ATOMS

1. The electron in a hydrogen atom makes a transition n1 → n 2 , where n1 and n 2 are the principal
quantum numbers of the two states. Assume the Bohr model to be valid. The time period of the
electron in the initial state is eight times that in the final state. The possible values of n1 and n2
are
(a) n1 = 4 , n 2 = 2 (b) n1 = 8, n 2 = 2
(c) n1 = 8, n 2 = 1 (d) n1 = 6, n 2 = 3

2. As per Bohr model, the minimum energy (in eV) required to remove an electron from the ground
state of doubly ionized Li atom (Z = 3) is
(a) 1.51 (b) 13.6
(c) 40.8 (d) 122.4

3. Orbital acceleration of electron is

n 2h2 n 2h2
(a) (b)
4 2m 2r 3 2n 2 r 3
4n 2h2 4n 2h2
(c) 2 2 3
(d)
m r 4 2m 2r 3

4. Which of the following is true for number of spectral lines in going form Layman series to Pfund
series
(a) Increases
(b) Decreases
(c) Unchanged
(d) May decreases or increases

5. The diagram shows-the energy levels for an electron in a certain atom. Which transition shown
represents the emission of a photon with the most energy [AIEEE 2005]
n=4
n=3

n=2

n=1
I II III IV

(a) I (b) II
(c) III (d) IV
6. In Bohr model of hydrogen atom, the force on the electron depends on the principal quantum
number as
(a) F 1 / n 3 (b) F 1 / n 4
(c) F 1 / n 5 (d) Does not depend on n

7. The energy level diagram for an hydrogen like atom is shown in the figure. The radius of its first
Bohr orbit is
0 eV n=

– 6.04 eV n=3

– 13.6 eV n=2

– 54.4 eV n=1

(a) 0.265 Å (b) 0.53 Å

(c) 0.132 Å (d) None of these

8. How much work must be done to pull apart the electron and the proton that make up the
Hydrogen atom, if the atom is initially in the state with n = 2
(a) 13 .6 1 .6 10 −19 J (b) 3 .4 1 .6 10 −19 J

(c) 1.51 1.6 10 −19 J (d) 0

9. The following diagram indicates the energy levels of a certain atom when the system moves from
4E level to E. A photon of wavelength 1 is emitted. The wavelength of photon produced during
7 1
it's transition from E level to E is 2. The ratio will be
3 2

4E

9 4
(a) (b)
4 9
3 7
(c) (d)
2 3

10. If in Rutherford’s experiment, the number of particles scattered at 90 o angle are 28 per min,
then number of scattered particles at an angle 60 o and 120 o will be
(a) 112/min, 12.5/min (b) 100/min, 200/min
(c) 50/min, 12.5/min (d) 117/min, 25/min
11. A double charged lithium atom is equivalent to hydrogen whose atomic number is 3. The
wavelength of required radiation for emitting electron from first to third Bohr orbit in Li + + will
be (Ionisation energy of hydrogen atom is 13.6eV)
(a) 182.51 Å (b) 177.17 Å
(c) 142.25 Å (d) 113.74 Å

12. The ionisation potential of H-atom is 13 .6 V . When it is excited from ground state by
monochromatic radiations of 970 .6 Å , the number of emission lines will be (according to Bohr’s
theory)
(a) 10 (b) 8
(c) 6 (d) 4

13. The transition from the state n = 4 to n = 3 in a hydrogen-like atom results in ultraviolet
radiation. Infrared radiation will be obtained in the transition
(a) 2 → 1 (b) 3 → 2
(c) 4 → 2 (d) 5 → 4

14. An electron passing through a potential difference of 4.9 V collides with a mercury atom and
transfers it to the first excited state. What is the wavelength of a photon corresponding to the
transition of the mercury atom to its normal state
(a) 2050 Å (b) 2240 Å
(c) 2525 Å (d) 2935 Å

15. In the Bohr model of the hydrogen atom, let R, v and E represent the radius of the orbit, the
speed of electron and the total energy of the electron respectively. Which of the following
quantity is proportional to the quantum number n
(a) R/E (b) E/v
(c) RE (d) vR

16. A Hydrogen atom and a Li + + ion are both in the second excited state. If l H and l Li are their
respective electronic angular momenta, and E H and E Li their respective energies, then
(a) lH lLi and | E H | | E Li | (b) lH = lLi and | E H | | E Li |
(c) lH = lLi and | E H | | E Li | (d) lH lLi and | E H | | E Li |

17. The first excited state of hydrogen atom is 10.2 eV above its ground state. The temperature is
needed to excite hydrogen atoms to first excited level, is
(a) 7 .9 10 4 K (b) 3.5 10 4 K
(c) 5.8 10 4 K (d) 14 10 4 K
 r
18. The electric potential between a proton and an electron is given by V = V0 ln , where r0 is a
r0
constant. Assuming Bohr’s model to be applicable, write variation of rn with n, n being the
principal quantum number
(a) rn n (b) rn 1/n

(c) rn n2 (d) rn 1/n 2

19. If the atom 100 Fm 257 follows the Bohr model and the radius of 100 Fm 257 is n times the Bohr radius,
then find n
(a) 100 (b) 200
1
(c) 4 (d)
4

20. The ratio of the speed of the electrons in the ground state of hydrogen to the speed of light in
vacuum is
(a) 1/2 (b) 2/137
(c) 1/137 (d) 1/237

21. In hydrogen atom, electron makes transition from n=4 to n=1 level. Recoil momentum of the H
atom will be
(a) 3.4 10 −27 N - sec (b) 6.8 10 −27 N - sec
(c) 3.4 10 −24 N - sec (d) 6.8 10 −24 N - sec

22. A sodium atom is in one of the states labeled 'Lowest excited levels'. It remains in that state for
an average time of 10–8 sec, before it makes a transition back to a ground state. What is the
uncertainty in energy of that excited state
(a) 6.56 10–8 eV (b) 2 10–8 eV
(c) 10–8 eV (d) 8 10–8 eV

23. An energy of 24.6 eV is required to remove one of the electrons from a neutral helium atom.
The energy (in eV) required to remove both the electrons from a neutral helium atom is
(a) 79.0 (b) 51.8
(c) 49.2 (d) 38.2

24. A hydrogen atom in its ground state absorbs 10.2 eV of energy. The orbital angular momentum
is increased by
(a) 1.05 10 −34 J-sec (b) 3.16 10 −34 J-sec
(c) 2.11 10 −34 J-sec (d) 4.22 10 −34 J-sec
(Given Planck constant h = 6.6 10 −34 J − sec)
25. Hydrogen (H), deuterium (D), singly ionized helium (He + ) and doubly ionized lithium (Li) all have
one electron around the nucleus. Consider n =2 to n = 1 transition. The wavelengths of emitted
radiations are 1 , 2 , 3 and 4 respectively. Then approximately
(a) 1 = 2 =4 3 =9 4 (b) 4 1 =2 2 =2 3 = 4

(c) 1 =2 2 =2 2 3 =3 2 4 (d) 1 = 2 =2 3 =3 2 4

26. The number of revolutions per second made by an electron in the first Bohr orbit of hydrogen
atom is of the order of 6.5 x ?
(a) 10 20 (b) 10 19
(c) 10 17 (d) 10 15

27. The angular momentum of an electron in a hydrogen atom is proportional to (where r is radius
of orbit)
1
(1)
√𝑟
1
(2) 𝑟
(3) √𝑟
(4) 𝑟 2

28. When a hydrogen atom is raised from the ground state to third state
(1) Both kinetic energy and potential energy increase
(2) Both kinetic energy and potential energy decrease
(3) Potential energy increases and kinetic energy decreases
(4) Potential energy decreases and kinetic energy increases

𝐸
29. The energy levels of a certain atom for first, second and third levels are E, 4 3 and 2E
respectively. A photon of wavelength is emitted for a transition 3 → 1. What will be the
wavelength of emission for transition 2 → 1?
(1) /3
(2) 3
(3) 3 /4
(4) 4 /3

30. The ground state energy of H - atom is –13.6 eV. The energy needed to ionise H - atom from its
second excited state is
(1) 1.51 eV
(2) 3.4 eV
(3) 13.6 eV
(4) 12.1 eV
31. Hypothetically if elements with principal quantum number n > 4 were not allowed in nature,
then the number of possible elements would be
(1) 60
(2) 32
(3) 4
(4) 64

32. The angular speed of electron in the nth orbit of hydrogen atom is
(1) Directly proportional to 𝑛2
(2) Directly proportional to n
(3) Inversely proportional to 𝑛3
(4) Inversely proportional to n

33. The magnetic field induction produced at the centre of orbit due to an electron revolving in nth
orbit of hydrogen atom is proportional to
(1) 𝑛−3
(2) 𝑛−5
(3) 𝑛5
(4) 𝑛3

34. The ratio of minimum to maximum wavelength of radiation emitted by transition of an

electron to ground state of Bohr’s hydrogen atom is
(1) 3/4
(2) 1/4
(3) 1/8
(4) 3/8

35. In Bohr’s model of the hydrogen atom, the ratio between the period of revolution of an
electron in the orbit of n = 1 to the period of revolution of the electron in the orbit n = 2 is
(1) 1 : 2
(2) 2 : 1
(3) 1 : 4
(4) 1 : 8
1. The relation between : wavelength of series limit of Lyman series,
1 2
: the wavelength of the
series limit of Balmer series & : the wavelength of first line of Lyman series is :
3

(1) 1 = 2 + 3 (2) 3 = 1 + 2 (3) 2 = 3 − 1 (4) none of these

2. Let 1
be the frequency of the series limited of the Lyman series, 2
be the frequency of the

first line of the Lyman series, and 3

be the frequency of the series limited of the Balmer series.

1
(1) 1
– 2
= 3
(2) 2
– 1
= 3
(3) 3
= ( 1
+ 3)
(4) 1
+ 2
= 3
2

3. The energy of a hydrogen-like atom in its ground state is – 54.4 eV. It may be

(1) hydrogen (2) deuterium (3) helium (4) lithium

4. When an electron in an hydrogen atom makes a transition from first Bohr orbit to second Bohr

orbit, how much energy it absorbs ?

(1) 3.4 eV (2) 10.2 eV (3) 13.6 eV (4) 1.51 eV

k
5. Suppose an electron is attracted towards the origin by a force where 'k' is a constant and
r
'r' is the distance of the electron from the origin. By applying Bohr model to this system, the
radius of the nth orbital of the electron is found to be 'rn' and the kinetic energy of the electron
to be 'Tn'. Then which of the following is true?

(1) Tn independent of n, rn n, Tn, n , rn n

1
(2) Tn ,r n
n n

1
(3) Tn n,r n2
n 1 n

1
(4) Tn ,r n2
n n

6. The ratio of the kinetic energy of the n = 2 electron for the H atom to that of He+ ion is :

n=2 H– He+ –

1 1
(1) (2) (3) 1 (4) 2
4 2
7. A hydrogen atom (ionisation potential 13.6 eV) makes a transition from third excited state to
first excited state. The energy of the photo emitted in the process is

(1) 1.89 eV (2) 2.55 eV (3) 12.09 eV (4) 1275 eV

8. In a mixture of H – He+ gas (He+ is singly ionized He atom), H atoms and He+ ions are excited to
their respective first excited states. Subsequently, H atoms transfer their total excitation
energy to He+ ions (by collisions). Assume that the Bohr model of atom is exactly valid. The
quantum number n of the state finally populated in He+ ions is :

(1) 2 (2) 3 (3) 4 (4) 5

9. In a hydrogen like atom electron make transition from an energy level with quantum number
n to another with quantum number (n–1). If n>>1, the frequency of radiation emitted is
proportional to :

1 1 1 1
(1) (2) (3) (4)
n n 2
n 3 n3
2

10. The ionization energy of the electron in the hydrogen atom in its ground state is 13.6 eV. The
atoms are excited to higher energy levels to emit radiations of 6 wavelengths. Maximum
wavelength of emitted radiation corresponds to the transition between

(1) n = 3 to n = 2 states (2) n = 3 to n = 1 states

(3) n = 2 to n = 1 states (4) n = 4 to n = 3 states

11. If an orbital electron of the hydrogen atom jumps from the ground state to a higher energy
state, its orbital speed reduces to half its initial value. If the radius of the electron orbit in the
ground state is r, then the radius of the new orbit would be
(a) 2r (b) 4r (c) 8r (d) 16r

12. If a hydrogen atom at rest, emits a photon of wavelength , the recoil speed of the atom of
mass m is given by
h mh
(a) (b) (c) mh (d)
m

13. In a hydrogen atom, the electron is in nth excited state. It comes down to first excited state
by emitting ten different wavelengths. The value of n is
(a) 6 (b) 7 (c) 8 (d) 9
14. The ratio of the maximum wavelength of the Lyman series in hydrogen spectrum to the
maximum wavelength in the Panchen series is
3 6 52 7
(a) (b) (c) (d)
105 15 7 108

15. When an electron in the hydrogen atom in ground state absorbs a photon of energy 12.1 eV,
its angular momentum
(a) decreases by 2.11 × 10-34 J-s (b) decreases by 1.055 × 10-34 J-s
(c) increases by 2.11 × 10-34 J-s (d) increases by 1.055 × 10-34 J-s
 Answer

1. (a,d) T n 3 . Given Tn1 = 8 Tn2 , hence n1 = 2n2

Therefore, option (a) and (d) both are correct.

2. (d) E = − Z 2 13 .6 eV = −9 13 .6 eV = −122 .4 eV
So ionisation energy = + 122.4 eV.

nh nh v2 n 2h2
3. (a) mvr = v= = .
2 2 mr r 4 2m 2r 3

4. (b) Maximum number of spectral lines are observed in Lymen series

hc 1 1
5. (c) Emitted energy E = − .
n12 n22

v2 1 1
F v F
6. (b) r also n and r n 2 n4

Z2 n2
7. a) We know that En = −13 .6 eV and rn = 0 .53 ( Å)
n2 Z

Here for n =1, E1 = – 54.4 eV

Z2
Therefore − 54 .4 = −13 .6 Z=2
11

0 .53 (1)2
Hence radius of first Bohr orbit r = = 0 . 265 Å
2

8. (b) The electrostatic P.E. is zero when the electron and proton are far apart from each other.
Work done in pulling electron and proton far away from each other
13 .6
W = E f − Ei = 0 − Ei = − − eV
n2
13 . 6
W= 1 . 6 10 −19 J = 3.4 1.6 10–19J.
(2)2

9. (b) Transition from 4E to E

hc hc
(4 E − E) = 1 = ...... (i)
1 3E
7
Transition from E to E
3
 7 hc 3 hc
E−E = 2 = ...... (i)
3 2 4E
4
From equation (i) and (ii) 1
=
2 9

1 1
10. (a) N N1 = 7 = 112
sin 4 / 2 (sin 30 o )4
1
and N 2 = 7 = 12 .5 .
(sin 60 o )4

Z2
11. (d) En = −13 .6 eV . Required energy for said transition
n2
1 1
E = E3 − E1 = 13 .6 Z 2 −
12 3 2

8
E = 13 .6 3 2 = 108 .8 eV
9

E = 108 .8 1 . 6 10 −19 J

hc
Now E = = 108 .8 1 .6 10 −19

6 . 6 10 −34 3 10 8
= = 0 .11374 10 −7 m = 113 . 74 Å
108 .8 1 .6 10 −19

1 1 1
12. (c) =R −
n12 n22

1 1 1
= 1 .097 10 7 2 − 2 n2 = 4
970 .6 10 −10 1 n2
n(n − 1) 4 3
Number of emission lines N = = =6
2 2

13. (d) As the transition n = 4 and n = 3 , results in UV radiation and infrared radiation involves
smaller amounts of energy UV. So we require a transition involving initial values of n greater
than 4 e.g. 5 → 4 .

hc
14. (c) =E = eV
hc 6 . 6 10 −34 3 10 8
= − = 2525 A
eV 1 . 6 10 −19 4 . 9

2 2
0nh
15. (d) Rydberg constant R =
mZe 2
Ze 2 mZ 2 e 4
Velocity v = and energy E = −
2 0 nh 8 02 n 2 h 2
Now, it is clear from above expressions R.v n
16. (b) In second excited state n = 3
h
So lH = lLi = 3
2
While E Z2 and ZH = 1, ZLi = 3
So |ELi| = 9|EH| or |EH|<|ELi|

17. (a) According to kinetic interpretation of temperature

1 3
K. E. = mv 2 = kT .
2 2
3
10 .2 1 .6 10 −19 = (1 .38 10 − 23 )T
2
T = 7.9 104K.

r
18. (a) Potential energy U = eV = eV0 ln
r0
dU eV0
Force F = − = .
dr r
mv 2 eV0 eV0
The force will provide the necessary centripetal force. Hence = v=
r r m
…..(i)
nh
and mvr = …..(ii)
2
nh m
From equation (i) and(ii) mr = or r n
2 eV0

m2 m2
19. (d) (rm ) = (0 .53 Å) = (n 0 .53 Å) =n
Z Z
m = 5 for 100 Fm 257 (the outermost shell)
(5 )2 1
and z = 100 n= =
100 4

e2
20. (c) Speed of electron in nth orbit of hydrogen atom v =
2 0n h

e2
In ground state n = 1 v=
2 0h

v e2 (1 .6 10 −19 )2
= =
c 2 0 ch 2 8 .85 10 −12 3 10 8 6 .6 10 − 34
1
= .
137

h
21. (b) Recoil momentum = momentum of photon =

1 1 hR 15
= hR − = = 6 .8 10 − 27 N sec
n12 n22 16
22. (a) The average time that the atom spends in this excited state is equal to t, so by using
h
E. t =
2
h/2
Uncertainty in energy =
t

6 . 6 10 −34
= = 1 .05 10 − 26 J = 6 . 56 10 − 8 eV
2 3 .14 10 − 8

23. (a) After the removal of first electron remaining atom will be hydrogen like atom.
22
So energy required to remove second electron from the atom E = 13 .6 = 54 .4 eV
1

Total energy required = 24.6 + 54.4 = 79 eV.

24. (a) Electron after absorbing 10.2 eV energy goes to its first excited state (n=2) from ground state
(n = 1).
h
Increase in momentum =
2

6 .6 10 −34
= = 1 .05 10 − 34 J-s .
6 .28

25. (a) Using E Z2 (∵ n 1 and n 2 are same)

hc
Z2 Z 2 = constant

2 2 2 2
1 Z1 = 2 Z2 = 3 Z3 = 4 Z4

1 1= 2 12 = 3 22 = 4 33

1 = 2 =4 3 =9 4 .

h
26. (d) mvr = (for first orbit)
2
h h h
m r2 = m 2 r2 = = 2
2 2 4 mr 2
6 .6 10 −34 rev
= = 6 .5 10 15
2
4 (3 .14 ) 9 .1 10 − 31 (0 .53 10 −10 )2 sec

27. Answer (3)

28. Answer (3)

29. Answer (2)

30. Answer (1)

31. Answer (1)

32. Answer (3)

33. Answer (2)

34. Answer (1)

35. Answer (4)

 K K
1. Sol.(4) = E – E1 = E – E2
1 2

K 1 1 1
= E2 – E7 – =
3 1 2 3

2. Sol.(1) E(1 to ) = E(1 to 2) + E(2 to )

3. Sol.(3) Energy of H-like atoms,

Z 2Rhc Z2 13.6 eV
En = – =–
n2 n2

For ground state

n=1

E1 = – 54.4 eV (given)

Z2 13.6
– 54.4 eV = eV
(1)2

Z2 = 4 or Z=2

Z = 2 is for helium.

4. Sol.(2) The energy of electron in nth Bohr orbit

13.6
E=–
n2

Energy absorbed by electron in transition from n = 1 → n = 2

13.6 13.6 13.6 13.6

E=– 2
– – 2
=– + = – 3.4 + 13.6 = 10.2 eV
2 1 4 1
 mv 2 K
5. Sol.(1) = ...(1)
r r

nh
mvr = ....(2)
2

Solve these equation

KH TEH
6. Sol.(1) K.E. = – T.E. =
K He TEHe

( )
2
TEH ZH 1
For same ‘n’ = =
( )
2 4
TEHe ZHe

1 1
7. Sol.(2) E = E0 − frist exited state (n = 2)
n12 n22

1 1
= 13.6 2
− & third exicited state (n = 4)
2 42

4 −1
= 13.6 = 2.55 eV
16

3
8. Sol.(3) EH = × 13.6 eV = Energy released by H atom. Let He+ go to nth state.
4

So energy required

3
EH = × 13.6 eV = H He+
4

1 1
EHe = 13.6 × 4 − eV EHe = EH
4 n2

3 1 1
× 13.6 = 13.6 × 4 − n=4 Ans. C
4 4 n2

9. Sol.(4) E= h

E 1 1 k2n
= =k − 2 =
h (n − 1)2
n n (n − 1)2
2
 2k 1
3
Ans. (4)
n n3

10. Sol.(4) Number of special lines obtained due to transition of electron from nth orbital to lower
orbital is

N=
n (n – 1) and for maximum wavelength the difference between the orbits of the series
2
should be minimum.

Number of special lines N =

n (n – 1)
2

n (n – 1)
=6
2

or n2 – n –12 = 0

or (n – 4) (n + 3) = 0

or n=4

Now as the first line of the series has the maximum wavelength, therefore electron jumps

from the 4th orbit to the third orbit.

11. (b)

12. (a)

13. (a)
14. (d)

15. (c)