiment, the fringe width is found to be 0.4 mm. If the whole
apparatus is immersed in water of refractive index (4 / 3) without disturbing the basic
arrangement, the new fringe width will be
(A) 0.30 mm (B) 0.40 mm (C) 0.53 mm (D) 0.35 mm
15. In a YDSE, a thin sheet of transparent material is kept in
front of slit S1. Owing to this, the fringe pattern
(A) Shifts upwards
(B) Shifts downwards
(C) Remains unchanged
(D) Shifts either upwards or downwards depending on the
thickness of the sheet

22
16. Microwave of frequency 3 × 104 MHz and ultrasonic waves of wavelength 1 cm of equal
energies are passed through a slit of width 2 cm. Appropriate detectors are used to see
whether diffraction occurs or not. Then diffraction is observed
(A) In the case of microwave only.
(B) In the case of ultrasonic wave only
(C) In both the cases, but the patterns differ in space distribution and intensity
distribution.
(D) In both the cases and the patterns are similar in space distribution and intensity
distribution.
17. In the diffraction pattern due to a single slit, along the direction normal to the plane
wavefront
(A) First order secondary maxima is formed
(B) First order diffraction minima is formed
(C) Central maximum is formed
(D) Second order secondary maxima is formed
18. In a single slit diffraction experiment, when the width of the slit decreases, the width of
the central maximum
(A) Remains the same
(B) Increases
(C) Decreases
(D) Can be any of these depending on the intensity of source
19. In a diffraction experiment at single slit, the wavelength of light used is 6000 𝐴°. The
first diffraction minimum is observed to be at 4 mm from the centre. The screen is at a
distance of 2 m from the slit. The slit width is
(A) 0.1 mm (B) 0.15 mm (C) 0.3 mm (D) 0.4 mm
20. The direction of the second order diffraction minimum due to Fraunhoffer: plane
wavefront diffraction at a single slit is (a is the slit width) given by
𝜆 2𝜆
(A) 𝜃 = sin−1 (2𝑎) (B) 𝜃 = sin−1 ( 𝑎 )
𝜆 𝜆
(C) 𝜃 = sin−1 (𝑎) (D) 𝜃 = sin−1 (4𝑎)

WORKSHEET 02
Assertion and Reason based questions
Directions: These questions consist of two statements, each printed as Assertion and
Reason. While answering these questions, you are required to choose any one of the
following four responses.
(a) Both Assertion and Reason are correct and the Reason is a correct explanation of the
Assertion.
(b) Both Assertion and Reason are correct but Reason is not a correct explanation of the
Assertion.
(c) Assertion is correct, Reason is incorrect
(d) Both Assertion and Reason are incorrect

23
1. Assertion: The speed of light in vacuum doesn't depend on nature of the source, direction
of propagation, motion of the source or observer wavelength and intensity of the wave.
Reason: The speed of light in vacuum is a universal constant independent of all the
factors listed and anything else.
2. Assertion: When monochromatic light is incident on a surface separating two media, the
reflected and refracted light both have the same frequency as the incident frequency.
Reason: At any interface between the two media, the electric (and magnetic) fields must
satisfy certain boundary conditions for all times and frequency determines the time
dependence of fields.
3. Assertion: In the wave picture of light, intensity of light is determined by the square of
the amplitude of the wave.
Reason: In the photon picture of light, for a given frequency, intensity of light is
determined by the number of photons per unit area.
4. Assertion: Thin film such as soap bubble or a thin layer of oil on water show beautiful
colours when illuminated by white light.
Reason: It happens due to the interference of light reflected from upper and lower face of
the thin film.
5. Assertion: No interference pattern is detected when two coherent sources are infinitely
close to each other.
Reason: The fringe width is inversely proportional to the distance between the two
sources.
6. Assertion: It is necessary to have two waves of equal intensity to study interference
pattern.
Reason: There will be an effect on clarity if the waves are of unequal intensity.
7. Assertion: White light falls on a double slit with one slit is covered by a green filter. The
bright fringes observed are of green colour.
Reason: The fringes observed are coloured.
8. Assertion: In YDSE, if a thin film is introduced in front of the upper slit, then the fringe
pattern shifts in the downward direction.
Reason: In YDSE if the slit widths are unequal, the minima will be completely dark.
9. Assertion: Diffraction takes place for all types of waves mechanical or non-mechanical,
transverse or longitudinal.
Reason: Diffraction’s effect are perceptible only if wavelength of wave is comparable to
dimensions of diffracting device.
10. Assertion: Coloured spectrum is seen when we look through a muslin cloth.
Reason: It is due the diffraction of white light on passing through fine slits.

WORKSHEET 03
1. What is the effect on the interference fringes in a Young’s double-slit experiment due to
each of the following operations:
a. The screen is moved away from the plane of the slits
b. the (monochromatic) source is replaced by another (monochromatic) source of
shorter wavelength

24
 c. the separation between the two slits is increased
d. the source slit is moved closer to the double slit plane
e. the width of the source slit is increased
f. the monochromatic source is replaced by a source of white light
2. A beam of light consisting of two wavelengths, 650 nm and 520 nm. Is used to obtain
interference fringes in a Young’s double-slit experiment.
a. Find the distance of the third bright fringe on the screen from the central
maximum for wavelength 650 nm.
b. What is the least distance from the central maximum where the bright fringes due
to both the wavelengths coincide?
3. In a double-slit experiment the angular width of a fringe is found to be 0.2° on a screen
placed 1 m away. The wavelength of light used is 600 nm. What will be the angular
width of the fringe if the entire experimental apparatus is immersed in water? Take
refractive index of water to be 4/3.
4. Monochromatic light is incident on a surface separating two media. The frequency of the
light after refraction remains unaffected but its wavelength changes. Why?
5. How is a wavefront defined? Using Huygen’s construction draw figure showing the
propagation of plain wave reflecting at the interface of the two media. Show that the
angle of incidence is equal to angle of reflection.
6. Differentiate between interference and diffraction.
7. In a Young's double slit experiment, fringes or obtained on a screen placed a certain
distance away from the slits. If the screen is moved by 5 cm towards the slit, the fringe
width changes by 30 µm. Given that the slits are 1 mm apart, calculate the wavelength of
the light used.
8. (a) In diffraction due to a single slit, the phase difference between light waves reaching a
point on the screen is 5𝜋. Explain whether a bright or a dark fringe will be formed at that
point.
(b) What should the width of each slit be to obtain eight maxima of two double slit
patterns within the central maximum of the single slit pattern?
(c) Draw the plot of intensity distribution in diffraction pattern due to a single slit.
[HOTS]
9. In Young’s double-slit experiment using monochromatic light of wavelength λ, the
intensity of light at a point on the screen where path difference is λ, is K units. What is
the intensity of light at a point where path difference is λ/3? [HOTS]
10. How is Huygen’s principle used to obtain the diffraction pattern due to a single slit?
Show the plot of variation of intensity with angle and state the reason for the reduction in
intensity of secondary maxima compared to central maximum. [HOTS]

25
TEST YOURSELF
1. In a Young's double slit experiment the intensity at a point where the path
𝜆 1
difference is 6 (λ is the wavelength of light used) is I. If Io denotes the
𝐼
maximum intensity, 𝐼 is equal to
𝑜
1 √3 1 3
(A) (B) (C) 2 (D) 4
√2 2
2. Two waves having intensity I and 9I produce interference. If the resultant 1
intensity at a point is 7I, what is the phase difference between the two waves?
(A) 0° (B) 60° (C) 90° (D) 120°
3. A YDSE is performed with white light. Choose the incorrect option. 1
(A) The central fringe will be white.
(B) There will not be completely dark fringe.
(C) The fringe next to central bright fringe will be red.
(D) The fringe next to central bright fringe will be violet.
4. A slit of width 12 x 10-7 m is illuminated by light of wavelength 6000 𝐴°. The 1
angular width of the central maximum is approximately
(A) 60° (B) 30° (C) 90° (D) 0°
5. A: According to Huygen’s principle, no backward wave-front is possible. 1
R: Amplitude of secondary wavelet is proportional to (1 + cosθ) where θ is the
angle between the ray at the point of consideration and the direction of
secondary wavelet.
6. A: In YDSE number of bright fringe or dark fringe cannot be unlimited 1
R: In YDSE path difference between the superposing waves cannot be more
than the distance between the slits.
7. (a) When monochromatic light is incident on a surface separating two media, 2
the reflected and refracted light both have the same frequency as the incident
frequency. Explain why?
(b) When light travels from a rarer to a denser medium, the speed decreases.
Does the reduction in speed imply a reduction in the energy carried by the light
wave?
8. What is the shape of the wavefront in each the following cases: 3
(a) Light diverging from a point source.
(b) Emerging out of a convex lens when a point source is placed at its focus.
(c) The portion of the wavefront of light from a distant star intercepted by the
Earth.
9. (a) State Huygen’s principle. 5
(b) Use Huygens' principle to show how a plane wavefront propagates from a
denser to rarer medium. Hence, verify Snell's law of refraction.
(c) How does the angular separation between fringes in single slit diffraction
experiment change when the distance of separation between the slit and screen
doubled?
10. According to Huygens principle, each point of the wavefront is the source of a 4
secondary disturbance. The wavelets from every point of a wavefront spread
out in all directions. These wavelets emanating from the wavefront are called
‘secondary wavelets.’ If we wish to determine the shape of the wavefront at
26
time t, we draw spheres of radius vt from each point on the spherical wavefront
where v represents the speed of the waves in the medium. If we draw common
tangent to all these spheres, we obtain a new position of wavefront.
Huygens principle could satisfactorily explain the phenomenon of reflection
and refraction. Amplitude of wavelets is given by 𝐴 ∝ (1 + 𝑐𝑜𝑠𝜃), For
wavefront in forward direction 𝜃 = 0°. For wavefront in backward direction
𝜃 = 180°.

1. We get spherical wavefront from point source, cylindrical wavefront from

line source, similarly plane wavefront from
(A) source at infinity (B) a point source (C) a plane (D) a circle
2. If the velocity of light emerging from source is ‘v’, the velocity of secondary
wavelets in that medium will be
(A) less than v (B) greater than v
(C) equal to v (D) may increase or decrease
3. According to Huygens theory we get wavelets in
(A) forward direction only (B) backward direction only
(C) both backward and forward direction (D) none of the above
4. The diagram represents a
(A) spherical wavefront
(B) diverging spherical wavefront
(C) portion of a spherical wavefront
(D) converging spherical wavefront.

27
CHAPTER 11: DUAL NATURE OF RADIATION AND MATTER

28
IMPORTANT FORMULAE
1. 𝐸 = 𝑚𝑐 2
1
2. 𝐼𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 ∝ (𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒)2
1
3. 𝐸𝑖𝑛𝑠𝑡𝑒𝑖𝑛′ 𝑠 𝑃ℎ𝑜𝑡𝑜𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐 𝐸𝑓𝑓𝑒𝑐𝑡 2 𝑚𝑣 2 = ℎ𝑓 − ℎ𝑓𝑜
ℎ𝑐
4. 𝑊𝑜𝑟𝑘 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝜑𝑜 = ℎ𝑓0 = 𝜆
𝑜
5. 𝐾𝐸𝑚𝑎𝑥 = 𝑒𝑉𝑜 ; where Vo is the stopping potential
ℎ𝑐 12375
6. 𝐸𝑛𝑒𝑟𝑔𝑦 𝑜𝑓 𝑝ℎ𝑜𝑡𝑜𝑛 𝐸 = ℎ𝑓 = = 𝜆 (𝑖𝑛 𝐴°) 𝑒𝑉
𝜆
𝐸 ℎ
7. 𝑀𝑜𝑚𝑒𝑛𝑡𝑢𝑚 𝑜𝑓 𝑝ℎ𝑜𝑡𝑜𝑛 𝑃 = =𝜆
𝑐
8. de – Broglie wavelength of a particle
ℎ
a. 𝜆 = 𝑚𝑣
ℎ
b. 𝜆 = ; V is the stopping potential
√𝑚𝑞𝑉
ℎ
c. 𝜆 =
√2𝑚𝐸
ℎ
d. 𝜆 = ; where k is the Boltzmann constant and T is absolute temperature.
√3𝑚𝑘𝑇

Classwork Questions
Photoelectric Effect
1. Photons of frequency ‘f’ are incident on the surface of two metals A and B of threshold
frequencies 3f/4 and 2f/3 respectively. Find the ratio of maximum kinetic energy of
electrons emitted from A to that from B.
2. Find the frequency of light which ejects electrons from a metal surface, fully stopped by a
retarding potential of 3.3 V. If photoelectric emission begins in this metal at a frequency
of 8 x 1014 Hz, calculate the work function (in eV) for this metal.
3. (a) Calculate the energy and momentum of a photon in a monochromatic beam of
wavelength 331.5 nm.
(b) How fast should a hydrogen atom travel in order to have the same momentum as that
of the photon in part (a)?
4. An alpha particle is accelerated through a potential difference of 100 V. Calculate:
a. The speed acquired by the alpha particle
b. The de – Broglie wavelength associated with it. (take mass of alpha particle as 6.4
x 10-27 kg)
5. The work function of a metal is 2.31 eV. Photoelectric emission occurs when light of
frequency 6.4 x 1014 Hz is incident on the metal surface. Calculate:
a. The energy of the incident radiation.
b. The maximum kinetic energy of the emitted electron.
c. The stopping potential of the surface. [Term – 2, 2022]

29
 6. The photon emitted during the de – excitation from the first excited level to the ground
state of hydrogen atom is used to irradiate a photo cathode in which stopping potential is
5 eV. Calculate the work function of the cathode used. [Delhi Set 2, 2023]
Dual Nature of matter
7. Plot a graph showing variation of de Broglie wavelength (λ) associated with a charged
1
particle of mass m, versus , where V is the potential difference through which the
√𝑉
particle is accelerated. How does this graph give us the information regarding the
magnitude of the charged particles?
8. The wavelength λ of a photon and the de – Broglie wavelength of an electron of mass m
2𝜆𝑚𝑐
have the same value. Show that the energy of the photon is times the kinetic energy
ℎ
of the electron, where c and h have their usual meanings.
Homework Questions
1. Why is it the frequency and not the intensity of light source that determines whether
emission of photoelectrons will occur or not? Explain.
2. Plot a graph showing the variation of photoelectric current as a function of anode
potential for two light beams having the same frequency but different intensities I1 and I2
(I1 > I2). Mention its important features. [Delhi Set 3 2023]
3. Radiation of frequency 1015 Hz is incident on three photosensitive metal surfaces A, B
and C. Following are the observations recorded:
a. Surface A: no photoelectric emission.
b. Surface B: photoemission occurs but the photoelectrons have zero kinetic energy.
c. Surface C: photoemission occurs and photoelectrons have some kinetic energy.
Using Einstein’s photoelectric equation, explain the three observations.
4. A proton and an alpha particle are accelerated by the same potential difference. Find the
ratio of their de – Broglie’s wavelengths (𝜆𝑝 : 𝜆∝ ).
5. Monochromatic light of frequency 6.0 x 1014 Hz is produced by a laser. The power
emitted is 2.0 x 10–3 W.
a. What is the energy of the photon in the light beam?
b. How many photons per second, on an average are emitted by the source?
6. The work function of caesium is 2.14 eV. Find
a. the threshold frequency for caesium, and
b. the wavelength of the incident light if the photocurrent is brought to zero by a
stopping potential of 0.60 V
WORKSHEET 01
1. Of the following, the graph which represents the variation of energy E of a photon with
wavelength λ of the radiation is

30
2. The threshold wavelength for sodium is 680nm. The photoelectric work function is
(A) 0.18 eV (B) 1.8 eV (C) 18 eV (D) 0.018 eV
3. Photons of energy 1.5eV and 2.5eV are incident on a metal surface of work function
0.5eV. The ratio of the maximum kinetic energy of the emitted photoelectrons is
(A) 1/4 (B) 1/2 (C) 4 (D) 2
4. In a photoelectric effect experiment, the stopping potential for a wavelength of 3000 Å is
2V. If the wavelength is decreased to 2000 Å, the stopping potential becomes
(A) 2 V (B) less than 2 V (C) greater than 2 V (D) 0
5. When a monochromatic source of light is at a distance of 0.2 m from a photocell, the
stopping potential (cut off voltage) and the saturation current are found to be respectively
1 V and 27 mA. If the same source is placed at a distance 0.6 m from the cell, then
(A) The stopping potential will be 0.3V and current will be 27 mA
(B) The stopping potential will be 1V and the current will be 3 mA
(C) The stopping potential will be 1V and the current will be 9 mA
(D) The stopping potential and the current will be same as before
6. A photosensitive metal is first incident with the radiation of wavelength 400nm and then
with radiations of wavelength 800nm. The change in the maximum kinetic energy of the
photoelectron is
(A) 0.55 eV (B) 1.55 eV (C) 15.5 eV (D) 5.5 eV
7. When a metal surface is illuminated by a monochromatic radiation of wavelength λ, the
stopping potential required is 3 V. If the same surface is illuminated with a light of
wavelength 2 λ, the stopping potential reduces to V. The threshold wavelength for the
metal surface is
(A) 8 λ (B) 6 λ (C) 4 λ (D) 2 λ
8. The work functions of three metals A, B and C are WA, WB and WC respectively. They
are in the decreasing order. The correct graph between stopping potential 0 V and
frequency f of incident radiation is

9. The velocity of a body of mass 10 g is 2 x 104 m s-1. The de Broglie wavelength

associated with it will be (h = 6.6 x 1034 J s)
(A) 3.3 x 10-33 m (B) 3.33 x 10-34 m
(C) 3.3 x 10-35 m (D) 3.3 x 10-36 m

31
10. The stopping potential as a function of incident radiation frequency is plotted for two
different photoelectric surfaces A and B. Then (WA − work
function of A and WB − work function of B)
(A) WA = WB
(B) WA > WB
(C) WA < WB
(D) None of these

11. In the graph shown fA, fB and fC represent threshold frequencies of photo emissive
materials A, B and C respectively. Then,
(A) fA > fB > fC
(B) fA < fB < fC
(C) fA < fB > fC
(D) fA > fB < fC

12. The energy that should be supplied to an electron to reduce its de Broglie wavelength
from 10-10 m to 0.5 x 10-10 m will be
(A) Four times the initial energy (B) Equal to the initial energy
(C) Twice the initial energy (D) Thrice the initial energy
13. An electron and a proton are moving with the same speed. Mass of proton is 1836 times
mass of electron. The ratio of their de Broglie wavelengths will be
(A) 1 (B) 1836 (C) 1/1836 (D) 918
14. A proton and an alpha particle are accelerated through the same potential difference. The
ratio of their de Broglie wavelengths will be
(A) 1:1 (B) 1:2 (C) 2:1 (D) 2√2: 1
15. The ratio of the de Broglie wavelengths of a proton and an alpha particle, if they have
same energy is
(A) 4:1 (B) 1:2 (C) 2:1 (D) 4:1

WORKSHEET 02
Assertion and Reason based questions
Directions: These questions consist of two statements, each printed as Assertion and
Reason. While answering these questions, you are required to choose any one of the
following four responses.
(a) Both Assertion and Reason are correct and the Reason is a correct explanation of the
Assertion.
(b) Both Assertion and Reason are correct but Reason is not a correct explanation of the
Assertion.
(c) Assertion is correct, Reason is incorrect
(d) Both Assertion and Reason are incorrect
1. Assertion: On increasing the intensity of light, the number of photoelectrons emitted is
more. Also the kinetic energy of each photon increases but the photoelectric current is
constant.

32
 Reason: Photoelectric current is independent of intensity but increases with increasing
frequency of incident radiation.
2. Assertion: The process of photoelectron emission and thermionic emission of electrons is
different.
Reason: Photoelectric emission does not depend upon temperature, whereas thermionic
emission is temperature dependent.
3. Assertion: Wave nature of particles is not visible in daily life.
Reason: In daily life, mass of particles is very high so their de Broglie wavelength is very
small.
4. Assertion: If a stationary nucleus emits an -particle, the de Broglie wavelengths of the
daughter nucleus and the-particle are equal.
Reason: The magnitudes of the linear momenta of the daughter nucleus and the -particle
are the same.
5. Assertion: The photoelectric effect is a proof of the quantized nature of the light.
Reason: Each photon in a light beam has same amount of energy.
6. Assertion: A photon cannot transfer all of its energy to an isolated electron.
Reason: When energy of a photon is more than 1.02 MeV, it can materialize into two
particles called electron and positron.
7. Assertion: There is almost no time-lag between the incidence of light and the emission of
photoelectrons.
Reason: A photon transfers almost all its energy to a single electron in a metal.
8. Assertion: Work function of aluminium is 4.2 eV. Emission of electrons will be possible
by two photons, each of 2.5 eV energy, striking the electron of aluminium.
Reason: Energy of a photon can be less than the work function of the metal, for
photoelectron emission
9. Assertion: As work function of a material increases by some mechanism, it requires
greater energy to excite the electrons from its surface.
Reason: A plot of stopping potential (V) versus frequency (𝜐) for different materials, has
greater slope for metals with greater work functions.
10. Assertion: For the radiation of a frequency greater than the threshold frequency,
photoelectric current is proportional to the intensity of the radiation.
Reason: Greater the number of energy quanta available, greater is the number of
electrons absorbing the energy quanta and greater is number of electrons coming out of
the metal.
WORKSHEET 03
2 and 3 mark questions
1. Write Einstein’s photoelectric equation and mention which important features in
photoelectric effect can be explained with the help of this equation. The maximum kinetic
energy of the photoelectrons gets doubled when the wavelength of light incident on the
surface changes from 𝜆1 and 𝜆2. Derive the expressions for the threshold wavelength 𝜆o
and work function for the metal surface.
2. Light of wavelength 2000 Å falls on a metal surface of work function 4.2 eV.

33
 a. What is the kinetic energy (in eV) of the fastest electrons emitted from the
surface?
b. What will be the change in the energy of the emitted electrons if the intensity of
light with same wavelength is doubled?
c. If the same light falls on another surface of work function 6.5 eV, what will be the
energy of the emitted electrons?
3. By how much would the stopping potential for a given photosensitive surface go up if the
frequency of the incident radiations were to be increased from 4 x 1015 Hz to 8 x 1015 Hz?
4. (i) Define the term threshold frequency as used in photoelectric effect.
(ii) Plot a graph showing the variation of photoelectric current as a function of anode
potential for two light beams having the same frequency but different intensities and (I1 >
I2)
5. Two monochromatic radiations, blue and violet of the same intensity are incident on a
photosensitive surface and cause photoelectric emission. Would (i) the number of
electrons emitted per second and (ii) the maximum kinetic energy of the electrons be
equal in the two cases? Justify your answer.
6. Two materials X and Y of different work functions (such that the work function of X is
smaller than that of Y) were radiated with X-rays. In which case would the kinetic energy
be higher?
7. Why is the wavelength of a large particle like a tennis ball not visible? [HOTS]
8. The graph shows variation of stopping potential V0 versus frequency of incident
radiation v for two photosensitive metals A and Which one of the two metals has higher
threshold frequency and why? [HOTS]

9. If K1 and K2 are maximum kinetic energies of photoelectrons emitted when lights of

wavelength λ1 and λ2 respectively incident on a metallic surface. If λ1 = 3λ2, then[HOTS]
𝐾2 𝐾2
(A) 𝐾1 > (B) 𝐾1 < (C) 𝐾1 = 3𝐾2 (D) 𝐾2 = 3𝐾1
3 3
10. If two particles have equal de Broglie wavelength then they must have equal magnitude
of [HOTS]
(A) Speed (B) Kinetic energy (C) Momentum (D) Charge
11. If kinetic energy of an electron is increased by 4% then percentage change in de – Broglie
wavelength [HOTS]
(A) Decreases by 2% (B) Decreases by 1%
(C) Increases by 5% (D) None of these

34
 12. 10–3 watt and 5000 Å light is directed on a photoelectric cell. If the current in the cell is
0.16 mA, the percentage of incident photons which produce photoelectrons, is [HOTS]
(A) 0.4% (B) 0.04% (C) 20% (D) 10%
TEST YOURSELF
1 A photosensitive substance emits _____when illuminated by light. 1
(A) Only electrons (B) Only neutrons
(C) Electrons and protons (D) Only protons
2 The work function of a metal is independent of 1
(A) Nature of the surface of the metal (B) Dimension of the metal
(C) Properties of the metal (D) Abundance of the metal
3 The graph is showing the photocurrent with the applied voltage of a 1
photoelectric effect experiment. Then

(A) A & B will have same intensity and B & C have same frequency
(B) B & C have same intensity and A & B have same frequency
(C) A & B will have same frequency and B & C have same intensity
(D) A & C will have same intensity and B & C have same frequency
4 The stopping potential is directly related to 1
(A) The work function of the metal
(B) Intensity of incident radiation
(C) The saturation current for the given frequency
(D) The kinetic energy gained by the photoelectrons
5 A: In process of photoelectric emission, all emitted electrons do not have 1
same kinetic energy.
R: If radiation falling on photosensitive surface of a metal consists of
different wavelength then energy acquired by electrons absorbing photons
of different wavelengths shall be different.
6 A: Photoelectric saturation current increases with the increase in frequency 1
of incident light.
R: Energy of incident photons increases with increase in frequency and as a
result photoelectric current increases.
7 The given graph shows the variations of photo-electric current (I) versus 2
applied voltage (V) for two different photosensitive materials and for two
different intensities of the incident radiations. Identify the pairs of curves
that correspond to different materials but same intensity of incident
radiation.

35
8 Sketch the graphs showing variation of stopping potential with frequency of 3
incident radiations for two photosensitive materials A and B having
threshold frequencies VA > VB
(i) In which case is the stopping potential more and why?
(ii) Does the slope of the graph depend on the nature of the material used?
Explain
9 (i) What is the (a) momentum (b) speed and, (c) de Broglie wavelength of 5
an electron with kinetic energy of 120 eV.
(ii) Radiation of frequency 1015 Hz is incident on two photosensitive surface
P and Q. There is no photosensitive from surface P. Photoemission occurs
from surface Q but photoelectrons have zero kinetic energy. Explain these
observations and find the value of work function for surface Q.
10 According to wave theory of light, the light of any frequency can emit 4
electrons from metallic surface provided the intensity of light be sufficient
to provide necessary energy for emission of electrons, but according to
experimental observations, the light of frequency less than threshold
frequency cannot emit electrons; whatever be the intensity of incident light.
Einstein also proposed that electromagnetic radiation is quantised. If
photoelectrons are ejected from a surface when light of wavelength λ1 = 550
nm is incident on it. The stopping potential for such electrons is Vs = 0.19
V. Suppose the radiation of wavelength λ2 = 190 nm is incident on the
surface.
(i) Photoelectric effect supports quantum nature of light because
(a) There is a minimum frequency of light below which no photoelectrons
are emitted.
(b) The maximum K.E. of photoelectric depends only on the frequency of
light and not on its intensity.
(c) Even when the metal surface is faintly illuminated, the photo electrons
leave the surface immediately.
(d) Electric charge of the photoelectrons is quantized
(A) a, b, c (B) c, d (C) b, c (D) a, d, c
(ii) In photoelectric effect, electrons are ejected from metals, if the incident
light has a certain minimum
(A) Wavelength (B) Amplitude (C) Frequency (D) Angle of incidence
(iii) Calculate the work function of the surface (in eV)
(A) 3.75 (B) 4.20 (C) 3.60 (D) 2.07
(iv) Calculate the threshold frequency for the surface
(A) 500 x 1012 Hz (B) 480 x 1013 Hz (C) 520 x 1011 Hz (D) 460 x 1013 Hz

36
CHAPTER 12: ATOMS

37
IMPORTANT FORMULAE
2𝑍𝑒 2
1. Distance of closest approach; 𝑟 = 1
4𝜋𝜀𝑜 ( 𝑚𝑣 2 )
2
𝑛ℎ
2. Bohr’s second postulate; 𝐿 = 𝑚𝑣𝑟 = 2𝜋
3. Bohr’s third postulate; ℎν = 𝐸2 − 𝐸1
𝑛 2 ℎ 2 𝜀𝑜 𝑛2
4. Radius of stationary orbits; 𝑟𝑛 = = 0.53 𝐴°
𝜋𝑚𝑒 2 𝑍
𝑍𝑒 2
5. Orbital speed; 𝑣𝑛 = 2𝑛ℎ𝜀
𝑜
𝑚𝑍 2 𝑒 4 13.6𝑍 2
6. Energy of the nth orbit; 𝐸𝑛 = − 8𝑛2 ℎ2 𝜀2 = − 𝑒𝑉
𝑜 𝑛2
TE = - KE; PE = 2 TE
𝑛3
7. Time period of revolution of electron in stationary orbits; 𝑇 ∝ 𝑍 2
𝑍2
8. Frequency of revolution of electron; 𝑓 ∝ 𝑛3
1 1 1 𝑚𝑒 4
9. Rydberg’s constant; 𝜆 = 𝑅 [𝑛2 − 𝑛2 ] ; 𝑅 = 8𝜀2 ℎ3 𝑐
1 2 𝑜

Classwork questions
1. What is the shortest wavelength present in the Paschen series of Spectral lines?
2. A difference of 2.3 eV separates two energy levels in an atom. What is the frequency of
radiation emitted when the atom make a transition from the upper level to the lower
level?
3. The ground state energy of hydrogen atom is –13.6 eV. What are the kinetic and potential
energies of the electron in this state?
4. A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n
= 4 level. Determine the wavelength and frequency of photon?
5. Determine the distance of closest approach when an alpha particle of kinetic energy 3.95
MeV approaches a nucleus of Z = 79, stops and reverses its directions. [Delhi Set 1,
2023]
6. The wavelength of the second line of the Balmer series in the hydrogen spectrum is 4861
A0. Calculate the wavelength of the first line of the same series.
7. Estimate the ratio of de – Broglie wavelengths associated with deuterons and alpha
particles when they are accelerated from rest through the same accelerating potential V.
8. The electron in a hydrogen atom is typically found at a distance of about 5.3 x 10-11 m
from the nucleus which has a diameter of about 1.0 x 10-15 m, assuming the hydrogen
atom to be a sphere of radius 5.3 x 10-11 m, what fraction of its volume is occupied by the
nucleus?
Homework questions
1. The radius of the innermost electron orbit of a hydrogen atom is 5.3 × 1011 m. What are
the radii of the n = 2 and n = 3 orbits?

38
2. A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature.
What series of wavelengths will be emitted? The total energy of an electron in the first
excited state of the hydrogen atom is about –3.4 eV.
a. What is the kinetic energy of the electron in this state?
b. What is the potential energy of the electron in this state?
c. Which of the answers above would change if the choice of the zero of potential
energy is changed?
3. The ground state energy of hydrogen atom is – 13.6 eV. The photon emitted during the
transition of electron from n = 3 to n = 1 state is incident on a photosensitive material of
unknown work function. The photoelectrons are emitted from the material with the
maximum kinetic energy of 9 eV. Calculate the threshold wavelength of the material
used. [SQP, 2023 – 24]
4. Use Bohr’s postulate to prove that the radius of nth orbit in a hydrogen atom is
proportional to n2.
WORKSHEET 01
1. The potential energy of an electron in the second excited state in hydrogen atom is
(A) – 3.4 eV (B) – 3.02 eV (C) – 1.51 eV (D) – 6.8 eV
2. To explain his theory, Bohr used
(A) Conservation of linear momentum (B) Quantization of angular momentum
(C) Conservation of quantum (D) None of these
3. When alpha particles are sent through a thin gold foil, most of them go straight through
the foil, because
(A) Alpha particles are positively charged
(B) The mass of an alpha particle is more than the mass of an electron
(C) Most of the atom is an empty space
(D) Alpha particles move with high velocity
4. An electron with angular momentum L moving around the nucleus has a magnetic
moment given by
𝑒𝐿 𝑒𝐿 𝑒𝐿 𝑒𝐿
(A) 2𝑚 (B) 3𝑚 (C) (D) 4𝑚
𝑚
5. Specify the transition of electron in the wavelength of the line in the Bohr model of
hydrogen atom which gives rise to the spectral line of highest wavelength.
(A) n = 3 to n = 1 (B) n = 3 to n = 2 (C) n = 4 to n = 1 (D) n = 4 to n = 2
6. When an electron in an atom goes from a lower to a higher orbit, its
(A) Kinetic energy increases, potential energy decreases
(B) Kinetic energy increases, potential energy increases
(C) Kinetic energy decreases, potential energy decreases
(D) Kinetic energy decreases, potential energy increases
7. In a hydrogen atom the electron in the nth exited state undergoes several possible
transitions, ultimately ending at the first excited state. Ten spectral lines are seen. Then
the value of n should be
(A) 5 (B) 7 (C) 9 (D) 6

39
8. The difference in the angular momentum of an electron in the two successive orbits of a
hydrogen atom is
ℎ ℎ ℎ ℎ
(A) (B) (C) (D) (𝑛 − 1)
2𝜋 𝜋 2 2𝜋
9. The radius of the first Bohr orbit of a hydrogen atom is 0.05nm. The radius of the 10th
orbit is
(A) 0.5 nm (B) 5 nm (C) 50 nm (D) 500 nm
10. The ratio of time taken by the electron to go once round the nucleus in the orbits of radii r
and 4r of hydrogen atom is
(A) 1:4 (B) 1:8 (C) 1:16 (D) 1:12
11. The ratio of the area of the first excited orbit of the hydrogen atom to the area of the
ground state orbit of the singly ionized helium atom is
(A) 1:32 (B) 32:1 (C) 1:64 (D) 64:1
12. The radius of the innermost electron orbit of a hydrogen atom is 5.3 × 10–11 m. The radius
of the n = 3 orbit is
(A) 1.01 x 10-10 m (B) 1.59 x 10-10 m (C) 2.12 x 10-10 m (D) 4.77 x 10-10 m
WORKSHEET 02
Assertion and Reason based questions
Directions: These questions consist of two statements, each printed as Assertion and
Reason. While answering these questions, you are required to choose any one of the
following four responses.
(a) Both Assertion and Reason are correct and the Reason is a correct explanation of the
Assertion.
(b) Both Assertion and Reason are correct but Reason is not a correct explanation of the
Assertion.
(c) Assertion is correct, Reason is incorrect
(d) Both Assertion and Reason are incorrect
1. Assertion: Both the Thomson's as well as the Rutherford's models constitute an unstable
system.
Reason: Thomson's model is unstable electrostatically while Rutherford's model is
unstable because of electromagnetic radiation of orbiting electrons.
2. Assertion: The total energy of an electron revolving in any stationary orbit is negative.
Reason: Energy can have positive or negative values.
3. Assertion: The electrons have orbital angular momentum.
Reason: Electrons have well-defined quantum states.
4. Assertion: Bohr's orbits are regions where the electron may be found with large
probability.
Reason: The orbital picture in Bohr's model of the hydrogen atom was inconsistent with
the uncertainty principle.
5. Assertion: In Bohr model, the frequency of revolution of an electron in its orbit is not
connected to the frequency of spectral line for smaller principal quantum number n.

40
 Reason: For transitions between large quantum number the frequency of revolution of an
electron in its orbit is connected to the frequency of spectral line, as per Bohr's
Correspondence principle.
WORKSHEET 03
1. In the Rutherford scattering experiment, the distance of closest approach for an 𝛼 –
particle is do. If 𝛼 – particle is replaced by a proton, how much kinetic energy in
comparison to 𝛼 – particle will it require to have the same distance of closest approach do.
2. Draw the graph showing the variation of the number (N) of scattered alpha particles with
scattering angle (𝜃) in Geiger – Marsden experiment. Infer two conclusions from the
graph.
3. The energy levels of an atom are given below in the diagram

a) Which of the transitions belong to Lyman and Balmer series? Give reason.
b) Calculate the ratio of the shortest wavelengths of the Lyman and the Balmer series of
the spectra.
4. Write shortcomings of Rutherford atomic model. Explain how these were overcome by
the postulates of Bohr’s atomic model.
5. A 12.5 eV electron beam is used to excite a gaseous hydrogen atom at room temperature.
Determine the wavelengths and the corresponding series of the lines emitted.
6. The ground state energy of hydrogen atom is – 13.6 eV. If an electron makes a transition
from an energy level – 1.51 eV to – 3.4 eV, calculate the wavelength of the spectral line
emitted and name the series of hydrogen spectrum to which it belongs.
7. Using Rutherford model of the atom, derive the expression for the total energy of the
electron in hydrogen atom. What is the significance of total negative energy possessed by
the electron?
8. Three stationary states 1, 2 and 3 of a certain atom possess energy values E1, E2, E3 such
that E1 > E2 > E3. If λ1, λ2 and λ3 are the wavelengths emitted corresponding to the
transitions from 1 to 2, 2 to 3 and 1 to 3 respectively then [HOTS]

41
 9. An excited hydrogen atom returns to the ground state by emitting a photon of wavelength
λ. The principal quantum number n of the excited state is [R is the Rydberg constant]
[HOTS]

10. An electron revolving in an orbit (of approximate radius 0.5Å) of an atom executes 1016
rps. Find the magnetic moment of the electron due to its orbital motion. [HOTS]
11. The figure indicates the energy levels of a hydrogen like atom. When the electron transits
from 2E level to E level, a photon of wavelength λ is emitted. Calculate the wavelength
of photon emitted during the transition from 4E/3 level to E level. [HOTS]

TEST YOURSELF
1 Which of the following statements is correct in case of Thomson’s atomic 1
model?
(A) It explains the phenomenon of thermionic emission, photoelectric
emission and ionization.
(B) It could not explain the emission of line spectra by elements.
(C) It could not explain the scattering of alpha particles.
(D) All of the above.
2 According to Rutherford’s atomic model, the electrons inside the atom are 1
(A) Stationary (B) Not stationary (C) Centralized (D) None of these
3 As the quantum number increases, the difference of energy between 1
consecutive energy levels
(A) Remain the same (B) Increases
(C) Decreases (D) May increase or decrease
4 In terms of Bohr radius r0, the radius of the second Bohr orbit of a hydrogen 1
atom is given by
(A) 4 ro (B) 2 ro (C) 8 ro (D) 16 r0

42
5 A: According to classical theory the proposed path of an electron in 1
Rutherford atom model will be parabolic.
R: According to electromagnetic theory an accelerated particle continuously
emits radiation.
6 A: Bohr had to postulate that the electrons in stationary orbits around the 1
nucleus do not radiate.
R: According to classical physics all moving electrons radiate.
7 A 12.5 eV electron beam is used to bombard gaseous hydrogen at room 2
temperature. What series of wavelengths will be emitted?
8 The total energy of an electron in the first excited state of the hydrogen atom 3
is about –3.4 eV.
(a) What is the kinetic energy of the electron in this state?
(b) What is the potential energy of the electron in this state?
(c) Which of the answers above would change if the choice of the zero of
potential energy is changed?
9 (a) A difference of 2.3 eV separates two energy levels in an atom. What is the 5
frequency of radiation emitted when the atom make a transition from the
upper level to the lower level?
(b) Why is the classical (Rutherford) model for an atom of electron orbiting
around the nucleus not able to explain the atomic structure?
(c) Show that the radius of the orbit in hydrogen atom varies as n², where n is
the principal quantum number of the atom.
10 The spectral series of hydrogen atom were accounted for by Bohr using the 4
1 1 1
relation 𝜆 = 𝑅 [𝑛2 − 𝑛2 ]; where R = Rydberg constant = 1.097 x 107 m-1.
1 2
Lyman series is obtained when an electron jumps to first orbit from any
subsequent orbit. Similarly, Balmer series is obtained when an electron jumps
to 2nd orbit from any subsequent orbit. Paschen series is obtained when an
electron jumps to 3rd orbit from any subsequent orbit. Whereas Lyman series
in U.V. region, Balmer series is in visible region and Paschen series lies in the
infrared region. Series limit is obtained when 𝑛2 = ∞.
(i) The wavelength of first spectral line of Lyman series is
(A) 1215.4 𝐴° (B) 1215.4 cm (C) 1215.4 m (D) 1215.4 mm
(ii) The wavelength limit of Lyman series is
(A) 1215.4 𝐴° (B) 951.6 𝐴° (C) 511.9 𝐴° (D) 911.6 𝐴°
(iii) Which of the following transitions in hydrogen atom emit photon of
highest frequency?
(A) n = 1 to n = 2 (B) n = 6 to n = 2 (C) n = 2 to n = 1 (D) n = 2 to n = 6
(iv) The ratio of minimum to maximum wavelength in Balmer series is
(A) 5:9 (B) 1:4 (C) 5:36 (D) 3:4

43
CHAPTER 13: NUCLEI

44
IMPORTANT FORMULAE
1. E = mc2
2. 1 amu = 1 u = 1.66 x 10-27 kg = 931 MeV
3. Nuclear radius; 𝑅 = 𝑅𝑜 𝐴1/3 ; 𝑤ℎ𝑒𝑟𝑒 𝑅𝑜 = 1.2 × 10−15 𝑚
4. Mass defect; ∆𝑚 = [𝑍𝑚𝑃 + (𝐴 − 𝑍)𝑚𝑛 ] − 𝑀𝑛𝑢𝑐𝑙𝑒𝑢𝑠
5. Binding energy; 𝐵𝐸 = ∆𝑚𝑐 2
𝑚𝑎𝑠𝑠 3𝑚
6. Density of nucleus; 𝜌 = 𝑣𝑜𝑙𝑢𝑚𝑒 = 4𝜋𝑅3
𝑜
𝑦𝑖𝑒𝑙𝑑𝑠
7. 𝐴 + 𝐵 → 𝐶+𝐷+𝑄
a. 𝑄 = [𝑚𝐴 + 𝑚𝐵 − (𝑚𝐶 + 𝑚𝐷 )]931 𝑀𝑒𝑉
b. 𝑄 = 𝐵𝐸𝐶+𝐷 − 𝐵𝐸𝐴+𝐵
𝑡𝑜𝑡𝑎𝑙 𝑒𝑛𝑒𝑟𝑔𝑦
8. Energy released per nucleon; 𝐸 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑛𝑢𝑐𝑙𝑒𝑜𝑛𝑠 𝑀𝑒𝑉

Classwork questions:
1. Calculate the energy equivalent of 1g of substance.
2. Find the energy equivalent of one atomic mass unit, first in Joules and then in MeV.
16 𝑀𝑒𝑉
Using this, express the mass defect of 8𝑂 𝑖𝑛 𝑐2
.
3. The fission properties of 239 235
94𝑃𝑢 are very similar to those of 92𝑈. The average energy
released per fission is 180 MeV. How much energy, in MeV, is released if all the atoms
in 1 kg of pure 239
94𝑃𝑢 undergo fission?
4. How long can an electric lamp of 100W be kept glowing by fusion of 2.0kg of
deuterium? Take the fusion reaction as
2 2 3
1𝐻 + 1𝐻 → 2𝐻𝑒 + 𝑛 + 3.27 𝑀𝑒𝑉
5. From the relation 𝑅 = 𝑅𝑜 𝐴1/3, where Ro is a constant and A is the mass number of a
nucleus, show that the nuclear matter density is nearly constant (ie independent of A).
6. Using the curve for the binding energy per nucleon as a function of mass number A, state
clearly how the release in energy in the processes of nuclear fission and nuclear fusion
can be explained.
7. Draw a plot of the binding energy per nucleon as a function of mass number for a large
number of nuclei 20 > A > 240. How do you explain the constancy of binding energy per
nucleon in the range of 30 < A?
8. A heavy nucleus X of mass number 240 and binding energy per nucleon 7.6 MeV
disintegrates into two fragments Y and Z of mass numbers 110 and 130. The binding
energy of nucleons in Y and Z is 8.5 MeV per nucleon. Calculate the energy released per
fission in MeV.
Homework questions:
1. (a) The mass of a nucleus in its ground state is always less than the total mass of its
constituent neutrons and protons. Explain.
(b) Plot a graph showing the variation of potential energy of a pair of nucleons as a
function of their separation.

45
2. Sketch a graph showing the variation of binding energy per nucleon as a function of mass
number A for large number of nuclei. State briefly from which region of the graph release
of energy in the process of nuclear fusion can be explained.
3. Write any four properties of nuclear force.
WORKSHEET 01
1. The curve of binding energy per nucleon as a function of atomic mass number has a sharp
peak for helium nucleus. This implies that helium nucleus is
(A) Radioactive (B) Easily fissionable
(C) More stable nucleus than its neighbours (D) Unstable
2. Which of the following statement about nuclear forces is not true?
(A) The nuclear force between two nucleons falls rapidly to zero as their distance is more
than a femtometers.
(B) The nuclear force is much weaker than the coulomb force.
(C) The force is attractive for distances larger than 0.8 fm and repulsive if they are
separated by distances less than 0.8 fm.
(D) The nuclear between neutron-neutron, proton-neutron and proton-proton is
approximately the same.
3. Energy in nuclear reactor is obtained due to
(A) Nuclear fission (B) Nuclear fusion (C) Photoelectric effect (D) None of these
4. Complete the equation of the following fission reaction 10𝑛 + 235 90
92𝑈 → 38𝑆𝑟 + ⋯ + ⋯

5. Nucleus of an atom whose atomic mass is 24 may consist of

(A) 11 electrons, 11 protons and 13 neutrons
(B) 11 electrons, 13 protons and 11 neutrons
(C) 11 protons and 13 neutrons
(D) 11 protons and 13 electrons
6. Out of the following pairs, the pair that is an isobar is

7. Atomic weight of boron is 10.81 and it has two isotopes, 105𝐵 𝑎𝑛𝑑 115𝐵. The ratio of the
two isotopes in nature would be
(A) 19:81 (B) 10:11 (C) 15:16 (D) 81:19
27 125
8. The ratio of the radii of the nuclei 13𝐴𝑙 𝑎𝑛𝑑 52𝑇𝑒 is approximately
(A) 3:5 (B) 13:52 (C) 27:125 (D) 9:25
9. Diameters of two nuclei are in the ratio 1:2. The ratio of their nuclear density is
(A) 1:2 (B) 2:1 (C) 1:1 (D) 1:4
10. The masses of neutron and proton are 1.0087u and 1.0073u respectively. If the neutrons
and protons combine to form a helium nucleus (alpha particle) of mass 4.0015u, the
binding energy of the helium nucleus will be
(A) 28.4 MeV (B) 20.4 MeV (C) 27.3 MeV (D) 26.4 Mev

46
 WORKSHEET 02
Assertion and Reason based questions
Directions: These questions consist of two statements, each printed as Assertion and
Reason. While answering these questions, you are required to choose any one of the
following four responses.
(a) Both Assertion and Reason are correct and the Reason is a correct explanation of the
Assertion.
(b) Both Assertion and Reason are correct but Reason is not a correct explanation of the
Assertion.
(c) Assertion is correct, Reason is incorrect
(d) Both Assertion and Reason are incorrect
1. Assertion: Mass is not conserved, but mass and energy are conserved as a single entity
called mass-energy.
Reason: Mass and energy are inter-convertible in accordance with Einstein’s relation, E
= mc2.
2. Assertion: Uncertainty principle demands that an electron confined to a nucleus must
have very high energy so that the electron cannot reside in a nucleus.
Reason: The electrostatic attraction between electron and proton is large at such a small
distance but is not enough to bind such a high-energy electron.
3. Assertion: Exothermic reactions are possible when two light nuclei fuse or when a heavy
nucleus undergoes fission into intermediate mass nuclei.
Reason: The nature of nuclear binding energy curve is such that it rises for lighter nuclei
and slightly decreasing for heavier nuclei.
4. Assertion: Only in low or medium energy nuclear reactions, the number of protons and
number of neutrons are separately conserved.
Reason: In high energy reactions, protons and neutrons can be converted into other
particles and a new quantum number, the Baryon number is however, always conserved.
5. Assertion: For fusion, the light nuclei must have sufficient initial energy to cross the
Coulomb barrier. Hence, fusion requires high temperature, however, the actual
temperature required is somewhat less than expected classically.
Reason: It is due to quantum mechanical tunneling of the potential barrier.

WORKSHEET 03
1. Write two characteristic features of nuclear force which distinguish it from coulomb’s
force.
2. Draw the graph showing the variation of binding energy per nucleon as a function of
mass number A. The binding energy per nucleon for heavy nuclei (A >170) decreases
with the increase in mass number. Explain.
64
3. The nuclear radius of 27
13𝐴𝑙 is 3.6 fermi. Find the nuclear radius of 29𝐶𝑢 .
4. Calculate the binding energy per nucleon of 3517𝐶𝑙 nucleus. Given that
35
𝑀𝑎𝑠𝑠 𝑜𝑓 17𝐶𝑙 = 34.980000 𝑢
𝑀𝑎𝑠𝑠 𝑜𝑓 𝑝𝑟𝑜𝑡𝑜𝑛 = 1.007825 𝑢

47
 𝑀𝑎𝑠𝑠 𝑜𝑓 𝑛𝑒𝑢𝑡𝑟𝑜𝑛 = 1.008665 𝑢
1 𝑎𝑚𝑢 = 931 𝑀𝑒𝑉
7 4
5. Given two nuclides 3𝑋 𝑎𝑛𝑑 3𝑌.
a. Are they the isotopes of the same element? Why?
b. Which one of the two is likely to be more stable? Explain. [HOTS]
6. A heavy nucleus X of mass number A =240 and binding energy per nucleon 7.6 MeV is
split into two nearly equal fragments Y and Z of mass numbers A1 =110 and A2 =130.
The binding energy of each one of these nuclei is 8.5 MeV per nucleon. Calculate the
total binding energy of each of the nuclei X, Y and Z and hence the energy released per
fission in MeV.
7. The graph of log 𝑒 (𝑅⁄𝑅 ) versus log (A) of nuclides will be a [A is mass number of a
0
nucleus and R is its radius and Ro = 1.3 fm] [HOTS]
(A) Circle (B) Parabola (C) Hyperbola (D) Straight line
8. If Fpp, Fpn and Fnn are the magnitudes of the nuclear force between proton-proton, proton-
neutron and neutron-neutron respectively, then [HOTS]

9. If Fpp, Fpn and Fnn are the net forces acting between proton-proton, proton-neutron,
neutron-neutron respectively, then [HOTS]

𝑚𝑎𝑠𝑠 𝑜𝑓 𝑓𝑖𝑠𝑠𝑖𝑜𝑛 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠

10. In any fission process, the ratio is [HOTS]
𝑚𝑎𝑠𝑠 𝑜𝑓 𝑝𝑎𝑟𝑒𝑛𝑡 𝑛𝑢𝑐𝑙𝑒𝑢𝑠
(A) Greater than 1 (B) Equal to 1
(C) Depends on the mass of the parent nucleus (D) Less than 1
TEST YOURSELF
1 Energy equivalent of 2g of a substance is 1
(A) 18 x 1013 mJ (B) 18 x 1013 J (C) 9 x 1013 J (D) 9 x 1013 mJ
2 Binding energy of hydrogen nucleus is 1
(A) – 13.6 eV (B) 13.6 eV (C) 0 (D) 6.8 eV
3 Why do stable nuclei have more neutrons than protons? 1
4 A: Nuclear density is almost same for all nuclei. 1
R: The radius (r) of a nucleus depends only on the mass number (A) as 𝑟 ∝
𝐴1/3
5 A: Neutrons penetrate matter more readily as compared to protons. 1
R: Neutrons are slightly more massive than protons.
6 If both the number of protons and the number of neutrons are conserved in 2
each nuclear reaction, in what way is mass converted into energy (or vice
versa) in a nuclear reaction?
7 Explain the processes of nuclear fission and nuclear fusion by using the plot of 2
binding energy per nucleon (BE/A) versus the mass number A.
8 Calculate the energy released in MeV in the following nuclear reaction: 3

48
 [All India 2012]
9 (a) Complete the following nuclear reactions 3

(b) Write two characteristic features of nuclear force.

49
CHAPTER 14: SEMICONDUCTOR ELECTRONICS – MATERIALS, DEVICES AND
SIMPLE CIRCUITS

50
IMPORTANT FORMULAE
1. Intrinsic semiconductor; ne = nh = ni
2. Extrinsic semiconductor; nenh = ni2
Classwork questions:
1. C, Si and Ge have same lattice structure. Why is C insulator while Si and Ge intrinsic
semiconductors?
2. Suppose a pure Si crystal has 5 x 1028 atoms m-3. It is doped by 1 part per million
concentration of pentavalent As. Calculate the number of electrons and holes. Given that
ni = 1.5 x 1016 m-3.
3. In half-wave rectification, what is the output frequency if the input frequency is 50 Hz.
What is the output frequency of a full-wave rectifier for the same input frequency?
4. In the figure given below, state the type of biasing of the diode.

WORKSHEET 01
1. Identify the property which is not characteristic for a semiconductor?
(A) At a very low temperature, it behaves like an insulator.
(B) At higher temperatures two types of charge carriers will cause conductivity
(C) The charge carriers are electrons and holes in the valence band at higher temperatures
(D) The semiconductor is electrically neutral
2. The energy required by an electron to jump the forbidden band in silicon at room
temperature is about
(A) 0.01 eV (B) 0.05 eV (C) 0.7 eV (D) 1.1 eV
11 3 12 3
3. It is given, ne = 7 x 10 per m and nh = 5 x 10 per m . The semiconductor is
(A) p – type (B) intrinsic (C) n – type (D) insulator
4. When an intrinsic semiconductor is doped with a small amount of trivalent impurity, then
(A) Its resistance increases
(B) It becomes a p – type semiconductor
(C) There will be more free electrons than holes in the semiconductor
(D) Dopant atoms become donor atoms
5. Electrical conductivity of a semiconductor
(A) Decreases with increase in temperature
(B) Increases with increase in temperature
(C) First increases then decreases with increase in temperature
(D) Does not change with temperature
6. The threshold voltage for a p-n junction diode used in the circuit is 0.7 V. The type of
biasing and current in the circuit are

51
 (A) Forward biasing, 0 A (B) Reverse biasing, 0 A
(C) Forward biasing, 5 mA (D) Reverse biasing, 2 mA
7. The circuit has two oppositely connected ideal diodes in parallel. What is the current
flowing in the circuit?

(A) 1.71 A (B) 2.0 A (C) 2.31 A (D) 1.33 A

8. In the classification of materials into conductors, insulators and semiconductors, we
consider the relative positions of
(A) Any valence band and any conduction band
(B) Highest valence band and lowest conduction band
(C) Lower valence band and highest conduction band
(D) Highest valence band and highest conduction band
9. The energy band which are either partially filled or completely empty at 0 K are called
(A) Conduction bands (B) Valence bands (C) Forbidden bands (D) Intrinsic bands
10. An n−type semiconductor is
(A) Positively charged
(B) Negatively charged
(C) Electrically neutral
(D) Maybe positively or negatively charged depending on the impurity concentration

WORKSHEET 02
Assertion and Reason based questions
Directions: These questions consist of two statements, each printed as Assertion and
Reason. While answering these questions, you are required to choose any one of the
following four responses.
(a) Both Assertion and Reason are correct and the Reason is a correct explanation of the
Assertion.

52
 (b) Both Assertion and Reason are correct but Reason is not a correct explanation of the
Assertion.
(c) Assertion is correct, Reason is incorrect
(d) Both Assertion and Reason are incorrect
1. Assertion: The conductivity of an intrinsic semiconductor at zero kelvin is zero.
Reason: The bond strength of the semiconductor at zero kelvin is much higher as
compared to the bond strength at room temperature.
2. Assertion: The conductivity of a pure semiconductor increases on doping.
Reason: Doping causes the reduction in bond strength.
3. Assertion: Semiconductors do not obey Ohm’s law.
Reason: In semiconductors the rate of flow of charge not only depends on the applied
electric field but also on the availability of charge carriers.
4. Assertion: When a pure semiconductor is doped with a pentavalent impurity, the number
of conduction electrons is increased while the number of holes is decreased.
Reason: Some of the holes get recombined with the conduction electrons as the
concentration of the conduction electrons is increased.
5. Assertion: If the temperature of a semiconductor is increased then its resistance
decreases.
Reason: The energy gap between conduction band and valence band is very small.

WORKSHEET 03
1. Why does the width of depletion layer of a p-n junction increase in reverse biasing?
2. If a small voltage is applied to a p-n junction diode how will the width of depletion layer
be affected when it is (i) forward biased, and (ii) reverse biased? Briefly explain.
3. What are donor and acceptor energy levels?
4. With the help of suitable diagram, describe briefly the two important processes involved
in the formation of a p-n junction. Define the terms depletion region and potential barrier.
5. For the circuit shown, find the current flowing through the 1 Ω resistor. Assume that the
two diodes are ideal diodes.

6. An a.c. signal is fed into two circuits X and Y and the corresponding output in the two
cases have the waveforms as shown. Name the circuits X and Y. Also, draw their detailed
circuit diagrams.

53
 7. A p-type semiconductor is electrically neutral although it has holes as the majority
carriers. Justify. [HOTS]
8. In the following diagram, which bulb of B1 and B2 will glow and why? [HOTS]

TEST YOURSELF
1 When a p – n junction is forward biased, the width of depletion layer 1
(A) Decreases (B) Increases (C) Remains unchanged (D) None of these
2 Out of the junction diodes shown in the following circuits, the one that is 1
forward biased is

3 A piece of copper and silicon are first heated to a temperature of 150 ℃ and then 1
gradually cooled. During the process
(A) The resistance of copper increases and that of silicon decreases
(B) The resistance of silicon increases and that of copper decreases
(C) The resistance of both silicon and copper increases
(D) The resistance of both silicon and copper decreases
4 To make a p-type semiconductor, an intrinsic semiconductor is doped with 1
(A) Phosphorous (B) Antimony (C) Aluminium (D) Arsenic
5 A: The conductivity of intrinsic semiconductors increases with an increase in 1
temperature.
R: Increase in temperature decreases the average time between collisions of
electrons.
6 A: Putting p-type semiconductor slab directly in physical contact with n type 1
semiconductor slab cannot form p-n junction.

54
 R: The roughness at contact will be much more than interatomic crystal spacing
and continuous flow of charge carriers is not possible.
7 In half-wave rectification, what is the output frequency if the input frequency is 2
50 Hz. What is the output frequency of a full-wave rectifier for the same input
frequency?
8 (a) Draw the energy band diagram when intrinsic semiconductor (Ge) is doped 3
with impurity atoms of Antimony (Sb). Name the extrinsic semiconductor so
obtained and majority charge carriers in it.
(b) At what temperature would an intrinsic semiconductor behave like a perfect
insulator?
9 (a) Distinguish between an intrinsic semiconductor and a p-type semiconductor. 5
Give reason why a p-type semiconductor crystal is electrically neutral, although
nh >> ne?
(b) With the help of a neat labeled diagram explain the working of a diode as a
full wave rectifier.
10 A pure semiconductor germanium or silicon, free of every impurity is called 4
intrinsic semiconductor. At room temperature, a pure semiconductor has very
small number of current carriers (electrons and holes). Hence its conductivity is
low.
When the impurity atoms of valance five or three are doped in a pure
semiconductor, we get respectively n- type or p- type extrinsic semiconductor. In
case of doped semiconductor. nenh = ni2 where 𝑛e and 𝑛h are the number density
of electron and hole charge carriers in a pure semiconductor. The conductivity of
extrinsic semiconductor is much higher than that of intrinsic semiconductor.
(i) Which of the following statements is not true?
(A) The resistance of intrinsic semiconductor decreases with increase of
temperature.
(B) Doping pure Si with trivalent impurities gives p- type semiconductors.
(C) The majority charges in n- type semiconductors are holes.
(D) All of the above
(ii) The impurity atoms with which pure Si should be doped to make a p- type
semiconductor is
(A) Phosphorous (B) Boron (C) Arsenic (D) Antimony
(iii) Holes are majority charge carriers in
(A) Metals (B) Intrinsic semiconductors
(C) n – type semiconductors (D) p – type semiconductors
(iv) At absolute zero, Si acts as
(A) Non – metal (B) Metal (C) Insulator (D) None of these

55