Modern Physics II JEE Main - Physics, Solution by DC Pandey NEET Notes | EduRev

 Page 1


Exercises 
For JEE Main 
  Subjective Questions 
  Note You can take approximations in the answers. 
  Radioactivity 
Q 1.  The disintegration rate of a certain radioactive sample at any instant is 4750 
disintegrations per minute. Five minutes later the rate becomes 2700 per minute. 
Calculate 
  (a) decay constant and   (b) half-life of the sample 
Q 2.  A radioactive sample contains l.00 × 10
15
 atoms and has an activity of 6.00 × 10
11
 Bq. 
What is its half-life? 
Q 3.  Obtain the amount of 
60
 Co necessary to provide a radioactive source of 8.0 Ci 
strength. The half-life of 
60
Co is 5.3 years? 
Q 4.  The half-life of 
238
92
U against alpha decay is 4.5 × 10
9
 year. How much disintegration 
per second occurs in 1 g of 
238
92
U ? 
Q 5.  What is the probability that a radioactive atom having a mean life of 10 days decays 
during the fifth day? 
Q 6.  In an ore containing Uranium, the ratio of 
238
Uto 
206
Pb nuclei is 3. Calculate the age of 
the ore, assuming that all the lead present in the ore is the final stable product of 
238
U. 
Take the half-life of 
238
U to be 4.5 × 10
9
 years. 
Q 7.  The half-lives of radioisotopes P
32
 and P
33
 are 14 days and 25 days respectively. 
These radioisotopes are mixed in the ratio of 4 :1 of their atoms. If the initial activity 
of the mixed sample is 3.0 m Ci, find the activity of the mixed isotopes after 60 year. 
  Nuclear Reactions 
Q 8.  Complete the following reactions. 
(a) 
226
88
Ra ? ? ? (b) 
19 19
89
OF ??  (c) 
25 25
13 12
AI Mg ??  
Q 9.  Consider two decay reactions. 
  (a) 
236 206
92 82
U Pb ?? 10 protons + 20 neutrons (b) 
236 206 4
92 82 2
U Pb 8 He ? ? ?
 
6 electrons 
  Are both the reactions possible? 
Q 10.  Obtain the binding energy of a nitrogen nucleus from the following data : 
   m H = 1.00783 u, m N = 1.00867 u, 
14
7
m( N) = 14.00307 u 
  Give your answer in units of MeV. [Remember 1 u = 931.5 Me V/c
2
 ] 
Q 11.  8 protons and 8 neutrons are separately at rest. How much energy will be released if 
we form 
16
8
O nucleus? 
  Given: Mass of 
16
8
O atom = 15.994915 u 
  Mass of neutron = 1.008665 u Mass of hydrogen atom =1.007825 u 
Q 12.  Assuming the splittng of U
235
 nucleus liberates 200 MeV energy, find 
  (a) the energy liberated in the fission of 1 kg of U
235
 and 
Page 2


Exercises 
For JEE Main 
  Subjective Questions 
  Note You can take approximations in the answers. 
  Radioactivity 
Q 1.  The disintegration rate of a certain radioactive sample at any instant is 4750 
disintegrations per minute. Five minutes later the rate becomes 2700 per minute. 
Calculate 
  (a) decay constant and   (b) half-life of the sample 
Q 2.  A radioactive sample contains l.00 × 10
15
 atoms and has an activity of 6.00 × 10
11
 Bq. 
What is its half-life? 
Q 3.  Obtain the amount of 
60
 Co necessary to provide a radioactive source of 8.0 Ci 
strength. The half-life of 
60
Co is 5.3 years? 
Q 4.  The half-life of 
238
92
U against alpha decay is 4.5 × 10
9
 year. How much disintegration 
per second occurs in 1 g of 
238
92
U ? 
Q 5.  What is the probability that a radioactive atom having a mean life of 10 days decays 
during the fifth day? 
Q 6.  In an ore containing Uranium, the ratio of 
238
Uto 
206
Pb nuclei is 3. Calculate the age of 
the ore, assuming that all the lead present in the ore is the final stable product of 
238
U. 
Take the half-life of 
238
U to be 4.5 × 10
9
 years. 
Q 7.  The half-lives of radioisotopes P
32
 and P
33
 are 14 days and 25 days respectively. 
These radioisotopes are mixed in the ratio of 4 :1 of their atoms. If the initial activity 
of the mixed sample is 3.0 m Ci, find the activity of the mixed isotopes after 60 year. 
  Nuclear Reactions 
Q 8.  Complete the following reactions. 
(a) 
226
88
Ra ? ? ? (b) 
19 19
89
OF ??  (c) 
25 25
13 12
AI Mg ??  
Q 9.  Consider two decay reactions. 
  (a) 
236 206
92 82
U Pb ?? 10 protons + 20 neutrons (b) 
236 206 4
92 82 2
U Pb 8 He ? ? ?
 
6 electrons 
  Are both the reactions possible? 
Q 10.  Obtain the binding energy of a nitrogen nucleus from the following data : 
   m H = 1.00783 u, m N = 1.00867 u, 
14
7
m( N) = 14.00307 u 
  Give your answer in units of MeV. [Remember 1 u = 931.5 Me V/c
2
 ] 
Q 11.  8 protons and 8 neutrons are separately at rest. How much energy will be released if 
we form 
16
8
O nucleus? 
  Given: Mass of 
16
8
O atom = 15.994915 u 
  Mass of neutron = 1.008665 u Mass of hydrogen atom =1.007825 u 
Q 12.  Assuming the splittng of U
235
 nucleus liberates 200 MeV energy, find 
  (a) the energy liberated in the fission of 1 kg of U
235
 and 
  (b) the mass of the coal with calorific value of 30 kJ/g which is equivalent to 1 kg of 
U
235
. 
Q 13.  
212
83
Bi decays as per following equation. 
   
212 208 4
83 82 2
Bi TI He ?? 
The kinetic energy of ?-particle emitted is 6.802 MeV. Calculate the kinetic energy of 
TI recoil atoms. 
Q 14.  In a neutron induced fission of 92U
235
 nucleus, usable energy of 185 MeV is released. 
If 92U
235 
reactor is continuously operating it at a power level of 100 MW how long 
will it take for 1 kg of uranium to be consumed in this reactor? 
Q 15.  Calculate the Q-values of the following fusion reactions : 
  (a) 
2 2 3 1
1 1 1 1
H H H H ? ? ? (b) 
2 2 3
1 1 2
H H He n ? ? ?  (c) 
2 3 4
1 1 2
H H He n ? ? ? 
  Atomic masses are 
2
1
m( H) = 2.014102u, 
3
1
m( H)
 
= 3.016049u, 
  
3
2
m( He) = 3.016029 u, 
4
2
m( He)
 
= 4.002603 u, 
1
1
m( H) = 1.007825 U 
Q 16.  Calculate the Q-value of the fusion reaction 
   4
He + 
4
He ? 
8
Be  
Is such a fusion energetically favourable?  
Atomic mass of 
8
Be is 8.0053 u and that of 
4
He is 4.0026 u. 
Solutions 
1.  (a) R = R0e
- ?t
 
 R = 2700 per minute, R0 = 4750 per minute t = 5 minute  
  Find ?. 
  (b)  
2. R = ?N 
   6 × 10
11
 =1.0 × l0
15
?
  
   
? = 6 × 10
-4
s 
    = 1155 s= 19.25 min 
3. R = ?N 
   
   = 7.14 × 10
19
 
   × 60gm = 7.11× 10
-3
gm 
4.  
    
    = 1.23 x 10
4
dps 5. = 10days  
Page 3


Exercises 
For JEE Main 
  Subjective Questions 
  Note You can take approximations in the answers. 
  Radioactivity 
Q 1.  The disintegration rate of a certain radioactive sample at any instant is 4750 
disintegrations per minute. Five minutes later the rate becomes 2700 per minute. 
Calculate 
  (a) decay constant and   (b) half-life of the sample 
Q 2.  A radioactive sample contains l.00 × 10
15
 atoms and has an activity of 6.00 × 10
11
 Bq. 
What is its half-life? 
Q 3.  Obtain the amount of 
60
 Co necessary to provide a radioactive source of 8.0 Ci 
strength. The half-life of 
60
Co is 5.3 years? 
Q 4.  The half-life of 
238
92
U against alpha decay is 4.5 × 10
9
 year. How much disintegration 
per second occurs in 1 g of 
238
92
U ? 
Q 5.  What is the probability that a radioactive atom having a mean life of 10 days decays 
during the fifth day? 
Q 6.  In an ore containing Uranium, the ratio of 
238
Uto 
206
Pb nuclei is 3. Calculate the age of 
the ore, assuming that all the lead present in the ore is the final stable product of 
238
U. 
Take the half-life of 
238
U to be 4.5 × 10
9
 years. 
Q 7.  The half-lives of radioisotopes P
32
 and P
33
 are 14 days and 25 days respectively. 
These radioisotopes are mixed in the ratio of 4 :1 of their atoms. If the initial activity 
of the mixed sample is 3.0 m Ci, find the activity of the mixed isotopes after 60 year. 
  Nuclear Reactions 
Q 8.  Complete the following reactions. 
(a) 
226
88
Ra ? ? ? (b) 
19 19
89
OF ??  (c) 
25 25
13 12
AI Mg ??  
Q 9.  Consider two decay reactions. 
  (a) 
236 206
92 82
U Pb ?? 10 protons + 20 neutrons (b) 
236 206 4
92 82 2
U Pb 8 He ? ? ?
 
6 electrons 
  Are both the reactions possible? 
Q 10.  Obtain the binding energy of a nitrogen nucleus from the following data : 
   m H = 1.00783 u, m N = 1.00867 u, 
14
7
m( N) = 14.00307 u 
  Give your answer in units of MeV. [Remember 1 u = 931.5 Me V/c
2
 ] 
Q 11.  8 protons and 8 neutrons are separately at rest. How much energy will be released if 
we form 
16
8
O nucleus? 
  Given: Mass of 
16
8
O atom = 15.994915 u 
  Mass of neutron = 1.008665 u Mass of hydrogen atom =1.007825 u 
Q 12.  Assuming the splittng of U
235
 nucleus liberates 200 MeV energy, find 
  (a) the energy liberated in the fission of 1 kg of U
235
 and 
  (b) the mass of the coal with calorific value of 30 kJ/g which is equivalent to 1 kg of 
U
235
. 
Q 13.  
212
83
Bi decays as per following equation. 
   
212 208 4
83 82 2
Bi TI He ?? 
The kinetic energy of ?-particle emitted is 6.802 MeV. Calculate the kinetic energy of 
TI recoil atoms. 
Q 14.  In a neutron induced fission of 92U
235
 nucleus, usable energy of 185 MeV is released. 
If 92U
235 
reactor is continuously operating it at a power level of 100 MW how long 
will it take for 1 kg of uranium to be consumed in this reactor? 
Q 15.  Calculate the Q-values of the following fusion reactions : 
  (a) 
2 2 3 1
1 1 1 1
H H H H ? ? ? (b) 
2 2 3
1 1 2
H H He n ? ? ?  (c) 
2 3 4
1 1 2
H H He n ? ? ? 
  Atomic masses are 
2
1
m( H) = 2.014102u, 
3
1
m( H)
 
= 3.016049u, 
  
3
2
m( He) = 3.016029 u, 
4
2
m( He)
 
= 4.002603 u, 
1
1
m( H) = 1.007825 U 
Q 16.  Calculate the Q-value of the fusion reaction 
   4
He + 
4
He ? 
8
Be  
Is such a fusion energetically favourable?  
Atomic mass of 
8
Be is 8.0053 u and that of 
4
He is 4.0026 u. 
Solutions 
1.  (a) R = R0e
- ?t
 
 R = 2700 per minute, R0 = 4750 per minute t = 5 minute  
  Find ?. 
  (b)  
2. R = ?N 
   6 × 10
11
 =1.0 × l0
15
?
  
   
? = 6 × 10
-4
s 
    = 1155 s= 19.25 min 
3. R = ?N 
   
   = 7.14 × 10
19
 
   × 60gm = 7.11× 10
-3
gm 
4.  
    
    = 1.23 x 10
4
dps 5. = 10days  
  ? ? = 0.1 day
-1  
  
Probability of decay 
    
    = 1 – e
- ?t
 = 1 - e-
0.1×5
 = 0.39  
6.  
   N0 = 3 + 1 = 4 N =3 
   
  From Eqs. (i) and (ii), we get t = 1.88 × 10
9
yr 
7.  (T= half life) 
    
  R01 + R02 = 8MCi   (is given) 
   
  From here we can find No. After t = 60 yr 
    
8.  See the answer. 
9.  (a) 82 + 10 = 92, 206 + 10 + 20 = 236  
  So this reaction is possible. 
  (b) 82 + 16 - 6 = 92, 206 + 32 = 238 
  But antineutrino is also emitted with ?
~1 
(or electron) decay. 
10.  Binding energy = ?m × 931.5 MeV 
   = (7 × 1.00783 + 7 × 1.00867-14.00307) 931.5 = 104.72 MeV 
11.  Energy released = binding energy 
   ?m
 
× 931.5MeV (8 × 1.007825 + 8 × 1.008665 - 15.994915) × 931.5 = 
127.62MeV 
12.  (a) Number of nuclei in 1 kg of U
235
 
    
  ?  Total energy released = (N × 200) MeV 
    (6.02 × 10
26
) (200) (1.6 × 10
-13
) 
   = 8.19 × 10
13
J 
  (b)   
   = 2.73 × 10
9
 gm = 2.73 × 10
6
 kg 
13.  Form momentum conservation, 
Page 4


Exercises 
For JEE Main 
  Subjective Questions 
  Note You can take approximations in the answers. 
  Radioactivity 
Q 1.  The disintegration rate of a certain radioactive sample at any instant is 4750 
disintegrations per minute. Five minutes later the rate becomes 2700 per minute. 
Calculate 
  (a) decay constant and   (b) half-life of the sample 
Q 2.  A radioactive sample contains l.00 × 10
15
 atoms and has an activity of 6.00 × 10
11
 Bq. 
What is its half-life? 
Q 3.  Obtain the amount of 
60
 Co necessary to provide a radioactive source of 8.0 Ci 
strength. The half-life of 
60
Co is 5.3 years? 
Q 4.  The half-life of 
238
92
U against alpha decay is 4.5 × 10
9
 year. How much disintegration 
per second occurs in 1 g of 
238
92
U ? 
Q 5.  What is the probability that a radioactive atom having a mean life of 10 days decays 
during the fifth day? 
Q 6.  In an ore containing Uranium, the ratio of 
238
Uto 
206
Pb nuclei is 3. Calculate the age of 
the ore, assuming that all the lead present in the ore is the final stable product of 
238
U. 
Take the half-life of 
238
U to be 4.5 × 10
9
 years. 
Q 7.  The half-lives of radioisotopes P
32
 and P
33
 are 14 days and 25 days respectively. 
These radioisotopes are mixed in the ratio of 4 :1 of their atoms. If the initial activity 
of the mixed sample is 3.0 m Ci, find the activity of the mixed isotopes after 60 year. 
  Nuclear Reactions 
Q 8.  Complete the following reactions. 
(a) 
226
88
Ra ? ? ? (b) 
19 19
89
OF ??  (c) 
25 25
13 12
AI Mg ??  
Q 9.  Consider two decay reactions. 
  (a) 
236 206
92 82
U Pb ?? 10 protons + 20 neutrons (b) 
236 206 4
92 82 2
U Pb 8 He ? ? ?
 
6 electrons 
  Are both the reactions possible? 
Q 10.  Obtain the binding energy of a nitrogen nucleus from the following data : 
   m H = 1.00783 u, m N = 1.00867 u, 
14
7
m( N) = 14.00307 u 
  Give your answer in units of MeV. [Remember 1 u = 931.5 Me V/c
2
 ] 
Q 11.  8 protons and 8 neutrons are separately at rest. How much energy will be released if 
we form 
16
8
O nucleus? 
  Given: Mass of 
16
8
O atom = 15.994915 u 
  Mass of neutron = 1.008665 u Mass of hydrogen atom =1.007825 u 
Q 12.  Assuming the splittng of U
235
 nucleus liberates 200 MeV energy, find 
  (a) the energy liberated in the fission of 1 kg of U
235
 and 
  (b) the mass of the coal with calorific value of 30 kJ/g which is equivalent to 1 kg of 
U
235
. 
Q 13.  
212
83
Bi decays as per following equation. 
   
212 208 4
83 82 2
Bi TI He ?? 
The kinetic energy of ?-particle emitted is 6.802 MeV. Calculate the kinetic energy of 
TI recoil atoms. 
Q 14.  In a neutron induced fission of 92U
235
 nucleus, usable energy of 185 MeV is released. 
If 92U
235 
reactor is continuously operating it at a power level of 100 MW how long 
will it take for 1 kg of uranium to be consumed in this reactor? 
Q 15.  Calculate the Q-values of the following fusion reactions : 
  (a) 
2 2 3 1
1 1 1 1
H H H H ? ? ? (b) 
2 2 3
1 1 2
H H He n ? ? ?  (c) 
2 3 4
1 1 2
H H He n ? ? ? 
  Atomic masses are 
2
1
m( H) = 2.014102u, 
3
1
m( H)
 
= 3.016049u, 
  
3
2
m( He) = 3.016029 u, 
4
2
m( He)
 
= 4.002603 u, 
1
1
m( H) = 1.007825 U 
Q 16.  Calculate the Q-value of the fusion reaction 
   4
He + 
4
He ? 
8
Be  
Is such a fusion energetically favourable?  
Atomic mass of 
8
Be is 8.0053 u and that of 
4
He is 4.0026 u. 
Solutions 
1.  (a) R = R0e
- ?t
 
 R = 2700 per minute, R0 = 4750 per minute t = 5 minute  
  Find ?. 
  (b)  
2. R = ?N 
   6 × 10
11
 =1.0 × l0
15
?
  
   
? = 6 × 10
-4
s 
    = 1155 s= 19.25 min 
3. R = ?N 
   
   = 7.14 × 10
19
 
   × 60gm = 7.11× 10
-3
gm 
4.  
    
    = 1.23 x 10
4
dps 5. = 10days  
  ? ? = 0.1 day
-1  
  
Probability of decay 
    
    = 1 – e
- ?t
 = 1 - e-
0.1×5
 = 0.39  
6.  
   N0 = 3 + 1 = 4 N =3 
   
  From Eqs. (i) and (ii), we get t = 1.88 × 10
9
yr 
7.  (T= half life) 
    
  R01 + R02 = 8MCi   (is given) 
   
  From here we can find No. After t = 60 yr 
    
8.  See the answer. 
9.  (a) 82 + 10 = 92, 206 + 10 + 20 = 236  
  So this reaction is possible. 
  (b) 82 + 16 - 6 = 92, 206 + 32 = 238 
  But antineutrino is also emitted with ?
~1 
(or electron) decay. 
10.  Binding energy = ?m × 931.5 MeV 
   = (7 × 1.00783 + 7 × 1.00867-14.00307) 931.5 = 104.72 MeV 
11.  Energy released = binding energy 
   ?m
 
× 931.5MeV (8 × 1.007825 + 8 × 1.008665 - 15.994915) × 931.5 = 
127.62MeV 
12.  (a) Number of nuclei in 1 kg of U
235
 
    
  ?  Total energy released = (N × 200) MeV 
    (6.02 × 10
26
) (200) (1.6 × 10
-13
) 
   = 8.19 × 10
13
J 
  (b)   
   = 2.73 × 10
9
 gm = 2.73 × 10
6
 kg 
13.  Form momentum conservation, 
   
14.  Number of nuclei in 1 kg of uranium, 
    
  Now, (6.02 × 10
26
) (185 × 1.6 × 10
-13
) 
   = (100 × l0
6
)t t = 7.58 × 10
5
 s 
    
   = 8.78days 
15.  Q-value = ( ?m)
 
(931.5) MeV 
  (a) Q-value = (2 × 2.014102 - 3.016049 - 1.007825) × 931.5 = 4.05 MeV 
  Similarly Q-value of other parts can also be obtained. 
16.  Q-value = ( ?m) × 931.5 MeV 
   = (2 × 4.0026 - 8.0053) × 931.5 = -0.0931 MeV = - 93.1 keV 
 
Objective Questions 
  Single Correct Option 
Q 1.  During a beta decay 
  (a) an atomic electron is ejected  
  (b) an electron present inside the nucleus is ejected 
  (c) a neutron in the nucleus decays emitting an electron 
  (d) a part of the binding energy is converted into electron 
Q 2.  In the nucleus of helium if Fl is the net force between two protons, F2 is the net force 
between two neutrons and F3 is the net force between a proton and a neutron. Then 
  (a) F1 = F2 = F3  (b) F1 > F2 > F3 (c) F2 > F3 > F1  (d) F2 = F3 > F1 
Q 3.  What are the respective number of ? and ?-particles emitted in the following 
radioactive decay? 
   
200 168
90 80
XY ? 
  (a) 6 and 8   (b) 6 and 6   (c) 8 and 8   (d) 8 and 6 
Q 4.  If an atom of 
235
92
U ,
 
after absorbing a slow neutron, undergoes fission to form an atom 
of 
138
54
Xe
 
and an atom of 
94
38
Sr , the other particles produced are 
  (a) one proton and two neutrons   (b) three neutrons 
  (c) two neutrons     (d) one proton and one neutron 
Q 5.  Nucleus A is converted into C through the following reactions 
   A ? B + ? 
   B ? C + 2 ? 
  then 
Page 5


Exercises 
For JEE Main 
  Subjective Questions 
  Note You can take approximations in the answers. 
  Radioactivity 
Q 1.  The disintegration rate of a certain radioactive sample at any instant is 4750 
disintegrations per minute. Five minutes later the rate becomes 2700 per minute. 
Calculate 
  (a) decay constant and   (b) half-life of the sample 
Q 2.  A radioactive sample contains l.00 × 10
15
 atoms and has an activity of 6.00 × 10
11
 Bq. 
What is its half-life? 
Q 3.  Obtain the amount of 
60
 Co necessary to provide a radioactive source of 8.0 Ci 
strength. The half-life of 
60
Co is 5.3 years? 
Q 4.  The half-life of 
238
92
U against alpha decay is 4.5 × 10
9
 year. How much disintegration 
per second occurs in 1 g of 
238
92
U ? 
Q 5.  What is the probability that a radioactive atom having a mean life of 10 days decays 
during the fifth day? 
Q 6.  In an ore containing Uranium, the ratio of 
238
Uto 
206
Pb nuclei is 3. Calculate the age of 
the ore, assuming that all the lead present in the ore is the final stable product of 
238
U. 
Take the half-life of 
238
U to be 4.5 × 10
9
 years. 
Q 7.  The half-lives of radioisotopes P
32
 and P
33
 are 14 days and 25 days respectively. 
These radioisotopes are mixed in the ratio of 4 :1 of their atoms. If the initial activity 
of the mixed sample is 3.0 m Ci, find the activity of the mixed isotopes after 60 year. 
  Nuclear Reactions 
Q 8.  Complete the following reactions. 
(a) 
226
88
Ra ? ? ? (b) 
19 19
89
OF ??  (c) 
25 25
13 12
AI Mg ??  
Q 9.  Consider two decay reactions. 
  (a) 
236 206
92 82
U Pb ?? 10 protons + 20 neutrons (b) 
236 206 4
92 82 2
U Pb 8 He ? ? ?
 
6 electrons 
  Are both the reactions possible? 
Q 10.  Obtain the binding energy of a nitrogen nucleus from the following data : 
   m H = 1.00783 u, m N = 1.00867 u, 
14
7
m( N) = 14.00307 u 
  Give your answer in units of MeV. [Remember 1 u = 931.5 Me V/c
2
 ] 
Q 11.  8 protons and 8 neutrons are separately at rest. How much energy will be released if 
we form 
16
8
O nucleus? 
  Given: Mass of 
16
8
O atom = 15.994915 u 
  Mass of neutron = 1.008665 u Mass of hydrogen atom =1.007825 u 
Q 12.  Assuming the splittng of U
235
 nucleus liberates 200 MeV energy, find 
  (a) the energy liberated in the fission of 1 kg of U
235
 and 
  (b) the mass of the coal with calorific value of 30 kJ/g which is equivalent to 1 kg of 
U
235
. 
Q 13.  
212
83
Bi decays as per following equation. 
   
212 208 4
83 82 2
Bi TI He ?? 
The kinetic energy of ?-particle emitted is 6.802 MeV. Calculate the kinetic energy of 
TI recoil atoms. 
Q 14.  In a neutron induced fission of 92U
235
 nucleus, usable energy of 185 MeV is released. 
If 92U
235 
reactor is continuously operating it at a power level of 100 MW how long 
will it take for 1 kg of uranium to be consumed in this reactor? 
Q 15.  Calculate the Q-values of the following fusion reactions : 
  (a) 
2 2 3 1
1 1 1 1
H H H H ? ? ? (b) 
2 2 3
1 1 2
H H He n ? ? ?  (c) 
2 3 4
1 1 2
H H He n ? ? ? 
  Atomic masses are 
2
1
m( H) = 2.014102u, 
3
1
m( H)
 
= 3.016049u, 
  
3
2
m( He) = 3.016029 u, 
4
2
m( He)
 
= 4.002603 u, 
1
1
m( H) = 1.007825 U 
Q 16.  Calculate the Q-value of the fusion reaction 
   4
He + 
4
He ? 
8
Be  
Is such a fusion energetically favourable?  
Atomic mass of 
8
Be is 8.0053 u and that of 
4
He is 4.0026 u. 
Solutions 
1.  (a) R = R0e
- ?t
 
 R = 2700 per minute, R0 = 4750 per minute t = 5 minute  
  Find ?. 
  (b)  
2. R = ?N 
   6 × 10
11
 =1.0 × l0
15
?
  
   
? = 6 × 10
-4
s 
    = 1155 s= 19.25 min 
3. R = ?N 
   
   = 7.14 × 10
19
 
   × 60gm = 7.11× 10
-3
gm 
4.  
    
    = 1.23 x 10
4
dps 5. = 10days  
  ? ? = 0.1 day
-1  
  
Probability of decay 
    
    = 1 – e
- ?t
 = 1 - e-
0.1×5
 = 0.39  
6.  
   N0 = 3 + 1 = 4 N =3 
   
  From Eqs. (i) and (ii), we get t = 1.88 × 10
9
yr 
7.  (T= half life) 
    
  R01 + R02 = 8MCi   (is given) 
   
  From here we can find No. After t = 60 yr 
    
8.  See the answer. 
9.  (a) 82 + 10 = 92, 206 + 10 + 20 = 236  
  So this reaction is possible. 
  (b) 82 + 16 - 6 = 92, 206 + 32 = 238 
  But antineutrino is also emitted with ?
~1 
(or electron) decay. 
10.  Binding energy = ?m × 931.5 MeV 
   = (7 × 1.00783 + 7 × 1.00867-14.00307) 931.5 = 104.72 MeV 
11.  Energy released = binding energy 
   ?m
 
× 931.5MeV (8 × 1.007825 + 8 × 1.008665 - 15.994915) × 931.5 = 
127.62MeV 
12.  (a) Number of nuclei in 1 kg of U
235
 
    
  ?  Total energy released = (N × 200) MeV 
    (6.02 × 10
26
) (200) (1.6 × 10
-13
) 
   = 8.19 × 10
13
J 
  (b)   
   = 2.73 × 10
9
 gm = 2.73 × 10
6
 kg 
13.  Form momentum conservation, 
   
14.  Number of nuclei in 1 kg of uranium, 
    
  Now, (6.02 × 10
26
) (185 × 1.6 × 10
-13
) 
   = (100 × l0
6
)t t = 7.58 × 10
5
 s 
    
   = 8.78days 
15.  Q-value = ( ?m)
 
(931.5) MeV 
  (a) Q-value = (2 × 2.014102 - 3.016049 - 1.007825) × 931.5 = 4.05 MeV 
  Similarly Q-value of other parts can also be obtained. 
16.  Q-value = ( ?m) × 931.5 MeV 
   = (2 × 4.0026 - 8.0053) × 931.5 = -0.0931 MeV = - 93.1 keV 
 
Objective Questions 
  Single Correct Option 
Q 1.  During a beta decay 
  (a) an atomic electron is ejected  
  (b) an electron present inside the nucleus is ejected 
  (c) a neutron in the nucleus decays emitting an electron 
  (d) a part of the binding energy is converted into electron 
Q 2.  In the nucleus of helium if Fl is the net force between two protons, F2 is the net force 
between two neutrons and F3 is the net force between a proton and a neutron. Then 
  (a) F1 = F2 = F3  (b) F1 > F2 > F3 (c) F2 > F3 > F1  (d) F2 = F3 > F1 
Q 3.  What are the respective number of ? and ?-particles emitted in the following 
radioactive decay? 
   
200 168
90 80
XY ? 
  (a) 6 and 8   (b) 6 and 6   (c) 8 and 8   (d) 8 and 6 
Q 4.  If an atom of 
235
92
U ,
 
after absorbing a slow neutron, undergoes fission to form an atom 
of 
138
54
Xe
 
and an atom of 
94
38
Sr , the other particles produced are 
  (a) one proton and two neutrons   (b) three neutrons 
  (c) two neutrons     (d) one proton and one neutron 
Q 5.  Nucleus A is converted into C through the following reactions 
   A ? B + ? 
   B ? C + 2 ? 
  then 
  (a) A and B are isotopes    (b) A and C are isobars 
  (c) A and B are isobars    (d) A and C are isotopes 
Q 6.  The binding energy of ?-particle is 
  (if mp =1.00785u, mn = 1.00866 u and m ? = 4.00274u)  
  (a) 56.42 MeV  (b) 2.821 MeV  (c) 28.21 MeV  (d) 32.4 MeV 
Q 7.  7/8 th of the active nuclei present in a radioactive sample has decayed in 8 s. The half 
life of the  sample is  
  (a) 2 s    (b) 1 s    (c) 7 s    (d) 
8
s
3
 
Q 8.  A radioactive element disintegrates for a time interval equal to its mean life. The 
fraction that has disintegrated is 
 (a) 
1
e
    (b) 
1
1
e
?   (c) 
0.693
e
   (d) 
1
0.693 1
e
??
?
??
??
 
Q 9.  Starting with a sample of pure 
66
3
Cu,
4
??
??
??
of it decays into Zn in 15 minutes. The 
corresponding half-life is  
  (a) 5 minutes   (b) 7.5 minutes (c) 10 minutes  (d) 3.5 minutes 
Q 10.  A sample of radioactive substance loses half of its activity in 4 days. The time in 
which its activity is reduced to 5% is 
  (a) 12 days  (b) 8.3 days  (c) 17.3 days   (d) None of these 
Q 11.  On bombardment of U
235
 by slow neutrons, 200 MeV energy is released. If the power 
output of atomic reactor is 1.6 MW, then the rate of fission will be 
  (a) 5 × 10
16
 per second    (b) 10 × 10
16
 per second 
  (c) 15 × 10
16
 per second    (d) 20 × 10
16
 per second 
Q 12.  Atomic masses of two heavy atoms are A 1 and A 2- Ratio of their respective nuclear 
densitities will be approximately 
 (a) 
1
2
A
A
   (b) 
1/3
1
2
A
A
??
??
??
   (c) 
1/3
2
1
A
A
??
??
??
   (d) 1 
Q 13.  A radioactive element is disintegrating having half-life 6.93 s. The fractional change 
in number of nuclei of the radioactive element during 10 s is 
  (a) 0.37   (b) 0.63   (c) 0.25   (d) 0.50 
Q 14.  The activity of a radioactive sample goes down to about 6% in a time of 2 hour. The 
half-life of the sample in minute is about 
  (a) 30    (b) 15    (c) 60    (d) 120 
Q 15.  What
 
is the probability of a radioactive nucleus to survive one mean life? 
 (a) 
1
e
    (b) 
1
e1 ?
   (c) 
1
1
e
?   (d) 
1
1
e
? 
Answers