JEE Physics Nuclei MCQs Set 23

Download JEE MCQs for JEE Physics: Nuclei

Access targeted multiple-choice questions for Nuclei designed to align with the latest JEE academic syllabus for JEE Physics. These objective practice sets help students evaluate their conceptual understanding and improve exam readiness.

Chapter-wise Objective Questions: Nuclei

View or download the dedicated Nuclei MCQ resource below. Practicing these 50 objective questions regularly builds familiarity with standard exam patterns and helps secure higher marks in final Physics evaluations.

Multiple Choice Questions

Question 1: The stable nucleus whose radius is one-third that of \( {}^{189}_{76}\mathrm{Os} \) is:
(a) \( {}^{4}_{2}\mathrm{He} \)
(b) \( {}^{10}_{5}\mathrm{B} \)
(c) \( {}^{7}_{3}\mathrm{Li} \)
(d) \( {}^{12}_{6}\mathrm{C} \)
Show Answer & Explanation

Answer: (c) \( {}^{7}_{3}\mathrm{Li} \)

Explanation:
1. Radius \( R=R_0A^{1/3} \), so \( A=189\times\left(\tfrac13\right)^3=7 \).
2. The nucleus with mass number 7 in the options is lithium-7.

Teacher's Note:
1. N
2. u
3. c
4. l
5. e
6. a
7. r
8.
9. r
10. a
11. d
12. i
13. u
14. s
15.
16. s
17. c
18. a
19. l
20. e
21. s
22.
23. a
24. s
25.
26. t
27. h
28. e
29.
30. c
31. u
32. b
33. e
34.
35. r
36. o
37. o
38. t
39.
40. o
41. f
42.
43. A
44. ,
45.
46. s
47. o
48.
49. a
50.
51. o
52. n
53. e
54. -
55. t
56. h
57. i
58. r
59. d
60.
61. r
62. a
63. d
64. i
65. u
66. s
67.
68. m
69. e
70. a
71. n
72. s
73.
74. o
75. n
76. e
77.
78. t
79. w
80. e
81. n
82. t
83. y
84. -
85. s
86. e
87. v
88. e
89. n
90. t
91. h
92.
93. o
94. f
95.
96. t
97. h
98. e
99.
100. n
101. u
102. c
103. l
104. e
105. o
106. n
107. s
108. .
109.
110. 1
111. 8
112. 9
113. /
114. 2
115. 7
116.
117. =
118.
119. 7
120. .

Question 2: Two lithium-6 nuclei in a lithium vapour at room temperature do not combine to form a carbon-12 nucleus because:
(a) a lithium nucleus is more tightly bound than a carbon nucleus
(b) carbon nucleus is an unstable particle
(c) it is not energetically favourable
(d) Coulomb repulsion does not allow the nuclei to come very close
Show Answer & Explanation

Answer: (d) Coulomb repulsion does not allow the nuclei to come very close

Explanation:
1. Fusion needs the nuclei to come within about 1 fm against their electrostatic repulsion.
2. At room temperature their thermal kinetic energy is far too small for that.

Teacher's Note:
1. F
2. u
3. s
4. i
5. o
6. n
7.
8. i
9. s
10.
11. e
12. n
13. e
14. r
15. g
16. e
17. t
18. i
19. c
20. a
21. l
22. l
23. y
24.
25. f
26. a
27. v
28. o
29. u
30. r
31. a
32. b
33. l
34. e
35.
36. h
37. e
38. r
39. e
40.
41. (
42. c
43. a
44. r
45. b
46. o
47. n
48. -
49. 1
50. 2
51.
52. i
53. s
54.
55. m
56. o
57. r
58. e
59.
60. t
61. i
62. g
63. h
64. t
65. l
66. y
67.
68. b
69. o
70. u
71. n
72. d
73.
74. p
75. e
76. r
77.
78. n
79. u
80. c
81. l
82. e
83. o
84. n
85. )
86. ,
87.
88. b
89. u
90. t
91.
92. t
93. h
94. e
95.
96. C
97. o
98. u
99. l
100. o
101. m
102. b
103.
104. b
105. a
106. r
107. r
108. i
109. e
110. r
111.
112. p
113. r
114. e
115. v
116. e
117. n
118. t
119. s
120.
121. i
122. t
123.
124. a
125. t
126.
127. l
128. o
129. w
130.
131. t
132. e
133. m
134. p
135. e
136. r
137. a
138. t
139. u
140. r
141. e
142. .

Question 3: The half-life of a radioactive substance A is 4 days. The probability that a nucleus will decay in two half-lives is:
(a) 3/4
(b) 1/4
(c) 1/2
(d) 1
Show Answer & Explanation

Answer: (a) 3/4

Explanation:
1. After two half-lives the fraction left is 1/4, so the fraction decayed is 3/4.
2. The probability of one nucleus decaying in that time equals this fraction: 3/4.

Teacher's Note:
1. D
2. e
3. c
4. a
5. y
6.
7. p
8. r
9. o
10. b
11. a
12. b
13. i
14. l
15. i
16. t
17. y
18.
19. o
20. v
21. e
22. r
23.
24. a
25.
26. t
27. i
28. m
29. e
30.
31. e
32. q
33. u
34. a
35. l
36. s
37.
38. t
39. h
40. e
41.
42. f
43. r
44. a
45. c
46. t
47. i
48. o
49. n
50.
51. o
52. f
53.
54. n
55. u
56. c
57. l
58. e
59. i
60.
61. e
62. x
63. p
64. e
65. c
66. t
67. e
68. d
69.
70. t
71. o
72.
73. d
74. e
75. c
76. a
77. y
78.
79. i
80. n
81.
82. i
83. t
84. .

Question 4: Two radioactive sources A and B initially contain equal numbers of atoms. A has half-life 1 hour and B has half-life 2 hours. At the end of 2 hours, the ratio of the rates of disintegration of A to that of B is:
(a) 1 : 2
(b) 1 : 1
(c) 2 : 1
(d) 1 : 4
Show Answer & Explanation

Answer: (b) 1 : 1

Explanation:
1. After 2 h, \( N_A=N_0/4 \) and \( N_B=N_0/2 \).
2. Rate \( =\lambda N \): \( \frac{R_A}{R_B}=\frac{\lambda_AN_A}{\lambda_BN_B}=\frac{2\lambda_B\cdot N_0/4}{\lambda_B\cdot N_0/2}=1 \).

Teacher's Note:
1. A
2.
3. s
4. h
5. o
6. r
7. t
8. e
9. r
10.
11. h
12. a
13. l
14. f
15. -
16. l
17. i
18. f
19. e
20.
21. m
22. e
23. a
24. n
25. s
26.
27. a
28.
29. h
30. i
31. g
32. h
33. e
34. r
35.
36. d
37. e
38. c
39. a
40. y
41.
42. c
43. o
44. n
45. s
46. t
47. a
48. n
49. t
50.
51. b
52. u
53. t
54.
55. a
56. l
57. s
58. o
59.
60. f
61. e
62. w
63. e
64. r
65.
66. r
67. e
68. m
69. a
70. i
71. n
72. i
73. n
74. g
75.
76. n
77. u
78. c
79. l
80. e
81. i
82. ;
83.
84. h
85. e
86. r
87. e
88.
89. t
90. h
91. e
92.
93. t
94. w
95. o
96.
97. e
98. f
99. f
100. e
101. c
102. t
103. s
104.
105. c
106. a
107. n
108. c
109. e
110. l
111. .

Question 5: As the mass number A increases, the binding energy per nucleon of a nucleus:
(a) increases
(b) decreases
(c) varies in a way that depends on the actual value of A
(d) remains the same
Show Answer & Explanation

Answer: (c) varies in a way that depends on the actual value of A

Explanation:
1. The curve rises steeply for light nuclei, reaches a broad maximum near iron (A about 56, about 8.8 MeV) and then decreases slowly for heavy nuclei.
2. So no single statement holds for all A; the behaviour depends on the value of A.

Teacher's Note:
1. F
2. u
3. s
4. i
5. o
6. n
7.
8. o
9. f
10.
11. l
12. i
13. g
14. h
15. t
16.
17. n
18. u
19. c
20. l
21. e
22. i
23.
24. a
25. n
26. d
27.
28. f
29. i
30. s
31. s
32. i
33. o
34. n
35.
36. o
37. f
38.
39. h
40. e
41. a
42. v
43. y
44.
45. n
46. u
47. c
48. l
49. e
50. i
51.
52. b
53. o
54. t
55. h
56.
57. r
58. e
59. l
60. e
61. a
62. s
63. e
64.
65. e
66. n
67. e
68. r
69. g
70. y
71.
72. b
73. e
74. c
75. a
76. u
77. s
78. e
79.
80. b
81. o
82. t
83. h
84.
85. m
86. o
87. v
88. e
89.
90. t
91. o
92. w
93. a
94. r
95. d
96. s
97.
98. t
99. h
100. e
101.
102. p
103. e
104. a
105. k
106.
107. o
108. f
109.
110. t
111. h
112. i
113. s
114.
115. c
116. u
117. r
118. v
119. e
120. .

Question 6: A neutral pion at rest decays into two photons of equal energy. If the wavelength of each photon is \( 1.8\times10^{-n} \) m (the mass of the pion is 135 MeV/\( c^2 \), \( hc=1240\ \mathrm{MeV\,fm} \)), the value of n/2 is:
(a) 8
(b) 6
(c) 9
(d) 7
Show Answer & Explanation

Answer: (d) 7

Explanation:
1. Each photon has energy \( 135/2=67.5 \) MeV.
2. \( \lambda=\frac{hc}{E}=\frac{1240}{67.5}=18.4\ \mathrm{fm}=1.8\times10^{-14}\ \mathrm{m} \), so n = 14 and n/2 = 7.

Teacher's Note:
1. M
2. o
3. m
4. e
5. n
6. t
7. u
8. m
9.
10. c
11. o
12. n
13. s
14. e
15. r
16. v
17. a
18. t
19. i
20. o
21. n
22.
23. r
24. e
25. q
26. u
27. i
28. r
29. e
30. s
31.
32. e
33. q
34. u
35. a
36. l
37.
38. a
39. n
40. d
41.
42. o
43. p
44. p
45. o
46. s
47. i
48. t
49. e
50.
51. p
52. h
53. o
54. t
55. o
56. n
57.
58. e
59. n
60. e
61. r
62. g
63. i
64. e
65. s
66. ,
67.
68. s
69. o
70.
71. e
72. a
73. c
74. h
75.
76. t
77. a
78. k
79. e
80. s
81.
82. h
83. a
84. l
85. f
86.
87. t
88. h
89. e
90.
91. r
92. e
93. s
94. t
95.
96. e
97. n
98. e
99. r
100. g
101. y
102. .

Question 7: A free neutron decays into a proton, an electron and:
(a) an antineutrino
(b) a neutrino
(c) an alpha particle
(d) a beta particle
Show Answer & Explanation

Answer: (a) an antineutrino

Explanation:
1. Lepton number must be conserved: the electron has lepton number +1, so the third particle must have lepton number -1.
2. That is the antineutrino: \( n\to p+e^-+\bar\nu \).

Teacher's Note:
1. N
2. e
3. u
4. t
5. r
6. i
7. n
8. o
9. s
10.
11. a
12. c
13. c
14. o
15. m
16. p
17. a
18. n
19. y
20.
21. p
22. o
23. s
24. i
25. t
26. i
27. v
28. e
29.
30. b
31. e
32. t
33. a
34.
35. d
36. e
37. c
38. a
39. y
40.
41. a
42. n
43. d
44.
45. e
46. l
47. e
48. c
49. t
50. r
51. o
52. n
53.
54. c
55. a
56. p
57. t
58. u
59. r
60. e
61. ;
62.
63. a
64. n
65. t
66. i
67. n
68. e
69. u
70. t
71. r
72. i
73. n
74. o
75. s
76.
77. a
78. c
79. c
80. o
81. m
82. p
83. a
84. n
85. y
86.
87. n
88. e
89. g
90. a
91. t
92. i
93. v
94. e
95.
96. b
97. e
98. t
99. a
100.
101. d
102. e
103. c
104. a
105. y
106. .

Question 8: The half-life of \( {}^{131}_{53}\mathrm{I} \) is 8 days. Given a sample of iodine-131 at time t = 0, we can assert that:
(a) No nucleus will decay before t = 4 days
(b) A given nucleus may decay at any time after t = 0
(c) No nucleus will decay before t = 8 days
(d) All nuclei will decay before t = 16 days
Show Answer & Explanation

Answer: (b) A given nucleus may decay at any time after t = 0

Explanation:
1. Radioactive decay is a random process: each nucleus has some probability of decaying in any interval.
2. So there is no time before which none decays and no time by which all must have decayed.

Teacher's Note:
1. H
2. a
3. l
4. f
5. -
6. l
7. i
8. f
9. e
10.
11. i
12. s
13.
14. a
15.
16. s
17. t
18. a
19. t
20. i
21. s
22. t
23. i
24. c
25. a
26. l
27.
28. p
29. r
30. o
31. p
32. e
33. r
34. t
35. y
36.
37. o
38. f
39.
40. a
41.
42. l
43. a
44. r
45. g
46. e
47.
48. s
49. a
50. m
51. p
52. l
53. e
54.
55. a
56. n
57. d
58.
59. s
60. a
61. y
62. s
63.
64. n
65. o
66. t
67. h
68. i
69. n
70. g
71.
72. c
73. e
74. r
75. t
76. a
77. i
78. n
79.
80. a
81. b
82. o
83. u
84. t
85.
86. a
87. n
88.
89. i
90. n
91. d
92. i
93. v
94. i
95. d
96. u
97. a
98. l
99.
100. n
101. u
102. c
103. l
104. e
105. u
106. s
107. .

Question 9: The half-life of \( {}^{215}_{85}\mathrm{At} \) is 100 microseconds. The time taken for its radioactivity to decay to 1/16 of the initial value is:
(a) \( 6.3\ \mu\mathrm{s} \)
(b) \( 40\ \mu\mathrm{s} \)
(c) \( 400\ \mu\mathrm{s} \)
(d) \( 300\ \mu\mathrm{s} \)
Show Answer & Explanation

Answer: (c) \( 400\ \mu\mathrm{s} \)

Explanation:
1. \( 1/16=(1/2)^4 \), so 4 half-lives are needed.
2. \( 4\times100=400\ \mu s \).

Teacher's Note:
1. R
2. e
3. d
4. u
5. c
6. e
7.
8. t
9. h
10. e
11.
12. f
13. r
14. a
15. c
16. t
17. i
18. o
19. n
20.
21. t
22. o
23.
24. a
25.
26. p
27. o
28. w
29. e
30. r
31.
32. o
33. f
34.
35. 1
36. /
37. 2
38.
39. t
40. o
41.
42. c
43. o
44. u
45. n
46. t
47.
48. h
49. a
50. l
51. f
52. -
53. l
54. i
55. v
56. e
57. s
58. .

Question 10: A radioactive sample S1 having an activity of 5 microcurie has twice the number of nuclei as another sample S2 which has an activity of 10 microcurie. The half-lives of S1 and S2 can be:
(a) 20 years and 10 years, respectively
(b) 10 years each
(c) 5 years each
(d) 20 years and 5 years, respectively
Show Answer & Explanation

Answer: (d) 20 years and 5 years, respectively

Explanation:
1. \( A=\lambda N \): \( \lambda_1N_1=5 \), \( \lambda_2N_2=10 \), \( N_1=2N_2 \).
2. \( \frac{\lambda_1}{\lambda_2}=\frac{5/N_1}{10/N_2}=\frac14 \), so \( T_1=4T_2 \).
3. 20 years and 5 years fit.

Teacher's Note:
1. H
2. a
3. l
4. f
5. -
6. l
7. i
8. f
9. e
10.
11. i
12. s
13.
14. i
15. n
16. v
17. e
18. r
19. s
20. e
21. l
22. y
23.
24. p
25. r
26. o
27. p
28. o
29. r
30. t
31. i
32. o
33. n
34. a
35. l
36.
37. t
38. o
39.
40. t
41. h
42. e
43.
44. d
45. e
46. c
47. a
48. y
49.
50. c
51. o
52. n
53. s
54. t
55. a
56. n
57. t
58. ,
59.
60. w
61. h
62. i
63. c
64. h
65.
66. i
67. s
68.
69. t
70. h
71. e
72.
73. a
74. c
75. t
76. i
77. v
78. i
79. t
80. y
81.
82. p
83. e
84. r
85.
86. n
87. u
88. c
89. l
90. e
91. u
92. s
93. .

Question 11: Nuclei X decay into nuclei Y by emitting alpha particles. The alpha particles have energies of only 1 MeV and 1.4 MeV. Neglecting the recoil of Y, the energy of the gamma photon emitted will be:
(a) 0.4 MeV
(b) 0.8 MeV
(c) 1.4 MeV
(d) 1 MeV
Show Answer & Explanation

Answer: (a) 0.4 MeV

Explanation:
1. Two alpha groups mean Y is left either in a lower state (alpha of 1.4 MeV) or in an excited state (alpha of 1 MeV).
2. The excited state decays by a gamma photon whose energy is the difference: \( 1.4-1.0=0.4 \) MeV.

Teacher's Note:
1. T
2. h
3. e
4.
5. g
6. a
7. m
8. m
9. a
10.
11. e
12. n
13. e
14. r
15. g
16. y
17.
18. e
19. q
20. u
21. a
22. l
23. s
24.
25. t
26. h
27. e
28.
29. e
30. n
31. e
32. r
33. g
34. y
35.
36. g
37. a
38. p
39.
40. b
41. e
42. t
43. w
44. e
45. e
46. n
47.
48. t
49. h
50. e
51.
52. t
53. w
54. o
55.
56. l
57. e
58. v
59. e
60. l
61. s
62.
63. o
64. f
65.
66. t
67. h
68. e
69.
70. d
71. a
72. u
73. g
74. h
75. t
76. e
77. r
78.
79. n
80. u
81. c
82. l
83. e
84. u
85. s
86. ,
87.
88. w
89. h
90. i
91. c
92. h
93.
94. i
95. s
96.
97. t
98. h
99. e
100.
101. d
102. i
103. f
104. f
105. e
106. r
107. e
108. n
109. c
110. e
111.
112. o
113. f
114.
115. t
116. h
117. e
118.
119. t
120. w
121. o
122.
123. a
124. l
125. p
126. h
127. a
128.
129. e
130. n
131. e
132. r
133. g
134. i
135. e
136. s
137. .

Question 12: Consider the nuclear decay \( {}^{236}_{92}U\to{}^{232}_{90}Th+X \) where the uranium nucleus is initially at rest. Which statement is true concerning the final nuclei?
(a) They have equal kinetic energies, but the thorium nucleus has much more momentum
(b) They have momenta of equal magnitude, but X has much more kinetic energy
(c) They have equal kinetic energies and momenta of equal magnitude
(d) They have momenta of equal magnitude, but the thorium nucleus has much more kinetic energy
Show Answer & Explanation

Answer: (b) They have momenta of equal magnitude, but X has much more kinetic energy

Explanation:
1. Momentum conservation from rest: \( p_X=p_{Th} \).
2. \( K=p^2/2m \), so the lighter X has the greater kinetic energy.

Teacher's Note:
1. F
2. o
3. r
4.
5. e
6. q
7. u
8. a
9. l
10.
11. m
12. o
13. m
14. e
15. n
16. t
17. a
18.
19. k
20. i
21. n
22. e
23. t
24. i
25. c
26.
27. e
28. n
29. e
30. r
31. g
32. y
33.
34. i
35. s
36.
37. i
38. n
39. v
40. e
41. r
42. s
43. e
44. l
45. y
46.
47. p
48. r
49. o
50. p
51. o
52. r
53. t
54. i
55. o
56. n
57. a
58. l
59.
60. t
61. o
62.
63. m
64. a
65. s
66. s
67. .

Question 13: A sample has two isotopes, A-150 of mass 50 g and a stable B of mass 30 g. A decays to A' (mass number 146) by emitting alpha particles, which escape; the half-life of A is 2 h. The mass of the total sample after 4 hours is nearly \( 4n\times10^{-n} \) kg. The value of n is:
(a) 3
(b) 1
(c) 2
(d) 4
Show Answer & Explanation

Answer: (c) 2

Explanation:
1. After 4 h = 2 half-lives, A left \( =50/4=12.5 \) g; decayed \( =37.5 \) g.
2. Mass of A' formed \( =37.5\times\frac{146}{150}=36.5 \) g.
3. Total \( =12.5+36.5+30=79 \) g \( =0.079 \) kg \( \approx4n\times10^{-n} \) with n = 2 (\( 8\times10^{-2} \)).

Teacher's Note:
1. T
2. h
3. e
4.
5. e
6. m
7. i
8. t
9. t
10. e
11. d
12.
13. a
14. l
15. p
16. h
17. a
18.
19. p
20. a
21. r
22. t
23. i
24. c
25. l
26. e
27. s
28.
29. e
30. s
31. c
32. a
33. p
34. e
35. ,
36.
37. s
38. o
39.
40. o
41. n
42. l
43. y
44.
45. t
46. h
47. e
48. i
49. r
50.
51. m
52. a
53. s
54. s
55.
56. i
57. s
58.
59. l
60. o
61. s
62. t
63.
64. f
65. r
66. o
67. m
68.
69. t
70. h
71. e
72.
73. s
74. a
75. m
76. p
77. l
78. e
79. .

Question 14: In the options below, E denotes the rest mass energy of a nucleus and n a neutron. For the fission \( {}^{236}U\to{}^{137}I+{}^{97}Y+n+n \) the correct option is:
(a) \( E({}^{236}_{92}U)(b) \( E({}^{236}_{92}U)=E({}^{137}_{53}I)+E({}^{97}_{39}Y)+2E(n) \)
(c) \( E({}^{236}_{92}U)(d) \( E({}^{236}_{92}U)>E({}^{137}_{53}I)+E({}^{97}_{39}Y)+2E(n) \)
Show Answer & Explanation

Answer: (d) \( E({}^{236}_{92}U)>E({}^{137}_{53}I)+E({}^{97}_{39}Y)+2E(n) \)

Explanation:
1. Fission is exothermic: the energy released comes from a decrease in rest mass.
2. So the rest energy of the uranium nucleus is greater than the total rest energy of the products.

Teacher's Note:
1. W
2. h
3. e
4. n
5. e
6. v
7. e
8. r
9.
10. a
11.
12. r
13. e
14. a
15. c
16. t
17. i
18. o
19. n
20.
21. r
22. e
23. l
24. e
25. a
26. s
27. e
28. s
29.
30. e
31. n
32. e
33. r
34. g
35. y
36. ,
37.
38. t
39. h
40. e
41.
42. p
43. r
44. o
45. d
46. u
47. c
48. t
49. s
50.
51. h
52. a
53. v
54. e
55.
56. l
57. e
58. s
59. s
60.
61. r
62. e
63. s
64. t
65.
66. e
67. n
68. e
69. r
70. g
71. y
72.
73. t
74. h
75. a
76. n
77.
78. t
79. h
80. e
81.
82. r
83. e
84. a
85. c
86. t
87. a
88. n
89. t
90. s
91. .

Question 15: Fusion reaction is possible at high temperature because:
(a) kinetic energy is high enough to overcome the repulsion between nuclei
(b) atoms are ionised at high temperature
(c) molecules break up at high temperature
(d) nuclei break up at high temperature
Show Answer & Explanation

Answer: (a) kinetic energy is high enough to overcome the repulsion between nuclei

Explanation:
1. Two positively charged nuclei repel each other strongly; they must approach to within the range of the nuclear force.
2. At very high temperature their thermal kinetic energy is large enough to overcome the Coulomb barrier.

Teacher's Note:
1. T
2. h
3. i
4. s
5.
6. i
7. s
8.
9. w
10. h
11. y
12.
13. f
14. u
15. s
16. i
17. o
18. n
19.
20. r
21. e
22. q
23. u
24. i
25. r
26. e
27. s
28.
29. t
30. e
31. m
32. p
33. e
34. r
35. a
36. t
37. u
38. r
39. e
40. s
41.
42. o
43. f
44.
45. m
46. i
47. l
48. l
49. i
50. o
51. n
52. s
53.
54. o
55. f
56.
57. k
58. e
59. l
60. v
61. i
62. n
63. ,
64.
65. a
66. s
67.
68. i
69. n
70.
71. s
72. t
73. a
74. r
75. s
76. .

Question 16: In a fission reaction \( {}^{236}_{92}\mathrm{U}\to{}^{117}X+{}^{117}Y+n+n \) the average binding energy per nucleon of X and Y is 8.5 MeV and that of \( {}^{236}U \) is 7.6 MeV. The total energy liberated will be about:
(a) 200 keV
(b) 200 MeV
(c) 2 MeV
(d) 220 MeV
Show Answer & Explanation

Answer: (b) 200 MeV

Explanation:
1. Binding energy of the two fragments: \( 234\times8.5=1989 \) MeV; of U-236: \( 236\times7.6=1793.6 \) MeV.
2. Energy released \( \approx1989-1793.6=195.4\approx200 \) MeV.

Teacher's Note:
1. T
2. h
3. e
4.
5. e
6. n
7. e
8. r
9. g
10. y
11.
12. r
13. e
14. l
15. e
16. a
17. s
18. e
19. d
20.
21. e
22. q
23. u
24. a
25. l
26. s
27.
28. t
29. h
30. e
31.
32. i
33. n
34. c
35. r
36. e
37. a
38. s
39. e
40.
41. i
42. n
43.
44. t
45. o
46. t
47. a
48. l
49.
50. b
51. i
52. n
53. d
54. i
55. n
56. g
57.
58. e
59. n
60. e
61. r
62. g
63. y
64. .

Question 17: Nuclei of a radioactive element A are produced at a constant rate \( \alpha \). The element has decay constant \( \lambda \), and there are \( N_0 \) nuclei at t = 0. Which statements are correct? (A) the number of nuclei at time t is \( \frac1\lambda[\alpha-(\alpha-\lambda N_0)e^{-\lambda t}] \), (B) the number is \( \frac1\lambda[(\alpha-\lambda N_0)e^{-\lambda t}] \), (C) if \( \alpha=2N_0\lambda \), the limiting value as t tends to infinity is \( 2N_0 \), (D) if \( \alpha=2N_0\lambda \), the number after one half-life is \( N_0/2 \). Select the correct combination.
(a) B and D only
(b) A and D only
(c) A and C only
(d) B and C only
Show Answer & Explanation

Answer: (c) A and C only

Explanation:
1. \( dN/dt=\alpha-\lambda N \) integrates to \( N=\frac{\alpha}{\lambda}-\left(\frac\alpha\lambda-N_0\right)e^{-\lambda t} \), so (A) is true and (B) false.
2. As t tends to infinity \( N\to\alpha/\lambda=2N_0 \): (C) is true.
3. After one half-life \( N=2N_0-N_0/2=1.5N_0 \), so (D) is false.

Teacher's Note:
1. T
2. h
3. e
4.
5. s
6. t
7. e
8. a
9. d
10. y
11.
12. s
13. t
14. a
15. t
16. e
17.
18. i
19. s
20.
21. r
22. e
23. a
24. c
25. h
26. e
27. d
28.
29. w
30. h
31. e
32. n
33.
34. p
35. r
36. o
37. d
38. u
39. c
40. t
41. i
42. o
43. n
44.
45. e
46. q
47. u
48. a
49. l
50. s
51.
52. d
53. e
54. c
55. a
56. y
57. :
58.
59. a
60. l
61. p
62. h
63. a
64.
65. e
66. q
67. u
68. a
69. l
70. s
71.
72. l
73. a
74. m
75. b
76. d
77. a
78.
79. t
80. i
81. m
82. e
83. s
84.
85. N
86. .

Question 18: For the fusion reaction \( {}^4He+{}^4He\to{}^8Be \) the Q-value is \( -(90+n) \) keV. Take 1 amu = \( 930/c^2 \) MeV and atomic masses of Be-8 = 8.0053 u, He-4 = 4.0026 u. The value of n is:
(a) 4
(b) 2
(c) 5
(d) 3
Show Answer & Explanation

Answer: (d) 3

Explanation:
1. Mass difference \( 8.0053-2\times4.0026=0.0001 \) u.
2. \( Q=-0.0001\times930\ \mathrm{MeV}=-0.093\ \mathrm{MeV}=-93\ \mathrm{keV} \).
3. So \( 90+n=93 \), n = 3.

Teacher's Note:
1. A
2.
3. n
4. e
5. g
6. a
7. t
8. i
9. v
10. e
11.
12. Q
13. -
14. v
15. a
16. l
17. u
18. e
19.
20. m
21. e
22. a
23. n
24. s
25.
26. e
27. n
28. e
29. r
30. g
31. y
32.
33. m
34. u
35. s
36. t
37.
38. b
39. e
40.
41. s
42. u
43. p
44. p
45. l
46. i
47. e
48. d
49.
50. f
51. o
52. r
53.
54. t
55. h
56. e
57.
58. r
59. e
60. a
61. c
62. t
63. i
64. o
65. n
66. .

Question 19: A fusion reactor is considered successful if the Lawson number \( nt_0 \) (deuteron density times confinement time) exceeds \( 5\times10^{14}\ \mathrm{s/cm^3} \). Which of the following designs is most promising by this criterion?
(a) deuteron density \( 8.0\times10^{14}\ \mathrm{cm^{-3}} \), confinement time \( 9.0\times10^{-1} \) s
(b) deuteron density \( 2.0\times10^{12}\ \mathrm{cm^{-3}} \), confinement time \( 5.0\times10^{-3} \) s
(c) deuteron density \( 4.0\times10^{23}\ \mathrm{cm^{-3}} \), confinement time \( 1.0\times10^{-11} \) s
(d) deuteron density \( 1.0\times10^{24}\ \mathrm{cm^{-3}} \), confinement time \( 4.0\times10^{-12} \) s
Show Answer & Explanation

Answer: (a) deuteron density \( 8.0\times10^{14}\ \mathrm{cm^{-3}} \), confinement time \( 9.0\times10^{-1} \) s

Explanation:
1. Products \( nt_0 \): \( 1\times10^{10} \), \( 7.2\times10^{14} \), \( 4\times10^{12} \), \( 4\times10^{12} \) in the order of the other options.
2. Only \( 7.2\times10^{14}>5\times10^{14} \) meets the criterion.

Teacher's Note:
1. M
2. u
3. l
4. t
5. i
6. p
7. l
8. y
9.
10. d
11. e
12. n
13. s
14. i
15. t
16. y
17.
18. b
19. y
20.
21. c
22. o
23. n
24. f
25. i
26. n
27. e
28. m
29. e
30. n
31. t
32.
33. t
34. i
35. m
36. e
37.
38. f
39. o
40. r
41.
42. e
43. a
44. c
45. h
46.
47. d
48. e
49. s
50. i
51. g
52. n
53.
54. a
55. n
56. d
57.
58. c
59. o
60. m
61. p
62. a
63. r
64. e
65.
66. w
67. i
68. t
69. h
70.
71. t
72. h
73. e
74.
75. L
76. a
77. w
78. s
79. o
80. n
81.
82. l
83. i
84. m
85. i
86. t
87. .

Question 20: In an ore containing uranium, the ratio (by number) of U-238 to Pb-206 is 3. Assuming all the lead is the final stable product of U-238 and the half-life of U-238 is \( 4.5\times10^9 \) years, the age of the ore is \( 1.868\times10^{n} \) years. Take \( \ln(4/3)=0.2876 \). The value of n is:
(a) 10
(b) 9
(c) 8
(d) 11
Show Answer & Explanation

Answer: (b) 9

Explanation:
1. If the ore started with N atoms of U, now U = 3k and Pb = k with \( N=4k \).
2. \( t=\frac{T_{1/2}}{\ln2}\ln\frac{N}{N_U}=\frac{4.5\times10^9}{0.693}\ln\frac43=1.868\times10^9 \) years.
3. So n = 9.

Teacher's Note:
1. I
2. n
3. i
4. t
5. i
6. a
7. l
8.
9. n
10. u
11. m
12. b
13. e
14. r
15.
16. o
17. f
18.
19. u
20. r
21. a
22. n
23. i
24. u
25. m
26.
27. a
28. t
29. o
30. m
31. s
32.
33. e
34. q
35. u
36. a
37. l
38. s
39.
40. t
41. h
42. e
43.
44. p
45. r
46. e
47. s
48. e
49. n
50. t
51.
52. u
53. r
54. a
55. n
56. i
57. u
58. m
59.
60. p
61. l
62. u
63. s
64.
65. t
66. h
67. e
68.
69. l
70. e
71. a
72. d
73.
74. f
75. o
76. r
77. m
78. e
79. d
80.
81. f
82. r
83. o
84. m
85.
86. i
87. t
88. .

Question 21: A U-238 sample of mass 1.0 g emits alpha particles at the rate \( 1.24\times10^4 \) per second (\( N_A=6.023\times10^{23} \)). Which statements are correct? (A) the half-life is \( 4.5\times10^9 \) years, (B) the half-life is \( 9\times10^9 \) years, (C) the activity of the prepared sample is \( 2.48\times10^4 \) per second, (D) the activity of the prepared sample is \( 1.24\times10^4 \) per second. Select the correct combination.
(a) B and C only
(b) A and C only
(c) A and D only
(d) B and D only
Show Answer & Explanation

Answer: (c) A and D only

Explanation:
1. Atoms \( N=\frac{6.023\times10^{23}}{238}=2.53\times10^{21} \); \( \lambda=\frac{1.24\times10^4}{2.53\times10^{21}}=4.9\times10^{-18}\ \mathrm{s^{-1}} \).
2. Half-life \( =\frac{0.693}{\lambda}=1.41\times10^{17}\ \mathrm{s}=4.5\times10^9 \) years, so (A) is true.
3. The sample's activity is the given rate, so (D) is true; (B) and (C) are false.

Teacher's Note:
1. C
2. o
3. m
4. p
5. u
6. t
7. e
8.
9. t
10. h
11. e
12.
13. h
14. a
15. l
16. f
17. -
18. l
19. i
20. f
21. e
22.
23. f
24. r
25. o
26. m
27.
28. t
29. h
30. e
31.
32. a
33. c
34. t
35. i
36. v
37. i
38. t
39. y
40.
41. o
42. f
43.
44. a
45.
46. k
47. n
48. o
49. w
50. n
51.
52. n
53. u
54. m
55. b
56. e
57. r
58.
59. o
60. f
61.
62. a
63. t
64. o
65. m
66. s
67. .

Question 22: The fraction of the original number of nuclei of a radioactive atom having a mean life of 10 days that decays during the 5th day is:
(a) 0.15
(b) 0.30
(c) 0.045
(d) 0.064
Show Answer & Explanation

Answer: (d) 0.064

Explanation:
1. Fraction remaining at the start of the 5th day (t = 4 d): \( e^{-0.4}=0.670 \); at the end (t = 5 d): \( e^{-0.5}=0.607 \).
2. Decayed during the 5th day \( =0.670-0.607=0.064 \).

Teacher's Note:
1. T
2. h
3. e
4.
5. f
6. r
7. a
8. c
9. t
10. i
11. o
12. n
13.
14. d
15. e
16. c
17. a
18. y
19. i
20. n
21. g
22.
23. i
24. n
25.
26. a
27. n
28.
29. i
30. n
31. t
32. e
33. r
34. v
35. a
36. l
37.
38. i
39. s
40.
41. t
42. h
43. e
44.
45. d
46. i
47. f
48. f
49. e
50. r
51. e
52. n
53. c
54. e
55.
56. o
57. f
58.
59. t
60. h
61. e
62.
63. r
64. e
65. m
66. a
67. i
68. n
69. i
70. n
71. g
72.
73. f
74. r
75. a
76. c
77. t
78. i
79. o
80. n
81. s
82.
83. a
84. t
85.
86. i
87. t
88. s
89.
90. e
91. n
92. d
93. s
94. .

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