DC Pandey Solutions (JEE Advance): Modern Physics- II | DC Pandey Solutions for JEE Physics PDF Download

 Page 1


For JEE Advanced 
  Assertion and Reason 
  Directions : Choose the correct option. 
(a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion. 
(b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion. 
(c) If Assertion is true, but the Reason is false. 
(d) If Assertion is false but the Reason is true. 
Q 1.  Assertion: Rate of radioactivity can not be increased or decreased by increasing or decreasing 
pressure or temperature. 
  Reason : Rate depends on number of nuclei present in the radioactive sample. 
Q 2.  Assertion: Only those nuclei which are heavier than lead are radioactive.  
  Reason : Nuclei of elements heavier than lead are unstable. 
Q 3.  Assertion: After emission of one particle and two ?-particles, atomic number remains 
unchanged.  
  Reason : Mass number changes by four. 
Q 4.  Assertion : ?-rays are produced by the transition of a nucleus from some higher energy state to 
some lower energy state. 
  Reason : Electromagnetic waves are always produced by the transition process. 
Q 5.  Assertion : During ?-decay a proton converts into a neutron and an electron. No other particle is 
emitted. 
  Reason: During ?-decay linear momentum of system should remains constant.  
Q 6.  Assertion : If we compare the stability of two nuclei, then that nucleus is more stable whose total 
binding energy is more. 
  Reason : More the mass defect during formation of a nucleus more will be the binding energy. 
Q 7.  Assertion : In a nuclear process energy is released if total binding energy of daughter nuclei is 
more than the total binding energy of parent nuclei. 
Reason : If energy is released then total mass of daughter nuclei is less than the total mass of 
parent nuclei. 
Q 8.  Assertion: Binding energy per nucleon is of the order of MeV.  
  Reason : 1 MeV = 1.6 X 10
-13
 J. 
Q 9.  Assertion: 1 amu is equal to 931.48 MeV. 
  Reason: 1 amu is equal to 
1
th
12
the mass of C
12
 atom.  
Q 10.  Assertion: Between ?, ? and ?
 
radiations, penetrating power of ?-rays is maximum.  
  Reason: Ionising power of -rays is least.  
Q 11.  Assertion : The nuclear energy can be obtained by the nuclear fission of heavier nuclei as well as 
by fusion of lighter nuclei. 
Reason : The binding energy per nucleon with increase in mass number, first increases and then 
decreases. 
Page 2


For JEE Advanced 
  Assertion and Reason 
  Directions : Choose the correct option. 
(a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion. 
(b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion. 
(c) If Assertion is true, but the Reason is false. 
(d) If Assertion is false but the Reason is true. 
Q 1.  Assertion: Rate of radioactivity can not be increased or decreased by increasing or decreasing 
pressure or temperature. 
  Reason : Rate depends on number of nuclei present in the radioactive sample. 
Q 2.  Assertion: Only those nuclei which are heavier than lead are radioactive.  
  Reason : Nuclei of elements heavier than lead are unstable. 
Q 3.  Assertion: After emission of one particle and two ?-particles, atomic number remains 
unchanged.  
  Reason : Mass number changes by four. 
Q 4.  Assertion : ?-rays are produced by the transition of a nucleus from some higher energy state to 
some lower energy state. 
  Reason : Electromagnetic waves are always produced by the transition process. 
Q 5.  Assertion : During ?-decay a proton converts into a neutron and an electron. No other particle is 
emitted. 
  Reason: During ?-decay linear momentum of system should remains constant.  
Q 6.  Assertion : If we compare the stability of two nuclei, then that nucleus is more stable whose total 
binding energy is more. 
  Reason : More the mass defect during formation of a nucleus more will be the binding energy. 
Q 7.  Assertion : In a nuclear process energy is released if total binding energy of daughter nuclei is 
more than the total binding energy of parent nuclei. 
Reason : If energy is released then total mass of daughter nuclei is less than the total mass of 
parent nuclei. 
Q 8.  Assertion: Binding energy per nucleon is of the order of MeV.  
  Reason : 1 MeV = 1.6 X 10
-13
 J. 
Q 9.  Assertion: 1 amu is equal to 931.48 MeV. 
  Reason: 1 amu is equal to 
1
th
12
the mass of C
12
 atom.  
Q 10.  Assertion: Between ?, ? and ?
 
radiations, penetrating power of ?-rays is maximum.  
  Reason: Ionising power of -rays is least.  
Q 11.  Assertion : The nuclear energy can be obtained by the nuclear fission of heavier nuclei as well as 
by fusion of lighter nuclei. 
Reason : The binding energy per nucleon with increase in mass number, first increases and then 
decreases. 
Answers 
1. (b) 2. (d) 3. (b) 4. (c) 5. (d) 6. (d) 7. (a or b) 8. (b) 9. (d) 10. (b) 11. (a or b) 
Solutions 
1.  Huge amont of energy is involved in any nuclear process, which cannot be increased or decreased 
by pressure or temperatrue. 
2.  Some lighter nuclei are also radioactive. 
3.  By emission of one ?-particle atomic number decreases by 2 and mass number by 4. But by the 
emission of one ?-particle, atomic number increases by 1 and mass number reamains uncharged. 
4.  In moving from lower energy state to higher energy state electromagnetic waves are absorbed. 
5.  Antineutrino is also produced during ?-decay. 
6.  Total binding energy per nucleon is more important for stability. 
7.  Solution is not required. 
8.  Solution is not required. 
9.  19(mu)(c
2
) = 931.48 MeV 
10.  ?-particles are heaviest. Hence, its ionising power is maximum. 
11.  In binding energy per nucleon versus mass number graph binding energy per nucleon of daughter 
nuclei should increase (for release of energy) or, the daughter nuclei should lie towards the peak of 
the graph. 
 
Objective Questions 
  Single Correct Option 
Q 1.  The count rate observed from a radioactive source at t second was N0 and at 4t second it was 
0
N
16
.
 
The count rate observed, at 
11
t
2
??
??
??
second will be 
 (a) 
0
N
128
   (b) 
0
N
64
   (c) 
0
N
32
   (d) None of these 
Q 2.  The half lives of a radioactive sample are 30 years and 60 years for two decay processes. If the 
sample decays by both the processes simultaneously. The time after which, only one-fourth of the 
sample will remain is 
  (a) 10 years   (b) 20 years   (c) 40 years   (d) 60 years 
Q 3.  Consider the nuclear fission reaction W ? Y + Y. What is the Q value (energy released) of the  
reaction? 
 
Page 3


For JEE Advanced 
  Assertion and Reason 
  Directions : Choose the correct option. 
(a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion. 
(b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion. 
(c) If Assertion is true, but the Reason is false. 
(d) If Assertion is false but the Reason is true. 
Q 1.  Assertion: Rate of radioactivity can not be increased or decreased by increasing or decreasing 
pressure or temperature. 
  Reason : Rate depends on number of nuclei present in the radioactive sample. 
Q 2.  Assertion: Only those nuclei which are heavier than lead are radioactive.  
  Reason : Nuclei of elements heavier than lead are unstable. 
Q 3.  Assertion: After emission of one particle and two ?-particles, atomic number remains 
unchanged.  
  Reason : Mass number changes by four. 
Q 4.  Assertion : ?-rays are produced by the transition of a nucleus from some higher energy state to 
some lower energy state. 
  Reason : Electromagnetic waves are always produced by the transition process. 
Q 5.  Assertion : During ?-decay a proton converts into a neutron and an electron. No other particle is 
emitted. 
  Reason: During ?-decay linear momentum of system should remains constant.  
Q 6.  Assertion : If we compare the stability of two nuclei, then that nucleus is more stable whose total 
binding energy is more. 
  Reason : More the mass defect during formation of a nucleus more will be the binding energy. 
Q 7.  Assertion : In a nuclear process energy is released if total binding energy of daughter nuclei is 
more than the total binding energy of parent nuclei. 
Reason : If energy is released then total mass of daughter nuclei is less than the total mass of 
parent nuclei. 
Q 8.  Assertion: Binding energy per nucleon is of the order of MeV.  
  Reason : 1 MeV = 1.6 X 10
-13
 J. 
Q 9.  Assertion: 1 amu is equal to 931.48 MeV. 
  Reason: 1 amu is equal to 
1
th
12
the mass of C
12
 atom.  
Q 10.  Assertion: Between ?, ? and ?
 
radiations, penetrating power of ?-rays is maximum.  
  Reason: Ionising power of -rays is least.  
Q 11.  Assertion : The nuclear energy can be obtained by the nuclear fission of heavier nuclei as well as 
by fusion of lighter nuclei. 
Reason : The binding energy per nucleon with increase in mass number, first increases and then 
decreases. 
Answers 
1. (b) 2. (d) 3. (b) 4. (c) 5. (d) 6. (d) 7. (a or b) 8. (b) 9. (d) 10. (b) 11. (a or b) 
Solutions 
1.  Huge amont of energy is involved in any nuclear process, which cannot be increased or decreased 
by pressure or temperatrue. 
2.  Some lighter nuclei are also radioactive. 
3.  By emission of one ?-particle atomic number decreases by 2 and mass number by 4. But by the 
emission of one ?-particle, atomic number increases by 1 and mass number reamains uncharged. 
4.  In moving from lower energy state to higher energy state electromagnetic waves are absorbed. 
5.  Antineutrino is also produced during ?-decay. 
6.  Total binding energy per nucleon is more important for stability. 
7.  Solution is not required. 
8.  Solution is not required. 
9.  19(mu)(c
2
) = 931.48 MeV 
10.  ?-particles are heaviest. Hence, its ionising power is maximum. 
11.  In binding energy per nucleon versus mass number graph binding energy per nucleon of daughter 
nuclei should increase (for release of energy) or, the daughter nuclei should lie towards the peak of 
the graph. 
 
Objective Questions 
  Single Correct Option 
Q 1.  The count rate observed from a radioactive source at t second was N0 and at 4t second it was 
0
N
16
.
 
The count rate observed, at 
11
t
2
??
??
??
second will be 
 (a) 
0
N
128
   (b) 
0
N
64
   (c) 
0
N
32
   (d) None of these 
Q 2.  The half lives of a radioactive sample are 30 years and 60 years for two decay processes. If the 
sample decays by both the processes simultaneously. The time after which, only one-fourth of the 
sample will remain is 
  (a) 10 years   (b) 20 years   (c) 40 years   (d) 60 years 
Q 3.  Consider the nuclear fission reaction W ? Y + Y. What is the Q value (energy released) of the  
reaction? 
 
  (a) E1N1 - (E2N2 + E3N 3)    (b) (E2N 2 + E3N3 - E1N1) 
  (c) E2N2 +E1N1 -E3N3    (d) E1N1+E3N3 - E2N 2 
Q 4.  Consider the following nuclear reaction 
   X
200
 ? A
110 
+ B
90 
+ Energy 
If the binding energy per nucleon for X, A and B are 7.4 MeV, 8.2 MeV and 8.2 MeV 
respectively, the energy released will be  
(a) 90 MeV   (b) 110 MeV   (c) 200 MeV   (d) 160 MeV 
Q 5.  The binding energy per nucleon for deuteron 
? ?
2
1
H and helium 
? ?
4
2
He are 1.1 MeV and 7.0 MeV, 
respectively. The energy released when two deutrons fuse to form a helium nucleus is  
  (a) 47.12 MeV  (b) 23.6 MeV   (c) 11.8 MeV   (d) 34.4 MeV 
Q 6.  The energy released by the fission of a single uranium nucleus is 200 MeV. The number of 
fissions of uranium nucleus per second required to produce 16 MW of power is 
  (Assume efficiency of the reactor is 50%) 
  (a) 2 × 10
6
   (b) 2.5 × 10
6
   (c) 5 × 10
6
   (d) None of these 
Q 7.  A radioactive isotope is being produced at a constant rate A. The isotope has a half-life T. Initially 
there are no nuclei, after a time t>>T, the number of nuclei becomes constant. The value of this 
constant is 
 (a) AT    (b) 
A
ln(2)
T
   (c) AT ln (2)   (d) 
AT
ln(2)
 
Q 8.  A moving hydrogen atom makes a head on collision with a stationary hydrogen atom. Before 
collision both atoms are in the ground state and after collision they move together. What is the 
velocity of the moving atom if after the collision one of the atom gets minimum excitation energy? 
  (Mass of hydrogen atom is 1.673 × 10
-27
 kg) 
  (a) 5.25 × 10
4
 m/s  (b) 4.25 × 10
4
 m/s  (c) 6.25 × 10
4
 m/s  (d) 10.25 × 10
4
 m/s 
Q 9.  A bone containing 200 g carbon-14 has a ?-decay rate of 375 decay/min. Calculate the time that 
has elapsed since the death of the living one. Given the rate of decay for the living organism is 
equal to 15 decay per min per gram of carbon and half-life of carbon-14 = 5730 years 
  (a) 27190 years  (b) 1190 years  (c) 17190 years  (d) None of these 
Q 10.  Two identical samples (same material and same amount) P and Q of a radioactive substance 
having mean life T are observed to have activities AP and AQ respectively at the time of 
observation. If P is older than Q, then the difference in their age is 
 (a) 
P
Q
A
T ln
A
??
??
??
??
  (b) 
Q
P
A
Tln
A
??
??
??
  (c) 
P
Q
A
T
A
??
??
??
??
   (d) 
Q
P
A
T
A
??
??
??
  
Q 11.  A star initially has 10
40
 deuterons. It produces energy via the processes 
2 2 2
1 1 1
H H H p ? ? ?
 
and  
2 3 4
1 1 2
H H He n ? ? ? .
 
Where the masses of the nuclei are : 
  m(
2
H) = 2.014 amu, m(p)= 1.007 amu, m(n)= 1.008 amu and m(
4
He) = 4.001 amu.  
If the average power radiated by the star is 10
16
 W, the deuteron supply of the star is exhausted in  
a time of the order of  
Page 4


For JEE Advanced 
  Assertion and Reason 
  Directions : Choose the correct option. 
(a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion. 
(b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion. 
(c) If Assertion is true, but the Reason is false. 
(d) If Assertion is false but the Reason is true. 
Q 1.  Assertion: Rate of radioactivity can not be increased or decreased by increasing or decreasing 
pressure or temperature. 
  Reason : Rate depends on number of nuclei present in the radioactive sample. 
Q 2.  Assertion: Only those nuclei which are heavier than lead are radioactive.  
  Reason : Nuclei of elements heavier than lead are unstable. 
Q 3.  Assertion: After emission of one particle and two ?-particles, atomic number remains 
unchanged.  
  Reason : Mass number changes by four. 
Q 4.  Assertion : ?-rays are produced by the transition of a nucleus from some higher energy state to 
some lower energy state. 
  Reason : Electromagnetic waves are always produced by the transition process. 
Q 5.  Assertion : During ?-decay a proton converts into a neutron and an electron. No other particle is 
emitted. 
  Reason: During ?-decay linear momentum of system should remains constant.  
Q 6.  Assertion : If we compare the stability of two nuclei, then that nucleus is more stable whose total 
binding energy is more. 
  Reason : More the mass defect during formation of a nucleus more will be the binding energy. 
Q 7.  Assertion : In a nuclear process energy is released if total binding energy of daughter nuclei is 
more than the total binding energy of parent nuclei. 
Reason : If energy is released then total mass of daughter nuclei is less than the total mass of 
parent nuclei. 
Q 8.  Assertion: Binding energy per nucleon is of the order of MeV.  
  Reason : 1 MeV = 1.6 X 10
-13
 J. 
Q 9.  Assertion: 1 amu is equal to 931.48 MeV. 
  Reason: 1 amu is equal to 
1
th
12
the mass of C
12
 atom.  
Q 10.  Assertion: Between ?, ? and ?
 
radiations, penetrating power of ?-rays is maximum.  
  Reason: Ionising power of -rays is least.  
Q 11.  Assertion : The nuclear energy can be obtained by the nuclear fission of heavier nuclei as well as 
by fusion of lighter nuclei. 
Reason : The binding energy per nucleon with increase in mass number, first increases and then 
decreases. 
Answers 
1. (b) 2. (d) 3. (b) 4. (c) 5. (d) 6. (d) 7. (a or b) 8. (b) 9. (d) 10. (b) 11. (a or b) 
Solutions 
1.  Huge amont of energy is involved in any nuclear process, which cannot be increased or decreased 
by pressure or temperatrue. 
2.  Some lighter nuclei are also radioactive. 
3.  By emission of one ?-particle atomic number decreases by 2 and mass number by 4. But by the 
emission of one ?-particle, atomic number increases by 1 and mass number reamains uncharged. 
4.  In moving from lower energy state to higher energy state electromagnetic waves are absorbed. 
5.  Antineutrino is also produced during ?-decay. 
6.  Total binding energy per nucleon is more important for stability. 
7.  Solution is not required. 
8.  Solution is not required. 
9.  19(mu)(c
2
) = 931.48 MeV 
10.  ?-particles are heaviest. Hence, its ionising power is maximum. 
11.  In binding energy per nucleon versus mass number graph binding energy per nucleon of daughter 
nuclei should increase (for release of energy) or, the daughter nuclei should lie towards the peak of 
the graph. 
 
Objective Questions 
  Single Correct Option 
Q 1.  The count rate observed from a radioactive source at t second was N0 and at 4t second it was 
0
N
16
.
 
The count rate observed, at 
11
t
2
??
??
??
second will be 
 (a) 
0
N
128
   (b) 
0
N
64
   (c) 
0
N
32
   (d) None of these 
Q 2.  The half lives of a radioactive sample are 30 years and 60 years for two decay processes. If the 
sample decays by both the processes simultaneously. The time after which, only one-fourth of the 
sample will remain is 
  (a) 10 years   (b) 20 years   (c) 40 years   (d) 60 years 
Q 3.  Consider the nuclear fission reaction W ? Y + Y. What is the Q value (energy released) of the  
reaction? 
 
  (a) E1N1 - (E2N2 + E3N 3)    (b) (E2N 2 + E3N3 - E1N1) 
  (c) E2N2 +E1N1 -E3N3    (d) E1N1+E3N3 - E2N 2 
Q 4.  Consider the following nuclear reaction 
   X
200
 ? A
110 
+ B
90 
+ Energy 
If the binding energy per nucleon for X, A and B are 7.4 MeV, 8.2 MeV and 8.2 MeV 
respectively, the energy released will be  
(a) 90 MeV   (b) 110 MeV   (c) 200 MeV   (d) 160 MeV 
Q 5.  The binding energy per nucleon for deuteron 
? ?
2
1
H and helium 
? ?
4
2
He are 1.1 MeV and 7.0 MeV, 
respectively. The energy released when two deutrons fuse to form a helium nucleus is  
  (a) 47.12 MeV  (b) 23.6 MeV   (c) 11.8 MeV   (d) 34.4 MeV 
Q 6.  The energy released by the fission of a single uranium nucleus is 200 MeV. The number of 
fissions of uranium nucleus per second required to produce 16 MW of power is 
  (Assume efficiency of the reactor is 50%) 
  (a) 2 × 10
6
   (b) 2.5 × 10
6
   (c) 5 × 10
6
   (d) None of these 
Q 7.  A radioactive isotope is being produced at a constant rate A. The isotope has a half-life T. Initially 
there are no nuclei, after a time t>>T, the number of nuclei becomes constant. The value of this 
constant is 
 (a) AT    (b) 
A
ln(2)
T
   (c) AT ln (2)   (d) 
AT
ln(2)
 
Q 8.  A moving hydrogen atom makes a head on collision with a stationary hydrogen atom. Before 
collision both atoms are in the ground state and after collision they move together. What is the 
velocity of the moving atom if after the collision one of the atom gets minimum excitation energy? 
  (Mass of hydrogen atom is 1.673 × 10
-27
 kg) 
  (a) 5.25 × 10
4
 m/s  (b) 4.25 × 10
4
 m/s  (c) 6.25 × 10
4
 m/s  (d) 10.25 × 10
4
 m/s 
Q 9.  A bone containing 200 g carbon-14 has a ?-decay rate of 375 decay/min. Calculate the time that 
has elapsed since the death of the living one. Given the rate of decay for the living organism is 
equal to 15 decay per min per gram of carbon and half-life of carbon-14 = 5730 years 
  (a) 27190 years  (b) 1190 years  (c) 17190 years  (d) None of these 
Q 10.  Two identical samples (same material and same amount) P and Q of a radioactive substance 
having mean life T are observed to have activities AP and AQ respectively at the time of 
observation. If P is older than Q, then the difference in their age is 
 (a) 
P
Q
A
T ln
A
??
??
??
??
  (b) 
Q
P
A
Tln
A
??
??
??
  (c) 
P
Q
A
T
A
??
??
??
??
   (d) 
Q
P
A
T
A
??
??
??
  
Q 11.  A star initially has 10
40
 deuterons. It produces energy via the processes 
2 2 2
1 1 1
H H H p ? ? ?
 
and  
2 3 4
1 1 2
H H He n ? ? ? .
 
Where the masses of the nuclei are : 
  m(
2
H) = 2.014 amu, m(p)= 1.007 amu, m(n)= 1.008 amu and m(
4
He) = 4.001 amu.  
If the average power radiated by the star is 10
16
 W, the deuteron supply of the star is exhausted in  
a time of the order of  
(a) 10
6
 s   (b) 10
8
 s   (c) 10
12
 s   (d) 10
16
 s 
Q 12.  Two radioactive samples of different elements (half lives t 1 and t2 respectively) have same number 
of nuclei at t = 0. The time after which their activities are same is 
 (a) 
1 2 2
2 1 1
t t t
ln
0.693(t t ) t ?
    (b) 
1 2 2
1
t t t
ln
0.693 t
  
 (c) 
1 2 2
1 2 1
t t t
ln
0.693(t t ) t ?
    (d) None of these 
Q 13.  A nucleus X initially at rest, undergoes alpha decay according to the equation 
   
232 A
Z 90
XY ? ? ? 
What fraction of the total energy released in the decay will be the kinetic energy of the alpha 
particle? 
  (a) 
90
92
   (b) 
228
232
   (c) 
228
232
   (d) 
1
2
 
Q 14.  A stationary nucleus of mass 24 amu emits a gamma photon. The energy of the emitted photon is 
 7 MeV. The recoil energy of the nucleus is 
  (a) 2.2 keV   (b) 1.1 keV   (c) 3.1 keV   (d) 22 keV 
Q 15.  A radioactive material of half-life T was kept in a nuclear reactor at two different instants. The 
quantity kept second time was twice of that kept first time. If now their present activities are A 1 
and A2 respectively then their age difference equals 
 (a) 
1
2
2A T
ln
ln 2 A
  (b) 
1
2
A
T ln
A
   (c) 
2
1
A T
ln
ln 2 2A
  (d) 
2
1
A
T ln
2A
 
Passage : (Q. No. 16 to 18) 
  The atomic masses of the hydrogen isotopes are 
  Hydrogen m 1H
1
 = 1.007825 amu 
  Deuterium m1H
2
 = 2.014102 amu 
  Tritium m1H
3
 = 3.016049 amu 
Q 16.  The energy released in the reaction  
   1H
2
 + 1H
2
 ? 1H
3
 + 1H
1
 is nearly  
  (a) 1 MeV   (b) 2 MeV   (c) 4 MeV   (d) 8 MeV 
Q 17.  The number of fusion reactions required to generate 1 kWh is nearly 
  (a) 10
8
    (b) 10
18
   (c) 10
28
   (d) 10
38
 
Q 18.  The mass of deuterium, 1 H
2
 that would be needed to generate 1 kWh  
  (a) 3.7 kg   (b) 3.7 g  (c) 3.7 × 10
-5
 kg  (d) 3.7 × 10
-8
 kg 
Answers 
  1.(b) 2.(c) 3.(b) 4.(d) 5.(b) 6.(d) 7.(d) 8.(c) 9.(c) 10.(b) 11.(c) 12.(a) 13.(b) 14.(b) 15.(c) 16.(c) 
  17.(b) 18.(d) 
Solutions 
1.  
Page 5


For JEE Advanced 
  Assertion and Reason 
  Directions : Choose the correct option. 
(a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion. 
(b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion. 
(c) If Assertion is true, but the Reason is false. 
(d) If Assertion is false but the Reason is true. 
Q 1.  Assertion: Rate of radioactivity can not be increased or decreased by increasing or decreasing 
pressure or temperature. 
  Reason : Rate depends on number of nuclei present in the radioactive sample. 
Q 2.  Assertion: Only those nuclei which are heavier than lead are radioactive.  
  Reason : Nuclei of elements heavier than lead are unstable. 
Q 3.  Assertion: After emission of one particle and two ?-particles, atomic number remains 
unchanged.  
  Reason : Mass number changes by four. 
Q 4.  Assertion : ?-rays are produced by the transition of a nucleus from some higher energy state to 
some lower energy state. 
  Reason : Electromagnetic waves are always produced by the transition process. 
Q 5.  Assertion : During ?-decay a proton converts into a neutron and an electron. No other particle is 
emitted. 
  Reason: During ?-decay linear momentum of system should remains constant.  
Q 6.  Assertion : If we compare the stability of two nuclei, then that nucleus is more stable whose total 
binding energy is more. 
  Reason : More the mass defect during formation of a nucleus more will be the binding energy. 
Q 7.  Assertion : In a nuclear process energy is released if total binding energy of daughter nuclei is 
more than the total binding energy of parent nuclei. 
Reason : If energy is released then total mass of daughter nuclei is less than the total mass of 
parent nuclei. 
Q 8.  Assertion: Binding energy per nucleon is of the order of MeV.  
  Reason : 1 MeV = 1.6 X 10
-13
 J. 
Q 9.  Assertion: 1 amu is equal to 931.48 MeV. 
  Reason: 1 amu is equal to 
1
th
12
the mass of C
12
 atom.  
Q 10.  Assertion: Between ?, ? and ?
 
radiations, penetrating power of ?-rays is maximum.  
  Reason: Ionising power of -rays is least.  
Q 11.  Assertion : The nuclear energy can be obtained by the nuclear fission of heavier nuclei as well as 
by fusion of lighter nuclei. 
Reason : The binding energy per nucleon with increase in mass number, first increases and then 
decreases. 
Answers 
1. (b) 2. (d) 3. (b) 4. (c) 5. (d) 6. (d) 7. (a or b) 8. (b) 9. (d) 10. (b) 11. (a or b) 
Solutions 
1.  Huge amont of energy is involved in any nuclear process, which cannot be increased or decreased 
by pressure or temperatrue. 
2.  Some lighter nuclei are also radioactive. 
3.  By emission of one ?-particle atomic number decreases by 2 and mass number by 4. But by the 
emission of one ?-particle, atomic number increases by 1 and mass number reamains uncharged. 
4.  In moving from lower energy state to higher energy state electromagnetic waves are absorbed. 
5.  Antineutrino is also produced during ?-decay. 
6.  Total binding energy per nucleon is more important for stability. 
7.  Solution is not required. 
8.  Solution is not required. 
9.  19(mu)(c
2
) = 931.48 MeV 
10.  ?-particles are heaviest. Hence, its ionising power is maximum. 
11.  In binding energy per nucleon versus mass number graph binding energy per nucleon of daughter 
nuclei should increase (for release of energy) or, the daughter nuclei should lie towards the peak of 
the graph. 
 
Objective Questions 
  Single Correct Option 
Q 1.  The count rate observed from a radioactive source at t second was N0 and at 4t second it was 
0
N
16
.
 
The count rate observed, at 
11
t
2
??
??
??
second will be 
 (a) 
0
N
128
   (b) 
0
N
64
   (c) 
0
N
32
   (d) None of these 
Q 2.  The half lives of a radioactive sample are 30 years and 60 years for two decay processes. If the 
sample decays by both the processes simultaneously. The time after which, only one-fourth of the 
sample will remain is 
  (a) 10 years   (b) 20 years   (c) 40 years   (d) 60 years 
Q 3.  Consider the nuclear fission reaction W ? Y + Y. What is the Q value (energy released) of the  
reaction? 
 
  (a) E1N1 - (E2N2 + E3N 3)    (b) (E2N 2 + E3N3 - E1N1) 
  (c) E2N2 +E1N1 -E3N3    (d) E1N1+E3N3 - E2N 2 
Q 4.  Consider the following nuclear reaction 
   X
200
 ? A
110 
+ B
90 
+ Energy 
If the binding energy per nucleon for X, A and B are 7.4 MeV, 8.2 MeV and 8.2 MeV 
respectively, the energy released will be  
(a) 90 MeV   (b) 110 MeV   (c) 200 MeV   (d) 160 MeV 
Q 5.  The binding energy per nucleon for deuteron 
? ?
2
1
H and helium 
? ?
4
2
He are 1.1 MeV and 7.0 MeV, 
respectively. The energy released when two deutrons fuse to form a helium nucleus is  
  (a) 47.12 MeV  (b) 23.6 MeV   (c) 11.8 MeV   (d) 34.4 MeV 
Q 6.  The energy released by the fission of a single uranium nucleus is 200 MeV. The number of 
fissions of uranium nucleus per second required to produce 16 MW of power is 
  (Assume efficiency of the reactor is 50%) 
  (a) 2 × 10
6
   (b) 2.5 × 10
6
   (c) 5 × 10
6
   (d) None of these 
Q 7.  A radioactive isotope is being produced at a constant rate A. The isotope has a half-life T. Initially 
there are no nuclei, after a time t>>T, the number of nuclei becomes constant. The value of this 
constant is 
 (a) AT    (b) 
A
ln(2)
T
   (c) AT ln (2)   (d) 
AT
ln(2)
 
Q 8.  A moving hydrogen atom makes a head on collision with a stationary hydrogen atom. Before 
collision both atoms are in the ground state and after collision they move together. What is the 
velocity of the moving atom if after the collision one of the atom gets minimum excitation energy? 
  (Mass of hydrogen atom is 1.673 × 10
-27
 kg) 
  (a) 5.25 × 10
4
 m/s  (b) 4.25 × 10
4
 m/s  (c) 6.25 × 10
4
 m/s  (d) 10.25 × 10
4
 m/s 
Q 9.  A bone containing 200 g carbon-14 has a ?-decay rate of 375 decay/min. Calculate the time that 
has elapsed since the death of the living one. Given the rate of decay for the living organism is 
equal to 15 decay per min per gram of carbon and half-life of carbon-14 = 5730 years 
  (a) 27190 years  (b) 1190 years  (c) 17190 years  (d) None of these 
Q 10.  Two identical samples (same material and same amount) P and Q of a radioactive substance 
having mean life T are observed to have activities AP and AQ respectively at the time of 
observation. If P is older than Q, then the difference in their age is 
 (a) 
P
Q
A
T ln
A
??
??
??
??
  (b) 
Q
P
A
Tln
A
??
??
??
  (c) 
P
Q
A
T
A
??
??
??
??
   (d) 
Q
P
A
T
A
??
??
??
  
Q 11.  A star initially has 10
40
 deuterons. It produces energy via the processes 
2 2 2
1 1 1
H H H p ? ? ?
 
and  
2 3 4
1 1 2
H H He n ? ? ? .
 
Where the masses of the nuclei are : 
  m(
2
H) = 2.014 amu, m(p)= 1.007 amu, m(n)= 1.008 amu and m(
4
He) = 4.001 amu.  
If the average power radiated by the star is 10
16
 W, the deuteron supply of the star is exhausted in  
a time of the order of  
(a) 10
6
 s   (b) 10
8
 s   (c) 10
12
 s   (d) 10
16
 s 
Q 12.  Two radioactive samples of different elements (half lives t 1 and t2 respectively) have same number 
of nuclei at t = 0. The time after which their activities are same is 
 (a) 
1 2 2
2 1 1
t t t
ln
0.693(t t ) t ?
    (b) 
1 2 2
1
t t t
ln
0.693 t
  
 (c) 
1 2 2
1 2 1
t t t
ln
0.693(t t ) t ?
    (d) None of these 
Q 13.  A nucleus X initially at rest, undergoes alpha decay according to the equation 
   
232 A
Z 90
XY ? ? ? 
What fraction of the total energy released in the decay will be the kinetic energy of the alpha 
particle? 
  (a) 
90
92
   (b) 
228
232
   (c) 
228
232
   (d) 
1
2
 
Q 14.  A stationary nucleus of mass 24 amu emits a gamma photon. The energy of the emitted photon is 
 7 MeV. The recoil energy of the nucleus is 
  (a) 2.2 keV   (b) 1.1 keV   (c) 3.1 keV   (d) 22 keV 
Q 15.  A radioactive material of half-life T was kept in a nuclear reactor at two different instants. The 
quantity kept second time was twice of that kept first time. If now their present activities are A 1 
and A2 respectively then their age difference equals 
 (a) 
1
2
2A T
ln
ln 2 A
  (b) 
1
2
A
T ln
A
   (c) 
2
1
A T
ln
ln 2 2A
  (d) 
2
1
A
T ln
2A
 
Passage : (Q. No. 16 to 18) 
  The atomic masses of the hydrogen isotopes are 
  Hydrogen m 1H
1
 = 1.007825 amu 
  Deuterium m1H
2
 = 2.014102 amu 
  Tritium m1H
3
 = 3.016049 amu 
Q 16.  The energy released in the reaction  
   1H
2
 + 1H
2
 ? 1H
3
 + 1H
1
 is nearly  
  (a) 1 MeV   (b) 2 MeV   (c) 4 MeV   (d) 8 MeV 
Q 17.  The number of fusion reactions required to generate 1 kWh is nearly 
  (a) 10
8
    (b) 10
18
   (c) 10
28
   (d) 10
38
 
Q 18.  The mass of deuterium, 1 H
2
 that would be needed to generate 1 kWh  
  (a) 3.7 kg   (b) 3.7 g  (c) 3.7 × 10
-5
 kg  (d) 3.7 × 10
-8
 kg 
Answers 
  1.(b) 2.(c) 3.(b) 4.(d) 5.(b) 6.(d) 7.(d) 8.(c) 9.(c) 10.(b) 11.(c) 12.(a) 13.(b) 14.(b) 15.(c) 16.(c) 
  17.(b) 18.(d) 
Solutions 
1.  
  So, 3t times is equivalent to four half lives. Hence one half life is equal to 
3t
4
. 
  The given time 
11 9
t t t
22
?? is equivalent to 6 half lives 
   
2. ? = ?1 + ?2 
   
  
1
th
4
 sample remains after 2 half lives or 40 yr. 
3.  Q-value = Final binding energy Initial binding energy 
   = E2N2 + E3N3 - E1N1 
4.  Energy released = Final binding energy - initial binding energy  
   = 110 × 8.2 + 90 × 8.2 - 200 × 7.4 
   = 160 MeV 
5.  Energy released = final binding energy - initial binding energy  
   = (7.0 - 1.1)4 
   = 23.6 MeV 
6.  It means we are getting only 100 MeV of energy by the fission of one uranium nucleus. 
  Number of nuclei per second 
    
7.  When the rate production = rate of disintegration, number of nuclei or maximum. 
   ?N = A 
   
8.  See the hint of Q. No- 24 of section, objective question (single correct option) for JEE Advanced 
of chapter-33. Minimum energy required is 20.4 eV. 
   
  Substituting the value of m, we can get V. 
9.  R0 = 15 × 200 = 3000 decay/min from 200g carbon. 
  Using,  
   
  ?  n = number of half lives = 3