Multiple Choice Questions (Atoms) the minimum distance of approach between the 15.
tance of approach between the 15. The ratio of the energies of the hydrogen atom in its
1. The size of the atom is approximately equal to: centres of the two is: first to second excited states is:
(a) 10-4cm or 10-6metre (b) 10-6 cm or 10-4metre (a) 8.4 10-15cm (b) 8.4 10-15m (a) 1/4 (b) 4/9 (c) 9/4 (d) 4
(c) 10-8 cm or 10-10metre (d) 10-12 cm or 10-14metre (c) 4.2 10 m
-15
(d) 4.2 10-15cm 16. If an electron in a hydrogen atom jumps form an
2. The Rutherford scattering of particles by atoms 9. The radius of electron’s second stationary orbit in orbit ni = 3 to an orbit with level nf = 2, the
Bohr’s atom is R. The radius of the third orbit will frequency of the emitted radiation is:
shows that:
be: (a) V = 36c/5R (b) v = cR/6
(a) The atom as a whole is positively charged
(a) 3R (b) 2.25R (c) 9 R (d) R/3 (c) v = 5Rc/36 (d) v = 6c/R
(b) The atom consists of uniformly distributed
10. When a hydrogen atom is raised from the ground 17. The speed of an electron in the orbit of hydrogen
positive and negative charged particles
state to fifth state: atom in the ground state is:
(c) There is no charged particle inside the atom
(a) Both KE and PE increase (a) c (b) c/10 (c) c/2 (d) c/137
(d) The atom has a very small positively charged
(b) Both KE and PE decrease 18. The ground state energy of H-atom is 13.6eV. The
core at the centre
(c) PE increase and KE decrease energy needed to ionize. H-atom from its second
3. According to classical theory the proposed circular excited state is:
path of an electron in Rutherford atom model will (d) PE decrease and KE increase
(a) 1.51eV (b) 3.4eV
be: 11. As the electron in Bohr orbit of hydrogen atom
passes from state n = 2 to n = 1, the KE (K) and PU (c) 13.6 Ev (d) 12.1 eV
(a) Circular (b) Straight line
(U) change is: 19. The series limit of Paschen series of hydrogen
(c) Parabolic (d) Spiral spectrum in Ao is:
(a) K two fold, U also two fold
4. According to Bohr’s atomic model:
(b) K four fold, U also four fold (a) 912 Ao (b) 912 4Ao
(a) An atom has heavy, positively charged nucleus
(c) K four fold, U two fold (c) 912 16Ao (d) 912 9 Ao
(b) The electron radiates energy only when it jumps 20. If an electron in n = 3 orbit of hydrogen atom jumps
to another orbit (d) K two fold, U four fold
down to n = 2 orbit, the amount of energy released
(c) The electron can move only in particular orbits 12. Consider a spectral line resulting from the transition
and the wavelength of radiation emitted are:
n = 5 to n = 1 in the atoms and ions given below.
(d) All the above statements are correct
The shortest wavelength produced by: (a) 0.85 eV, 6566 Ao (b) 1.89eV, 1240 Ao
o
5. In an atom, two electrons move around the nucleus
(a) Helium atom (b) Deurtiem atom (c) 1.89 eV, 6566 A (d) 1.5eV, 6566 Ao
in circular orbits of radii R and 4R. The ratio of the 21. Hydrogen atoms are excited from ground state to the
time taken by them to complete one revolution is: (c) Singly ionized helium
state of principal quantum number 4. Then the
(a) 1/4 (b) 4/1 (c) 8/1 (d) 1/8 (d) Ten times ionized sodium atom
number of spectral lines observed will be:
13. An electron jumps from the 4th orbit to the 2nd orbit
6. According to Bohr’s postulates which of the (a) 3 (b) 6 (c) 5 (d) 2
of a hydrogen atom. Given the Rydberg’s constant R
following quantities takes discrete values? 22. If the ionization potential of hydrogen atom is 13.6
= 105 cm-1, the frequency in Hz of the emitted
(a) Kinetic energy (b) Potential energy radiation will be: V, the energy required to remove the electron from
(a) 3/16 105 (b) 3/16 1015
(c) Angular momentum (d) Momentum the third orbit of hydrogen atom is:
(c) 9/16 10 (d) 3/4 1015
7. According to Bohr when an electron jumps from any 15 (a) 1.5eV (b) 1.5V (c) 4.5eV (d) 3.4 V
higher orbit to the third orbit, the spectral lines so 23. The first excitation potential of the hydrogen atom
14. With increasing quantum number, the energy
emitted are called: in the ground state is:
difference between adjacent energy levels in atoms:
(a) Balmer series (b) Paschen series (a) 13.6 V (b) 10.2 V (c) 3.4 V (d) 1.89 V
(a) Decrease (b) Increases
(c) Lyman series (d) None of these (c) Remains constant
8. An particle of 10MeV collides head – on with a (d) decreases for low Z and increases for high Z
copper nucleus (Z = 29) and is deflected back. Then atoms
ATOMS Page 1
Ans: =1/137. The fine structure constant has no 19. Name the series of hydrogen spectrum which lies
Very Short Type Questions units and no dimensions. in the visible region of electromagnetic
[Atomic Physics] 10. What is the diameter of hydrogen atom? spectrum?
1. Can a hydrogen atom absorb a photon whose Ans: The diameter of hydrogen atom is about 1.06Ao. Ans: Blamer series lies in the visible region.
energy exceeds its binding energy? 11. Write the relation for the distance of closest 20. The ionization potential of helium atom is 24.6V.
Ans: Yes, it can be absorb. approach. How much energy will be required to ionize it?
2. In Bohr’s theory of hydrogen atom. What is the Ans: The closest approach is Ze (2e) Ans: Energy required to ionize helium atom is 24.6eV
implication of the fact that the potential energy is ro
1 21. The wavelength of some of the spectral lines
negative and is greater in magnitude than the 4 o mv 2
2 obtained in hydrogen spectrum are 1216Ao, 6463
kinetic energy. 12. State Bohr’s frequency condition. Ao and 9546Ao. Which one of these wavelength
Ans: The implication is that electron revolving in any Ans: The frequency f of a radiation emitted on jumping of belongs to the Paschen series?
stationary orbit is bound to the nucleus, and canot an electron from outer orbit to inner orbit of an atom Ans: =9546Ao belongs to the Paschen series.
leave the nucleus on its own. is given by hf= E2-E1. Where E1, E2 = total energy of Numerical Problem with Solution
3. Name a physical quantity whose dimensions are the electron in inner and outer orbits respectively. 1. The second member of Lyman series in hydrogen
the same as those of Planck’s constant. 13. Name the series of hydrogen spectrum lying in atom has wavelength 5400Ao. What is the
Ans: Angular momentum. wavelength of first member?
the infarad region.
4. What is the energy possessed by an electron for n Sol: The wavelength of spectral line is given by 1/ =
Ans: Paschen series, Bracket series, Pfund series and
= hampery series.
2
R(1/12 - 1/ n2 ). If1 and 2 be the wavelength of
Ans: Zero. This follows from En= -13.6/n2 eV, first and second lines respectively, then 1/ 1 R(1/12 -
14. Write an empirical relation for Paschen series
when n = 1/22)
lines of hydrogen spectrum.
5. What is the ground state energy of electron in
Ans: = R(1/33-1/n22), where n2 = 4, 5, 6, ……. where = 3/4R, 1/ 2 = R(1/12 - 1/32) = 8/9R
case of 3Li7?
=1/ = wave number. Dividing, 1 /2 = 32/27.
Ans: Here, Z = 3, n = 2. En= -13.6Z2/n2eV
= -13.6(3)2/22 = -30.4eV. 15. What is the ionization potential of hydrogen Or 1 = 32/27 5400 = 6400Ao.
6. What is the order of radius of helium atom? atom? 2. The energy of an excited hydrogen atom is -3.
Ans: It is of the order of 10-10 m. Ans: 13.6V 4eV. Calculate the angular momentum of
16. What are the values of first and second excitation electron according to Bohr’s theory.
7. What is the order of velocity of electron in a
potential of hydrogen atom? Sol: The energy of an electron in the nth level of
hydrogen atom in ground state? hydrogen atom, En= -(13.6/n2)eV
Ans: 106 m-1 Ans: 10.2V; 12.09V
So, -3.4 = -(13.6/n2) or n = 2.
8. Name the series of hydrogen atom which lie in 17. Define energy level. How is it represented? From Bohr’s theory, angular momentum mvr = nh/2
U.V. region. Ans: Energy level is represented by a horizontal line = 2 6.63 10-34/2 3.14 = 2.11 10-34J sec.
Ans: Lyman series in U.V. region. drawn according to some suitable energy scale 3. How many times does the electron go round the
which represents the total energy of electron in a first Bohr orbit of hydrogen in it?
9. Write an expression for fine structure constant.
stationary orbit of an atom. Sol: The time taken by an electron to move round first
What is its value? Does its have any units and
18. What is the value of Rydberg constant? Bohr orbit is T = 2 r1/v1 = 2 3.14 0.53 10-10
dimensions? /2.2 106
Ans: 1.097 107 m-1
No. of times the electron goes round = frequency
= f = 1/T = 2.2 106/2 3.14 0.53 10-10
ATOMS Page 2
= 6.6 1015Hz. Sol: The wavelength ( ) of different spectral lines of 03. The diameter of the innermost orbit of hydrogen is
4. Hydrogen atom in the ground state is excited by 1.06 Å. What is the diameter of the 10th orbit?
Ballmer series is given by 1/ = R(1/2 -1/ n
2 2
radiation of wavelength 975Ao. How many 2 ). 04. Calculate the energy of the hydrogen atom in the
different lines are possible in the resulting For longest wavelength n2=3 so 1/ L states n = 4 and n = 2. Determine the frequency and
spectrum? = R(1/22-1/32) 1/ L= R(1/4 -1/9) = 5R/36 wavelength of the emitted radiation in a transition
Sol: Energy of the incident photon or L= 36/5R from n = 4 to n = 2 state. Is this radiation visible?
h = hc/ = 12400/975 = 12.75eV For shortest wavelength n2 = so 1/ S 05. Calculate the frequency of the photon, which can
From Bohr’s frequency condition, excite the electron to 3.4 eV from 13.6 eV.
= R(1/22-1/ 2) 1/ S = R(1/4 - 0) or S = 4/R.
06. The ground state energy of hydrogen atom is 13.6
L/ S = (36/5R) (R/4) = 9/5.
2 2
hv = Eni - En f = 13.6(1/ n f -1/ ni ) From ground
eV. If an electron makes a transition from an energy
2 9. Which level of the doubly ionized lithium has the level 0.85 eV to 3.4 eV, calculate the wavelength
state, nf= 1, Or, 12.75 = 13.6 (1/12-1/ ni ) same energy as the ground state energy of the of the spectral line emitted. To which series of
2 hydrogen atom ? Compare the orbital radii of the
Or, 1/ ni = 1-(12.75/13.6). Solving ni= 4 hydrogen spectrum, does this wavelength belong?
two levels. 07. The P.E. of a normal hydrogen atom in ground state
The possible quantum transitions are Sol: We know, total energy of electron in nth orbit E
n = 4, (4→3), (4→2), (4→1) is 27 eV. Calcualte its K.E. and total energy in the
n = 3, (3→2), (3→1) Z2/n2As [E]Li = [E]H Z 2 / n 2 Z 2 / n 2 same state.
Li H
n = 2, (2→1), This six lines are possible. 9/n2 = 1/1 or n2 = 9 or n = 3 08. A photon of energy 12.09 eV is absorbed by an
6. The wavelength of the first member of Balmer Again radius of nth orbit r (n2/Z) electron in ground state of a hydrogen atoms. What
series in the hydrogen spectrum is 6573Ao. will be the energy level of electron? The energy of
r3(Li)/r1(H) = [n 2 / Z ]Li /[n 2 / Z ]H = (9/3)/1 = 3 electron in the ground state of hydrogen atom is
Calculate the wavelength of the first member of
Lyman series. 10. The Rydberg constant for hydrogen is 1.097 107 13.6 eV.
Sol: For the first member of the Balmer series m-1. Calculate the long and short wavelength
09. Show that the shortest wavelength lines in Lyman,
1/ = R[1/22 - 1/32] = 5R/36 limits of Lyman series.
Balmer and Paschen series have their wavelengths in
For the first member of Lyman series Sol: The wavelength ( ) of different spectral lines of the ratio 1 : 4 : 9.
1/ = R(1/12 - 1/22) = 3R/4 Lyman series is given by 1/ = R(1/12-1/ n2 ).
2
10. In the ground state of H-atom, its Bohr’s radius is
/ = 5 4/36 3 = 5/27 For longest wavelength n2 = 2 so 1/ L= R(1/12- given as 5.3 1011m. The atom is excited such
= (5/27) = 5/27 6563 = 1215Ao. 1/22) that the radius becomes 21.2 1011m. Find
7. Calculate the radius of the 3rd Bohr orbit of 1/ L= R(1 -1/4) = 3R/4 or L= 4/3R (i) the value of the principal quantum number and (ii)
hydrogen atom and energy of electron in that = 4/(3 1.097 107 m-1) = 1.2154 10-7 m = 1215Ao the total energy of the atom in this excited state.
11. v21 and v31 are frequencies of the first and second
orbit. For shortest wavelength n2 = so 1/ S = R(1/12-1/
lines of Lyman series. If v32 is the frequency of the
Sol: The radius of nth orbit of hydrogen atom is given by 2)
rn = (0.53 10-10) n2 meter. first line of Balmer series, then establish the relation
1/ S = R or S = 1/R = 1/1.097 10-7 m-1 =
For n = 3, r3 = (0.53 10-10) 9 = 4.77 10-10m among v21, v31 and v32.
911.5Ao 12. The total energy of an electron in the first excited
= 4.77Ao.
The energy of electron in nth orbit of hydrogen atom
Numerical Problems state of the H-atom is about 3.4 eV.
is given by En= -13.6/n2 eV. 01. An -particle of kinetic energy 7.68 MeV is (i)What is the kinetic energy of the electron
For n = 3, E3 = -13.6/9 = -1.51 eV. projected towards the nucleus of copper (Z = 29). (ii) What is the potential energy of the electron
Calculate its distance of nearest approach. (iii) Which of the answers above would change, if
8. Calculate the ratio of the longest and shortest
02. What is the impact parameter at which the scattering the choice of the zero of potential energy is changed?
wavelength in the Ballmer series of hydrogen
atom. angle is 10° for Z = 79 and initial energy of the -
particle is 5 MeV?
ATOMS Page 3
