PHYSICS

Bohr’s Theory

1. The energy levels of the hydrogen spectrum is shown in figure. There are some transitions A, B,
C, D and E. Transition A, B and C respectively represent
n= – 0.00 eV
n=6 – 0.36 eV
n=5 – 0.54 eV
n=4 – 0.85 eV
n=3 C – 1.51 eV
B D
n=2 – 3.39 eV

A E

n=1 – 13.5 eV

(a) First member of Lyman series, third spectral line of Balmer series and the second spectral
line of Paschen series
(b) Ionization potential of hydrogen, second spectral line of Balmer series and third spectral line
of Paschen series
(c) Series limit of Lyman series, third spectral line of Balmer series and second spectral line of
Paschen series
(d) Series limit of Lyman series, second spectral line of Balmer series and third spectral line of
Paschen series

2. In the above figure D and E respectively represent

(a) Absorption line of Balmer series and the ionization potential of hydrogen
(b) Absorption line of Balmer series and the wavelength lesser than lowest of the Lyman series
(c) Spectral line of Balmer series and the maximum wavelength of Lyman series
(d) Spectral line of Lyman series and the absorption of greater wavelength of limiting value of
Paschen series

3. Energy levels A, B, C of a certain atom corresponding to increasing values of energy i.e.

E A  E B  E C . If 1 ,  2 ,  3 are the wavelengths of radiations corresponding to the transitions C to B,
B to A and C to A respectively, which of the following statements is correct
1  2 C
(a)  3  1   2 (b) 3  1
1   2
B
(c) 1   2   3  0 (d) 23  12   22 2 3
A

4. An electron jumps from the 4th orbit to the 2nd orbit of hydrogen atom. Given the Rydberg's
constant R  10 5 cm 1 . The frequency in Hz of the emitted radiation will be
3 3
(a)  10 5 (b)  10 15
16 16
9 3
(c)  10 15 (d)  10 15
16 4

5. The ratio of the energies of the hydrogen atom in its first to second excited state is
(a) 1/ 4 (b) 4/9
(c) 9/ 4 (d) 4

R DIANCE
 PHYSICS
6. If the wavelength of the first line of the Balmer series of hydrogen is 6561 Å , the wavelength of
the second line of the series should be
(a) 13122 Å (b) 3280 Å (c) 4860 Å (d) 2187 Å

7. Ionization potential of hydrogen atom is 13.6 V.

Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy
12.1 eV. The spectral lines emitted by hydrogen atoms according to Bohr's theory will be
(a) One (b) Two
(c) Three (d) Four

8. The following diagram indicates the energy levels of a certain atom when the system moves
from 2E level to E, a photon of wavelength  is emitted. The wavelength of photon produced
4E
during its transition from level to E is
3
(a)  / 3 (b) 3  / 4 2E

(c) 4  / 3 (d) 3 

4/3E

9. Consider an electron in the nth orbit of a hydrogen atom in the Bohr model. The circumference of
the orbit can be expressed in terms of the de Broglie wavelength  of that electron as
(a) (0 .259 ) n  (b) n

(c) (13 .6 )  (d) n 

10. An electron makes a transition from orbit n = 4 to the orbit n = 2 of a hydrogen atom. The wave
number of the emitted radiations (R = Rydberg's constant) will be
16 2R
(a) (b)
3R 16
3R 4R
(c) (d)
16 16

11. The ratio of the frequencies of the long wavelength limits of Lyman and Balmer series of
hydrogen spectrum is
(a) 27 : 5 (b) 5 : 27
(c) 4 : 1 (d) 1 : 4

12. The velocity of an electron in the second orbit of sodium atom (atomic number = 11) is v. The
velocity of an electron in its fifth orbit will be
22
(a) v (b) v
5
5 2
(c) v (d) v
2 5

R DIANCE
 PHYSICS
13. In the Bohr model of a hydrogen atom, the centripetal force is furnished by the coulomb
attraction between the proton and the electron. If a0 is the radius of the ground state orbit, m is
the mass, e is the charge on the electron and  0 is the vacuum permittivity, the speed of the
electron is
e
(a) 0 (b)
 0 a0 m

e 4  0 a0 m
(c) (d)
4 0 a0 m e

14. 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) none of these

15. The third line of Balmer series of an ion equivalent to hydrogen atom has wavelength of 108.5
nm. The ground state energy of an electron of this ion will be
(a) 3.4 eV (b) 13.6 eV
(c) 54.4 eV (d) 122.4 eV

16. The radius of hydrogen atom in its ground state is 5 .3  10 11 m . After collision with an electron it is
found to have a radius of 21 .2  10 11 m . What is the principal quantum number n of the final state
of the atom
(a) n = 4 (b) n = 2
(c) n = 16 (d) n = 3

17. The ratio of the speed of the electron in the first Bohr orbit of hydrogen and the speed of light is
equal to (where e, h and c have their usual meanings)
(a) 2hc /e 2 (b) e 2 h/2c
(c) e 2 c/2h (d) 2e 2 /hc

18. The magnetic moment ( ) of a revolving electron around the nucleus varies with principal
quantum number n as
(a)   n (b)   1 / n
(c)   n 2
(d)   1 / n 2

Answer Keys

1. C 2. A 3. B 4. C 5. C 6. C 7. C 8. D 9. D 10. C 11. A 12. D

13. c 14. A 15. C 16. B 17. D 18. A

R DIANCE