Modern Physics-I: JEE Advanced - Physics, Solution by DC Pandey NEET Notes | EduRev

 Page 1


For JEE Advanced 
Objective Questions 
  Single Correct Option 
Q 1.  If we assume only gravitational attraction between proton and electron in hydrogen atom and the 
Bohr's quantization rule to be followed, then the expression for the ground state energy of the 
atom will be (the mass of proton is M and that of electron is m.) 
 (a) 
2 2 2
2
G M m
h
   (b) 
2 2 2 3
2
2 G M m
h
?
  (c) 
2 2 3
2
2 GM m
h
?
?
 
(d) None of these 
Q 2.  An electron in a hydrogen atom makes a transition from first excited state to ground state. The 
magnetic moment due to circulating electron 
  (a) increases two times (b) decreases two times (c) increases four times (d) remains same 
Q 3.  The excitation energy of a hydrogen-like ion to its first excited state is 40.8 eV. The energy 
needed to remove the electron from the ion in the ground state is 
  (a) 54.4 eV   (b) 62.6 eV   (c) 72.6 eV   (d) 58.6 eV 
Q 4.  An electron in a hydrogen atom makes a transition from first excited state to ground state. The  
equivalent current due to circulating electron 
  (a) increases 4 times (b) decreases 4 times (c) increases 8 times (d) decreases 8 times 
Q 5.  In a sample of hydrogen like atoms all of which are in ground state, a photon beam containing 
photons of various energies is passed. In absorption spectrum, five dark lines are observed. The 
number of bright lines in the emission spectrum will be 
  (assume that all transitions take place) 
  (a) 21   (b) 10    (c) 15    (d) None of these 
Q 6.  Let A
n
 be the area enclosed by the nth orbit in a hydrogen atom. The graph of ln (A
n
/A
1
 )against ln 
(n) 
  (a) will not pass through origin   (b) will be a straight line with slope 4 
  (c) will be a rectangular hyperbola   (d) will be a parabola 
Q 7.  In the hydrogen atom, an electron makes a transition from n = 2 to n = 1. The magnetic field 
produced by the circulating electron at the nucleus 
  (a) decreases 16 times (b) increases 4 times (c) decreases 4 times (d) increases 32 times 
Q 8.  A stationary hydrogen atom emits photon corresponding to the first line of Lymann series. If R is 
the Rydberg's constant and M is the mass of the atom, then the velocity acquired by the atom is 
  (a) 
3Rh
4M
   (b) 
4M
3Rh
   (c) 
Rh
4M
   (d) 
4M
Rh
 
Q 9.  Light wave described by the equation 200 V/m sin (1.5 × 10
15
 s
-1
 )t cos (0.5 × 10
15
 s
-1
 )t falls on 
metal surface having work function 2.0 eV. Then the maximum kinetic energy of photoelectrons is 
  (a) 3.27 eV   (b) 2.2 eV  (c) 2.85 eV   (d) None of these 
Q 10.  A hydrogen like atom is excited using a radiation. Consequently six spectral lines are observed in 
the spectrum. The wavelength of emission radiation is found to be equal or smaller than the 
radiation used. This concludes that the gas was initially at 
  (a) ground state     (b) first excited state  
Page 2


For JEE Advanced 
Objective Questions 
  Single Correct Option 
Q 1.  If we assume only gravitational attraction between proton and electron in hydrogen atom and the 
Bohr's quantization rule to be followed, then the expression for the ground state energy of the 
atom will be (the mass of proton is M and that of electron is m.) 
 (a) 
2 2 2
2
G M m
h
   (b) 
2 2 2 3
2
2 G M m
h
?
  (c) 
2 2 3
2
2 GM m
h
?
?
 
(d) None of these 
Q 2.  An electron in a hydrogen atom makes a transition from first excited state to ground state. The 
magnetic moment due to circulating electron 
  (a) increases two times (b) decreases two times (c) increases four times (d) remains same 
Q 3.  The excitation energy of a hydrogen-like ion to its first excited state is 40.8 eV. The energy 
needed to remove the electron from the ion in the ground state is 
  (a) 54.4 eV   (b) 62.6 eV   (c) 72.6 eV   (d) 58.6 eV 
Q 4.  An electron in a hydrogen atom makes a transition from first excited state to ground state. The  
equivalent current due to circulating electron 
  (a) increases 4 times (b) decreases 4 times (c) increases 8 times (d) decreases 8 times 
Q 5.  In a sample of hydrogen like atoms all of which are in ground state, a photon beam containing 
photons of various energies is passed. In absorption spectrum, five dark lines are observed. The 
number of bright lines in the emission spectrum will be 
  (assume that all transitions take place) 
  (a) 21   (b) 10    (c) 15    (d) None of these 
Q 6.  Let A
n
 be the area enclosed by the nth orbit in a hydrogen atom. The graph of ln (A
n
/A
1
 )against ln 
(n) 
  (a) will not pass through origin   (b) will be a straight line with slope 4 
  (c) will be a rectangular hyperbola   (d) will be a parabola 
Q 7.  In the hydrogen atom, an electron makes a transition from n = 2 to n = 1. The magnetic field 
produced by the circulating electron at the nucleus 
  (a) decreases 16 times (b) increases 4 times (c) decreases 4 times (d) increases 32 times 
Q 8.  A stationary hydrogen atom emits photon corresponding to the first line of Lymann series. If R is 
the Rydberg's constant and M is the mass of the atom, then the velocity acquired by the atom is 
  (a) 
3Rh
4M
   (b) 
4M
3Rh
   (c) 
Rh
4M
   (d) 
4M
Rh
 
Q 9.  Light wave described by the equation 200 V/m sin (1.5 × 10
15
 s
-1
 )t cos (0.5 × 10
15
 s
-1
 )t falls on 
metal surface having work function 2.0 eV. Then the maximum kinetic energy of photoelectrons is 
  (a) 3.27 eV   (b) 2.2 eV  (c) 2.85 eV   (d) None of these 
Q 10.  A hydrogen like atom is excited using a radiation. Consequently six spectral lines are observed in 
the spectrum. The wavelength of emission radiation is found to be equal or smaller than the 
radiation used. This concludes that the gas was initially at 
  (a) ground state     (b) first excited state  
  (c) second excited state    (d) third excited state 
Q 11.  The time period of the electron in the ground state of hydrogen atom is two times the time period 
of the electron in the first excited state of a certain hydrogen like atom (Atomic Number 2). The 
value of Z is 
  (a) 2    (b) 3    (c) 4    (d) None of these 
Q 12.  The wavelengths of K
?
 
X-rays from lead isotopes Pb
204
,Pb
206
 and Pb
208
 are ?
1
, ?
2
 and ?
3
 
respectively. Choose the correct alternative. 
 (a) ?
1
 < ?
2
 < ?
3
 (b) ?
1
 > ?
2
 > ?
3
 (c) ?
1
 = ?
2
 = ?
3
  (d) None of these 
Q 13.  In case of hydrogen atom, whenever a photon is emitted in the Balmer series, 
  (a) there is a probability of emitting another photon in the Lyman series 
  (b) there is a probability of emitting another photon of wavelength 1213 Å 
(c) the wavelength of radiation emitted in Lyman series is always shorter than the wavelength 
emitted in the Balmer series 
  (d) All of the above 
Q 14.  An electron of kinetic energy K collides elastically with a stationary hydrogen atom in the ground 
state. Then 
  (a) K > 13.6 eV  (b) K > 10.2 eV  (c) K < 10.2 eV  (d) data insufficient 
Q 15.  In a stationary hydrogen atom, an electron jumps from n = 3 to n = 1. The recoil speed of the 
hydrogen atom is about 
  (a) 4m/s   (b) 4 cm/s   (c) 4 mm/s   (d) 4 × 10
-4
m/s 
Q 16.  An X-ray tube is operating at 150 kV and 10 mA. If only 1% of the electric power supplied is 
converted into X-rays, the rate at which the target is heated in calorie per second is 
  (a) 3.55   (b) 35.5   (c) 355   (d) 3550 
Q 17.  An electron revolves round a nucleus of atomic number Z. If 32.4 eV of energy is required to 
excite an electron from the n = 3 state to n = 4 state, then the value of Z is 
  (a) 5    (b) 6    (c) 4    (d) 7 
Q 18.  If the de-Broglie wavelength of a proton is 10
-13
 m, the electric potential through which it must 
have been accelerated is 
  (a) 4.07 × 10
4
V  (b) 8.15 × 10
4
V  (c) 8.15 × 10
3
V  (d) 4.07 × 10
5
V 
Q 19.  If E
n
 and L
n
 denote the total energy and the angular momentum of an electron in the nth orbit of  
Bohr atom, then 
 (a) E
n
 ? L
n
  (b) 
n
n
1
E
L
?   (c) 
2
nn
EL ?   (d) 
n 2
n
1
E
L
? 
Q 20.  An orbital electron in the ground state of hydrogen has the magnetic moment ?
1
. This orbital 
electron is excited to 3rd excited state by some energy transfer to the hydrogen atom. The new 
magnetic moment of the electron is ?
2
, then 
 (a) ?
1
 = 4 ?
2
  (b) 2 ?
1
 = ?
2
  (c) 16 ?
1
 = ?
2
  (d) 4 ?
1
 = ?
2
 
Q 21.  A moving hydrogen atom makes a head-on collision with a stationary hydrogen atom. Before 
collision, both atoms are in ground state and after collision they move together. The minimum 
Page 3


For JEE Advanced 
Objective Questions 
  Single Correct Option 
Q 1.  If we assume only gravitational attraction between proton and electron in hydrogen atom and the 
Bohr's quantization rule to be followed, then the expression for the ground state energy of the 
atom will be (the mass of proton is M and that of electron is m.) 
 (a) 
2 2 2
2
G M m
h
   (b) 
2 2 2 3
2
2 G M m
h
?
  (c) 
2 2 3
2
2 GM m
h
?
?
 
(d) None of these 
Q 2.  An electron in a hydrogen atom makes a transition from first excited state to ground state. The 
magnetic moment due to circulating electron 
  (a) increases two times (b) decreases two times (c) increases four times (d) remains same 
Q 3.  The excitation energy of a hydrogen-like ion to its first excited state is 40.8 eV. The energy 
needed to remove the electron from the ion in the ground state is 
  (a) 54.4 eV   (b) 62.6 eV   (c) 72.6 eV   (d) 58.6 eV 
Q 4.  An electron in a hydrogen atom makes a transition from first excited state to ground state. The  
equivalent current due to circulating electron 
  (a) increases 4 times (b) decreases 4 times (c) increases 8 times (d) decreases 8 times 
Q 5.  In a sample of hydrogen like atoms all of which are in ground state, a photon beam containing 
photons of various energies is passed. In absorption spectrum, five dark lines are observed. The 
number of bright lines in the emission spectrum will be 
  (assume that all transitions take place) 
  (a) 21   (b) 10    (c) 15    (d) None of these 
Q 6.  Let A
n
 be the area enclosed by the nth orbit in a hydrogen atom. The graph of ln (A
n
/A
1
 )against ln 
(n) 
  (a) will not pass through origin   (b) will be a straight line with slope 4 
  (c) will be a rectangular hyperbola   (d) will be a parabola 
Q 7.  In the hydrogen atom, an electron makes a transition from n = 2 to n = 1. The magnetic field 
produced by the circulating electron at the nucleus 
  (a) decreases 16 times (b) increases 4 times (c) decreases 4 times (d) increases 32 times 
Q 8.  A stationary hydrogen atom emits photon corresponding to the first line of Lymann series. If R is 
the Rydberg's constant and M is the mass of the atom, then the velocity acquired by the atom is 
  (a) 
3Rh
4M
   (b) 
4M
3Rh
   (c) 
Rh
4M
   (d) 
4M
Rh
 
Q 9.  Light wave described by the equation 200 V/m sin (1.5 × 10
15
 s
-1
 )t cos (0.5 × 10
15
 s
-1
 )t falls on 
metal surface having work function 2.0 eV. Then the maximum kinetic energy of photoelectrons is 
  (a) 3.27 eV   (b) 2.2 eV  (c) 2.85 eV   (d) None of these 
Q 10.  A hydrogen like atom is excited using a radiation. Consequently six spectral lines are observed in 
the spectrum. The wavelength of emission radiation is found to be equal or smaller than the 
radiation used. This concludes that the gas was initially at 
  (a) ground state     (b) first excited state  
  (c) second excited state    (d) third excited state 
Q 11.  The time period of the electron in the ground state of hydrogen atom is two times the time period 
of the electron in the first excited state of a certain hydrogen like atom (Atomic Number 2). The 
value of Z is 
  (a) 2    (b) 3    (c) 4    (d) None of these 
Q 12.  The wavelengths of K
?
 
X-rays from lead isotopes Pb
204
,Pb
206
 and Pb
208
 are ?
1
, ?
2
 and ?
3
 
respectively. Choose the correct alternative. 
 (a) ?
1
 < ?
2
 < ?
3
 (b) ?
1
 > ?
2
 > ?
3
 (c) ?
1
 = ?
2
 = ?
3
  (d) None of these 
Q 13.  In case of hydrogen atom, whenever a photon is emitted in the Balmer series, 
  (a) there is a probability of emitting another photon in the Lyman series 
  (b) there is a probability of emitting another photon of wavelength 1213 Å 
(c) the wavelength of radiation emitted in Lyman series is always shorter than the wavelength 
emitted in the Balmer series 
  (d) All of the above 
Q 14.  An electron of kinetic energy K collides elastically with a stationary hydrogen atom in the ground 
state. Then 
  (a) K > 13.6 eV  (b) K > 10.2 eV  (c) K < 10.2 eV  (d) data insufficient 
Q 15.  In a stationary hydrogen atom, an electron jumps from n = 3 to n = 1. The recoil speed of the 
hydrogen atom is about 
  (a) 4m/s   (b) 4 cm/s   (c) 4 mm/s   (d) 4 × 10
-4
m/s 
Q 16.  An X-ray tube is operating at 150 kV and 10 mA. If only 1% of the electric power supplied is 
converted into X-rays, the rate at which the target is heated in calorie per second is 
  (a) 3.55   (b) 35.5   (c) 355   (d) 3550 
Q 17.  An electron revolves round a nucleus of atomic number Z. If 32.4 eV of energy is required to 
excite an electron from the n = 3 state to n = 4 state, then the value of Z is 
  (a) 5    (b) 6    (c) 4    (d) 7 
Q 18.  If the de-Broglie wavelength of a proton is 10
-13
 m, the electric potential through which it must 
have been accelerated is 
  (a) 4.07 × 10
4
V  (b) 8.15 × 10
4
V  (c) 8.15 × 10
3
V  (d) 4.07 × 10
5
V 
Q 19.  If E
n
 and L
n
 denote the total energy and the angular momentum of an electron in the nth orbit of  
Bohr atom, then 
 (a) E
n
 ? L
n
  (b) 
n
n
1
E
L
?   (c) 
2
nn
EL ?   (d) 
n 2
n
1
E
L
? 
Q 20.  An orbital electron in the ground state of hydrogen has the magnetic moment ?
1
. This orbital 
electron is excited to 3rd excited state by some energy transfer to the hydrogen atom. The new 
magnetic moment of the electron is ?
2
, then 
 (a) ?
1
 = 4 ?
2
  (b) 2 ?
1
 = ?
2
  (c) 16 ?
1
 = ?
2
  (d) 4 ?
1
 = ?
2
 
Q 21.  A moving hydrogen atom makes a head-on collision with a stationary hydrogen atom. Before 
collision, both atoms are in ground state and after collision they move together. The minimum 
value of the kinetic energy of the moving hydrogen atom, such that one of the atoms reaches one 
of the excitation state is  
  (a) 20.4 eV   (b) 10.2 eV   (c) 54.4 eV   (d) 13.6 eV 
Q 22.  In an excited state of hydrogen like atom an electron has total energy of- 3.4 eV. If the kinetic 
energy of the electron is E and its de-Broglie wavelength is ?, then 
  (a) ? = 6.6 Å   (b) E = 3.4eV   (c) Both are correct  (d) Both are wrong 
Passage : (Q. No. 23 to 25) 
When a surface is irradiated with light of wavelength 4950Å, a photocurrent appears which 
vanishes if a retarding potential greater than 0.6 volt is applied across the phototube. When a 
second source of light is used, it is found that the critical retarding potential is changed to 1.1 volt. 
Q 23.  The work function of the emitting surface is 
  (a) 2.2 eV   (b) 1.5 eV   (c) 1.9 eV   (d) 1.1 eV 
Q 24.  The wavelength of the second source is  
  (a) 6150 Å  (b) 5150 Å   (c) 4125 Å   (d) 4500 Å 
Q 25.  If the photoelectrons (after emission from the source) are subjected to a magnetic field of 10 tesla, 
the two retarding potentials would 
  (a) uniformly increase (b) uniformly decrease (c) remain the same (d) None of these 
Passage : (Q. No. 26 to 28) 
In an experimental set up to study the photoelectric effect a point-source of light of power 3.2 × 
10
-3
 W was taken. The source can emit mono energetic photons of energy 5 eV and is located at a 
distance of 0.8 m from the centre of a stationary metallic sphere of work function 3.0 eV. The 
radius of the sphere is r = 8 × 10
-3
 m. The efficiency of photoelectric emission is one for every 10
6
 
incident photons. Based on the information given above answer the questions given below. 
(Assume that the sphere is isolated and photo-electrons are instantly swept away after the 
emission). 
Q 26.  de-Broglie wavelength of the fastest moving photo-electron is 
 (a) 6.63 Å   (b) 8.69 Å   (c) 2Å    (d) 5.26 Å 
Q 27.  It was observed that after some time emission of photo-electrons from the sphere stopped. Charge 
on the sphere when the photon emission stops is 
 (a) 16 ? ?
0
r Coulomb    (b) 8 ? ?
0
r Coulomb 
  (c) 15 ? ?
0
r Coulomb    (d) 20 ? ?
0
r Coulomb 
Q 28.  Time after which photo-electric emission stops is  
  (a) 100 s   (b) 121 s  (c) 111s   (d) 141 s 
Answers 
  1. (b) 2. (b) 3. (a) 4. (c) 5. (c) 6. (b) 7. (d) 8. (a) 9. (d) 10. (c) 11. (c) 12. (c) 13. (d) 14. (c) 15. (a) 
  16. (c) 17. (d) 18. (b) 19. (d) 20. (d) 21. (a) 22. (c) 23. (c) 24. (c) 25. (c) 26. (b) 27. (b) 28. (c) 
Solutions 
1.  
   
Page 4


For JEE Advanced 
Objective Questions 
  Single Correct Option 
Q 1.  If we assume only gravitational attraction between proton and electron in hydrogen atom and the 
Bohr's quantization rule to be followed, then the expression for the ground state energy of the 
atom will be (the mass of proton is M and that of electron is m.) 
 (a) 
2 2 2
2
G M m
h
   (b) 
2 2 2 3
2
2 G M m
h
?
  (c) 
2 2 3
2
2 GM m
h
?
?
 
(d) None of these 
Q 2.  An electron in a hydrogen atom makes a transition from first excited state to ground state. The 
magnetic moment due to circulating electron 
  (a) increases two times (b) decreases two times (c) increases four times (d) remains same 
Q 3.  The excitation energy of a hydrogen-like ion to its first excited state is 40.8 eV. The energy 
needed to remove the electron from the ion in the ground state is 
  (a) 54.4 eV   (b) 62.6 eV   (c) 72.6 eV   (d) 58.6 eV 
Q 4.  An electron in a hydrogen atom makes a transition from first excited state to ground state. The  
equivalent current due to circulating electron 
  (a) increases 4 times (b) decreases 4 times (c) increases 8 times (d) decreases 8 times 
Q 5.  In a sample of hydrogen like atoms all of which are in ground state, a photon beam containing 
photons of various energies is passed. In absorption spectrum, five dark lines are observed. The 
number of bright lines in the emission spectrum will be 
  (assume that all transitions take place) 
  (a) 21   (b) 10    (c) 15    (d) None of these 
Q 6.  Let A
n
 be the area enclosed by the nth orbit in a hydrogen atom. The graph of ln (A
n
/A
1
 )against ln 
(n) 
  (a) will not pass through origin   (b) will be a straight line with slope 4 
  (c) will be a rectangular hyperbola   (d) will be a parabola 
Q 7.  In the hydrogen atom, an electron makes a transition from n = 2 to n = 1. The magnetic field 
produced by the circulating electron at the nucleus 
  (a) decreases 16 times (b) increases 4 times (c) decreases 4 times (d) increases 32 times 
Q 8.  A stationary hydrogen atom emits photon corresponding to the first line of Lymann series. If R is 
the Rydberg's constant and M is the mass of the atom, then the velocity acquired by the atom is 
  (a) 
3Rh
4M
   (b) 
4M
3Rh
   (c) 
Rh
4M
   (d) 
4M
Rh
 
Q 9.  Light wave described by the equation 200 V/m sin (1.5 × 10
15
 s
-1
 )t cos (0.5 × 10
15
 s
-1
 )t falls on 
metal surface having work function 2.0 eV. Then the maximum kinetic energy of photoelectrons is 
  (a) 3.27 eV   (b) 2.2 eV  (c) 2.85 eV   (d) None of these 
Q 10.  A hydrogen like atom is excited using a radiation. Consequently six spectral lines are observed in 
the spectrum. The wavelength of emission radiation is found to be equal or smaller than the 
radiation used. This concludes that the gas was initially at 
  (a) ground state     (b) first excited state  
  (c) second excited state    (d) third excited state 
Q 11.  The time period of the electron in the ground state of hydrogen atom is two times the time period 
of the electron in the first excited state of a certain hydrogen like atom (Atomic Number 2). The 
value of Z is 
  (a) 2    (b) 3    (c) 4    (d) None of these 
Q 12.  The wavelengths of K
?
 
X-rays from lead isotopes Pb
204
,Pb
206
 and Pb
208
 are ?
1
, ?
2
 and ?
3
 
respectively. Choose the correct alternative. 
 (a) ?
1
 < ?
2
 < ?
3
 (b) ?
1
 > ?
2
 > ?
3
 (c) ?
1
 = ?
2
 = ?
3
  (d) None of these 
Q 13.  In case of hydrogen atom, whenever a photon is emitted in the Balmer series, 
  (a) there is a probability of emitting another photon in the Lyman series 
  (b) there is a probability of emitting another photon of wavelength 1213 Å 
(c) the wavelength of radiation emitted in Lyman series is always shorter than the wavelength 
emitted in the Balmer series 
  (d) All of the above 
Q 14.  An electron of kinetic energy K collides elastically with a stationary hydrogen atom in the ground 
state. Then 
  (a) K > 13.6 eV  (b) K > 10.2 eV  (c) K < 10.2 eV  (d) data insufficient 
Q 15.  In a stationary hydrogen atom, an electron jumps from n = 3 to n = 1. The recoil speed of the 
hydrogen atom is about 
  (a) 4m/s   (b) 4 cm/s   (c) 4 mm/s   (d) 4 × 10
-4
m/s 
Q 16.  An X-ray tube is operating at 150 kV and 10 mA. If only 1% of the electric power supplied is 
converted into X-rays, the rate at which the target is heated in calorie per second is 
  (a) 3.55   (b) 35.5   (c) 355   (d) 3550 
Q 17.  An electron revolves round a nucleus of atomic number Z. If 32.4 eV of energy is required to 
excite an electron from the n = 3 state to n = 4 state, then the value of Z is 
  (a) 5    (b) 6    (c) 4    (d) 7 
Q 18.  If the de-Broglie wavelength of a proton is 10
-13
 m, the electric potential through which it must 
have been accelerated is 
  (a) 4.07 × 10
4
V  (b) 8.15 × 10
4
V  (c) 8.15 × 10
3
V  (d) 4.07 × 10
5
V 
Q 19.  If E
n
 and L
n
 denote the total energy and the angular momentum of an electron in the nth orbit of  
Bohr atom, then 
 (a) E
n
 ? L
n
  (b) 
n
n
1
E
L
?   (c) 
2
nn
EL ?   (d) 
n 2
n
1
E
L
? 
Q 20.  An orbital electron in the ground state of hydrogen has the magnetic moment ?
1
. This orbital 
electron is excited to 3rd excited state by some energy transfer to the hydrogen atom. The new 
magnetic moment of the electron is ?
2
, then 
 (a) ?
1
 = 4 ?
2
  (b) 2 ?
1
 = ?
2
  (c) 16 ?
1
 = ?
2
  (d) 4 ?
1
 = ?
2
 
Q 21.  A moving hydrogen atom makes a head-on collision with a stationary hydrogen atom. Before 
collision, both atoms are in ground state and after collision they move together. The minimum 
value of the kinetic energy of the moving hydrogen atom, such that one of the atoms reaches one 
of the excitation state is  
  (a) 20.4 eV   (b) 10.2 eV   (c) 54.4 eV   (d) 13.6 eV 
Q 22.  In an excited state of hydrogen like atom an electron has total energy of- 3.4 eV. If the kinetic 
energy of the electron is E and its de-Broglie wavelength is ?, then 
  (a) ? = 6.6 Å   (b) E = 3.4eV   (c) Both are correct  (d) Both are wrong 
Passage : (Q. No. 23 to 25) 
When a surface is irradiated with light of wavelength 4950Å, a photocurrent appears which 
vanishes if a retarding potential greater than 0.6 volt is applied across the phototube. When a 
second source of light is used, it is found that the critical retarding potential is changed to 1.1 volt. 
Q 23.  The work function of the emitting surface is 
  (a) 2.2 eV   (b) 1.5 eV   (c) 1.9 eV   (d) 1.1 eV 
Q 24.  The wavelength of the second source is  
  (a) 6150 Å  (b) 5150 Å   (c) 4125 Å   (d) 4500 Å 
Q 25.  If the photoelectrons (after emission from the source) are subjected to a magnetic field of 10 tesla, 
the two retarding potentials would 
  (a) uniformly increase (b) uniformly decrease (c) remain the same (d) None of these 
Passage : (Q. No. 26 to 28) 
In an experimental set up to study the photoelectric effect a point-source of light of power 3.2 × 
10
-3
 W was taken. The source can emit mono energetic photons of energy 5 eV and is located at a 
distance of 0.8 m from the centre of a stationary metallic sphere of work function 3.0 eV. The 
radius of the sphere is r = 8 × 10
-3
 m. The efficiency of photoelectric emission is one for every 10
6
 
incident photons. Based on the information given above answer the questions given below. 
(Assume that the sphere is isolated and photo-electrons are instantly swept away after the 
emission). 
Q 26.  de-Broglie wavelength of the fastest moving photo-electron is 
 (a) 6.63 Å   (b) 8.69 Å   (c) 2Å    (d) 5.26 Å 
Q 27.  It was observed that after some time emission of photo-electrons from the sphere stopped. Charge 
on the sphere when the photon emission stops is 
 (a) 16 ? ?
0
r Coulomb    (b) 8 ? ?
0
r Coulomb 
  (c) 15 ? ?
0
r Coulomb    (d) 20 ? ?
0
r Coulomb 
Q 28.  Time after which photo-electric emission stops is  
  (a) 100 s   (b) 121 s  (c) 111s   (d) 141 s 
Answers 
  1. (b) 2. (b) 3. (a) 4. (c) 5. (c) 6. (b) 7. (d) 8. (a) 9. (d) 10. (c) 11. (c) 12. (c) 13. (d) 14. (c) 15. (a) 
  16. (c) 17. (d) 18. (b) 19. (d) 20. (d) 21. (a) 22. (c) 23. (c) 24. (c) 25. (c) 26. (b) 27. (b) 28. (c) 
Solutions 
1.  
   
  Solving these two equations we can find v and r. Then, 
    
2.   
   M ? L 
   
  ?  M ? n 
3.  E
2 
- E
1
= 40.8 eV 
   
  or   E
1
 = - 54.4 eV 
   | E
1
 | = 54.4 eV 
4.  
   
5.  n
f
 = 6 
  Total emission lines = 
6. A = ?r
2
 
   
  Therefore, In versus ln(n) graph is a straight 
  line of slope 4.  
7.  
   
  See the hint of Q.No. (4) of same section. 
   
   
8.    
Page 5


For JEE Advanced 
Objective Questions 
  Single Correct Option 
Q 1.  If we assume only gravitational attraction between proton and electron in hydrogen atom and the 
Bohr's quantization rule to be followed, then the expression for the ground state energy of the 
atom will be (the mass of proton is M and that of electron is m.) 
 (a) 
2 2 2
2
G M m
h
   (b) 
2 2 2 3
2
2 G M m
h
?
  (c) 
2 2 3
2
2 GM m
h
?
?
 
(d) None of these 
Q 2.  An electron in a hydrogen atom makes a transition from first excited state to ground state. The 
magnetic moment due to circulating electron 
  (a) increases two times (b) decreases two times (c) increases four times (d) remains same 
Q 3.  The excitation energy of a hydrogen-like ion to its first excited state is 40.8 eV. The energy 
needed to remove the electron from the ion in the ground state is 
  (a) 54.4 eV   (b) 62.6 eV   (c) 72.6 eV   (d) 58.6 eV 
Q 4.  An electron in a hydrogen atom makes a transition from first excited state to ground state. The  
equivalent current due to circulating electron 
  (a) increases 4 times (b) decreases 4 times (c) increases 8 times (d) decreases 8 times 
Q 5.  In a sample of hydrogen like atoms all of which are in ground state, a photon beam containing 
photons of various energies is passed. In absorption spectrum, five dark lines are observed. The 
number of bright lines in the emission spectrum will be 
  (assume that all transitions take place) 
  (a) 21   (b) 10    (c) 15    (d) None of these 
Q 6.  Let A
n
 be the area enclosed by the nth orbit in a hydrogen atom. The graph of ln (A
n
/A
1
 )against ln 
(n) 
  (a) will not pass through origin   (b) will be a straight line with slope 4 
  (c) will be a rectangular hyperbola   (d) will be a parabola 
Q 7.  In the hydrogen atom, an electron makes a transition from n = 2 to n = 1. The magnetic field 
produced by the circulating electron at the nucleus 
  (a) decreases 16 times (b) increases 4 times (c) decreases 4 times (d) increases 32 times 
Q 8.  A stationary hydrogen atom emits photon corresponding to the first line of Lymann series. If R is 
the Rydberg's constant and M is the mass of the atom, then the velocity acquired by the atom is 
  (a) 
3Rh
4M
   (b) 
4M
3Rh
   (c) 
Rh
4M
   (d) 
4M
Rh
 
Q 9.  Light wave described by the equation 200 V/m sin (1.5 × 10
15
 s
-1
 )t cos (0.5 × 10
15
 s
-1
 )t falls on 
metal surface having work function 2.0 eV. Then the maximum kinetic energy of photoelectrons is 
  (a) 3.27 eV   (b) 2.2 eV  (c) 2.85 eV   (d) None of these 
Q 10.  A hydrogen like atom is excited using a radiation. Consequently six spectral lines are observed in 
the spectrum. The wavelength of emission radiation is found to be equal or smaller than the 
radiation used. This concludes that the gas was initially at 
  (a) ground state     (b) first excited state  
  (c) second excited state    (d) third excited state 
Q 11.  The time period of the electron in the ground state of hydrogen atom is two times the time period 
of the electron in the first excited state of a certain hydrogen like atom (Atomic Number 2). The 
value of Z is 
  (a) 2    (b) 3    (c) 4    (d) None of these 
Q 12.  The wavelengths of K
?
 
X-rays from lead isotopes Pb
204
,Pb
206
 and Pb
208
 are ?
1
, ?
2
 and ?
3
 
respectively. Choose the correct alternative. 
 (a) ?
1
 < ?
2
 < ?
3
 (b) ?
1
 > ?
2
 > ?
3
 (c) ?
1
 = ?
2
 = ?
3
  (d) None of these 
Q 13.  In case of hydrogen atom, whenever a photon is emitted in the Balmer series, 
  (a) there is a probability of emitting another photon in the Lyman series 
  (b) there is a probability of emitting another photon of wavelength 1213 Å 
(c) the wavelength of radiation emitted in Lyman series is always shorter than the wavelength 
emitted in the Balmer series 
  (d) All of the above 
Q 14.  An electron of kinetic energy K collides elastically with a stationary hydrogen atom in the ground 
state. Then 
  (a) K > 13.6 eV  (b) K > 10.2 eV  (c) K < 10.2 eV  (d) data insufficient 
Q 15.  In a stationary hydrogen atom, an electron jumps from n = 3 to n = 1. The recoil speed of the 
hydrogen atom is about 
  (a) 4m/s   (b) 4 cm/s   (c) 4 mm/s   (d) 4 × 10
-4
m/s 
Q 16.  An X-ray tube is operating at 150 kV and 10 mA. If only 1% of the electric power supplied is 
converted into X-rays, the rate at which the target is heated in calorie per second is 
  (a) 3.55   (b) 35.5   (c) 355   (d) 3550 
Q 17.  An electron revolves round a nucleus of atomic number Z. If 32.4 eV of energy is required to 
excite an electron from the n = 3 state to n = 4 state, then the value of Z is 
  (a) 5    (b) 6    (c) 4    (d) 7 
Q 18.  If the de-Broglie wavelength of a proton is 10
-13
 m, the electric potential through which it must 
have been accelerated is 
  (a) 4.07 × 10
4
V  (b) 8.15 × 10
4
V  (c) 8.15 × 10
3
V  (d) 4.07 × 10
5
V 
Q 19.  If E
n
 and L
n
 denote the total energy and the angular momentum of an electron in the nth orbit of  
Bohr atom, then 
 (a) E
n
 ? L
n
  (b) 
n
n
1
E
L
?   (c) 
2
nn
EL ?   (d) 
n 2
n
1
E
L
? 
Q 20.  An orbital electron in the ground state of hydrogen has the magnetic moment ?
1
. This orbital 
electron is excited to 3rd excited state by some energy transfer to the hydrogen atom. The new 
magnetic moment of the electron is ?
2
, then 
 (a) ?
1
 = 4 ?
2
  (b) 2 ?
1
 = ?
2
  (c) 16 ?
1
 = ?
2
  (d) 4 ?
1
 = ?
2
 
Q 21.  A moving hydrogen atom makes a head-on collision with a stationary hydrogen atom. Before 
collision, both atoms are in ground state and after collision they move together. The minimum 
value of the kinetic energy of the moving hydrogen atom, such that one of the atoms reaches one 
of the excitation state is  
  (a) 20.4 eV   (b) 10.2 eV   (c) 54.4 eV   (d) 13.6 eV 
Q 22.  In an excited state of hydrogen like atom an electron has total energy of- 3.4 eV. If the kinetic 
energy of the electron is E and its de-Broglie wavelength is ?, then 
  (a) ? = 6.6 Å   (b) E = 3.4eV   (c) Both are correct  (d) Both are wrong 
Passage : (Q. No. 23 to 25) 
When a surface is irradiated with light of wavelength 4950Å, a photocurrent appears which 
vanishes if a retarding potential greater than 0.6 volt is applied across the phototube. When a 
second source of light is used, it is found that the critical retarding potential is changed to 1.1 volt. 
Q 23.  The work function of the emitting surface is 
  (a) 2.2 eV   (b) 1.5 eV   (c) 1.9 eV   (d) 1.1 eV 
Q 24.  The wavelength of the second source is  
  (a) 6150 Å  (b) 5150 Å   (c) 4125 Å   (d) 4500 Å 
Q 25.  If the photoelectrons (after emission from the source) are subjected to a magnetic field of 10 tesla, 
the two retarding potentials would 
  (a) uniformly increase (b) uniformly decrease (c) remain the same (d) None of these 
Passage : (Q. No. 26 to 28) 
In an experimental set up to study the photoelectric effect a point-source of light of power 3.2 × 
10
-3
 W was taken. The source can emit mono energetic photons of energy 5 eV and is located at a 
distance of 0.8 m from the centre of a stationary metallic sphere of work function 3.0 eV. The 
radius of the sphere is r = 8 × 10
-3
 m. The efficiency of photoelectric emission is one for every 10
6
 
incident photons. Based on the information given above answer the questions given below. 
(Assume that the sphere is isolated and photo-electrons are instantly swept away after the 
emission). 
Q 26.  de-Broglie wavelength of the fastest moving photo-electron is 
 (a) 6.63 Å   (b) 8.69 Å   (c) 2Å    (d) 5.26 Å 
Q 27.  It was observed that after some time emission of photo-electrons from the sphere stopped. Charge 
on the sphere when the photon emission stops is 
 (a) 16 ? ?
0
r Coulomb    (b) 8 ? ?
0
r Coulomb 
  (c) 15 ? ?
0
r Coulomb    (d) 20 ? ?
0
r Coulomb 
Q 28.  Time after which photo-electric emission stops is  
  (a) 100 s   (b) 121 s  (c) 111s   (d) 141 s 
Answers 
  1. (b) 2. (b) 3. (a) 4. (c) 5. (c) 6. (b) 7. (d) 8. (a) 9. (d) 10. (c) 11. (c) 12. (c) 13. (d) 14. (c) 15. (a) 
  16. (c) 17. (d) 18. (b) 19. (d) 20. (d) 21. (a) 22. (c) 23. (c) 24. (c) 25. (c) 26. (b) 27. (b) 28. (c) 
Solutions 
1.  
   
  Solving these two equations we can find v and r. Then, 
    
2.   
   M ? L 
   
  ?  M ? n 
3.  E
2 
- E
1
= 40.8 eV 
   
  or   E
1
 = - 54.4 eV 
   | E
1
 | = 54.4 eV 
4.  
   
5.  n
f
 = 6 
  Total emission lines = 
6. A = ?r
2
 
   
  Therefore, In versus ln(n) graph is a straight 
  line of slope 4.  
7.  
   
  See the hint of Q.No. (4) of same section. 
   
   
8.    
   
    = momentum of photon 
  From conservation of linear momentum, momentum of photon = momentum of hydrogen atom 
   
9. ?
amx
 
=1.5 × 10
15 
rad/s = 2 ?f
max
 
   
   ? 1.0 eV  
  Since, E < W, no photo emission can take place. 
10.  
   
  From n
i
 = 2, energy of six emission lines is either greater than less or equal to the energy of 
absorption line. 
11.  
   
   Z = 4 
12.  
K
?
?
 
will depends on atomic number Z and values Z is same of all three isotopes. 
13.