JEE Chemistry Nuclear Chemistry MCQs Set 06

Answer: (d) 5 hours

Explanation:
1. \( \frac1{16}=\left(\frac12\right)^4 \), so 4 half-lives = \( 20 h \).
2. Half-life = 5 hours.

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

Answer: (d) 10 hours

Explanation:
1. \( \tau=\frac1\lambda=\frac{t_{1/2}}{0.693} \).
2. \( \tau=\frac{6.93}{0.693}=10 h \).

Teacher's Note:
1. \( M \)
2. \( e \)
3. a
4. \( n \)
5.
6. \( l \)
7. \( i \)
8. \( f \)
9. \( e \)
10.
11. \( i \)
12. \( s \)
13.
14. a
15. \( b \)
16. \( o \)
17. \( u \)
18. \( t \)
19.
20. 1
21. .
22. 4
23. 4
24.
25. \( t \)
26. \( i \)
27. \( m \)
28. \( e \)
29. \( s \)
30.
31. \( t \)
32. \( h \)
33. \( e \)
34.
35. \( h \)
36. a
37. \( l \)
38. \( f \)
39. -
40. \( l \)
41. \( i \)
42. \( f \)
43. \( e \)
44. .

Answer: (b) 10⁻³ s⁻¹

Explanation:
1. \( \lambda=\frac{0.693}{t_{1/2}}=\frac{0.693}{693} \).
2. \( \lambda = 10^{-3} s^{-1} \).

Teacher's Note:
1. \( D \)
2. \( e \)
3. \( c \)
4. a
5. \( y \)
6.
7. \( c \)
8. \( o \)
9. \( n \)
10. \( s \)
11. \( t \)
12. a
13. \( n \)
14. \( t \)
15.
16. \( i \)
17. \( s \)
18.
19. \( t \)
20. \( h \)
21. \( e \)
22.
23. \( r \)
24. \( e \)
25. \( c \)
26. \( i \)
27. \( p \)
28. \( r \)
29. \( o \)
30. \( c \)
31. a
32. \( l \)
33.
34. \( o \)
35. \( f \)
36.
37. \( m \)
38. \( e \)
39. a
40. \( n \)
41.
42. \( l \)
43. \( i \)
44. \( f \)
45. \( e \)
46. .

Answer: (c) 1/e (about 36.8 %)

Explanation:
1. \( N=N_0e^{-\lambda t} \) and \( t=\tau=\frac1\lambda \).
2. \( N/N_0=e^{-1}=0.368 \).

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

Answer: (b) 31 minutes

Explanation:
1. \( N=0.8N_0 \) at \( t = 10 \min \): \( \lambda=\frac{\ln(1/0.8)}{10}=0.0223 \min^{-1} \).
2. \( t_{1/2}=\frac{0.693}{0.0223}\approx31 \min \).

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

Answer: (c) 31.2 cm³

Explanation:
1. 69.2 days = half a half-life: Po left = \( (1/2)^{0.5} = 0.7071 g \), so \( 0.2929 g \) decayed.
2. Each decayed atom gives one He atom: moles He = \( 0.2929/210 = 1.395 \times 10^{-3} \).
3. Volume = \( 1.395 \times 10^{-3} \times 22400 = 31.2 \) cm³.

Teacher's Note:
1. \( E \)
2. a
3. \( c \)
4. \( h \)
5.
6. α
7.
8. \( p \)
9. a
10. \( r \)
11. \( t \)
12. \( i \)
13. \( c \)
14. \( l \)
15. \( e \)
16.
17. \( b \)
18. \( e \)
19. \( c \)
20. \( o \)
21. \( m \)
22. \( e \)
23. \( s \)
24.
25. \( o \)
26. \( n \)
27. \( e \)
28.
29. \( h \)
30. \( e \)
31. \( l \)
32. \( i \)
33. \( u \)
34. \( m \)
35.
36. a
37. \( t \)
38. \( o \)
39. \( m \)
40. .

Answer: (c) 11460 years

Explanation:
1. One quarter means two half-lives have passed.
2. Age = \( 2 \times 5730 = 11460 \) years.

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

Answer: (d) the capture of a neutron (from cosmic rays) by ¹⁴N followed by emission of a proton

Explanation:
1. Cosmic-ray neutrons strike atmospheric nitrogen: \( ^{14}_{7}N + ^{1}_{0}n \to ^{14}_{6}C + ^{1}_{1}p \).

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

Answer: (c) 3.7 × 10¹⁰ disintegrations per second

Explanation:
1. The curie is the activity of \( 1 g \) of radium: 3.7 × 10¹⁰ dps.
2. 10⁶ dps is a rutherford, and 1 dps is 1 becquerel.

Teacher's Note:
1. 1
2.
3. \( C \)
4. \( i \)
5.
6. =
7.
8. 3
9. .
10. 7
11.
12. ×
13.
14. 1
15. 0
16. ⁴
17.
18. \( r \)
19. \( u \)
20. \( t \)
21. \( h \)
22. \( e \)
23. \( r \)
24. \( f \)
25. \( o \)
26. \( r \)
27. \( d \)
28.
29. =
30.
31. 3
32. .
33. 7
34.
35. ×
36.
37. 1
38. 0
39. ¹
40. ⁰
41.
42. \( B \)
43. \( q \)
44. .

Answer: (b) 2 × 10⁹

Explanation:
1. \( \frac{dN}{dt}=R-\lambda N=0 \) in the steady state.
2. \( N=\frac R\lambda=\frac{2\times10^6}{10^{-3}}=2\times10^9 \).

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

Answer: (b) \( \lambda N_A/M \)

Explanation:
1. Number of nuclei in \( 1 g =\frac{N_A}{M} \).
2. Specific activity \( =\lambda\times\frac{N_A}M \).

Teacher's Note:
1. \( S \)
2. \( p \)
3. \( e \)
4. \( c \)
5. \( i \)
6. \( f \)
7. \( i \)
8. \( c \)
9.
10. a
11. \( c \)
12. \( t \)
13. \( i \)
14. \( v \)
15. \( i \)
16. \( t \)
17. \( y \)
18.
19. \( i \)
20. \( s \)
21.
22. a
23. \( c \)
24. \( t \)
25. \( i \)
26. \( v \)
27. \( i \)
28. \( t \)
29. \( y \)
30.
31. \( p \)
32. \( e \)
33. \( r \)
34.
35. \( u \)
36. \( n \)
37. \( i \)
38. \( t \)
39.
40. \( m \)
41. a
42. \( s \)
43. \( s \)
44. .

Answer: (b) emit a β⁻ particle

Explanation:
1. A high \( n/p \) ratio is reduced by converting a neutron into a proton: \( n \to p + e^{-} \) + antineutrino.
2. This is β⁻ emission.

Teacher's Note:
1. \( N \)
2. \( e \)
3. \( u \)
4. \( t \)
5. \( r \)
6. \( o \)
7. \( n \)
8. -
9. \( r \)
10. \( i \)
11. \( c \)
12. \( h \)
13.
14. \( n \)
15. \( u \)
16. \( c \)
17. \( l \)
18. \( e \)
19. \( i \)
20.
21. \( u \)
22. \( n \)
23. \( d \)
24. \( e \)
25. \( r \)
26. \( g \)
27. \( o \)
28.
29. β
30. ⁻
31.
32. \( d \)
33. \( e \)
34. \( c \)
35. a
36. \( y \)
37. .

Answer: (b) increases from 1.45 to 1.49

Explanation:
1. Before: \( n = 115, p = 79, n/p = 1.456 \). After: \( n = 116, p = 78, n/p = 1.487 \).
2. A proton is converted to a neutron, so the ratio increases.

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

Answer: (c) 8 α and 6 β⁻

Explanation:
1. Mass number falls by 32, so \( 32/4 = 8 \alpha \) particles; this lowers \( Z \) by 16.
2. \( Z \) actually falls by 10, so 6 β⁻ particles (each raising \( Z \) by 1) are needed.

Teacher's Note:
1. \( C \)
2. \( o \)
3. \( u \)
4. \( n \)
5. \( t \)
6.
7. α
8.
9. \( f \)
10. \( r \)
11. \( o \)
12. \( m \)
13.
14. \( t \)
15. \( h \)
16. \( e \)
17.
18. \( m \)
19. a
20. \( s \)
21. \( s \)
22.
23. \( n \)
24. \( u \)
25. \( m \)
26. \( b \)
27. \( e \)
28. \( r \)
29. ,
30.
31. \( t \)
32. \( h \)
33. \( e \)
34. \( n \)
35.
36. β
37.
38. \( f \)
39. \( r \)
40. \( o \)
41. \( m \)
42.
43. \( t \)
44. \( h \)
45. \( e \)
46.
47. \( c \)
48. \( h \)
49. a
50. \( r \)
51. \( g \)
52. \( e \)
53. .

Answer: (a) ²³⁴₉₀Th

Explanation:
1. An α particle is ⁴₂He: \( A \) falls by 4 and \( Z \) falls by 2.
2. \( ^{238}_{92}U \) → ²³⁴₉₀Th + ⁴₂He.

Teacher's Note:
1. α
2.
3. \( d \)
4. \( e \)
5. \( c \)
6. a
7. \( y \)
8.
9. \( l \)
10. \( o \)
11. \( w \)
12. \( e \)
13. \( r \)
14. \( s \)
15.
16. A
17.
18. \( b \)
19. \( y \)
20.
21. 4
22.
23. a
24. \( n \)
25. \( d \)
26.
27. \( Z \)
28.
29. \( b \)
30. \( y \)
31.
32. 2
33. .

Answer: (b) γ and α

Explanation:
1. γ rays have no charge and penetrate the most.
2. α particles have the largest charge and mass and ionise the most.

Teacher's Note:
1. \( P \)
2. \( e \)
3. \( n \)
4. \( e \)
5. \( t \)
6. \( r \)
7. a
8. \( t \)
9. \( i \)
10. \( o \)
11. \( n \)
12.
13. a
14. \( n \)
15. \( d \)
16.
17. \( i \)
18. \( o \)
19. \( n \)
20. \( i \)
21. \( s \)
22. \( i \)
23. \( n \)
24. \( g \)
25.
26. \( p \)
27. \( o \)
28. \( w \)
29. \( e \)
30. \( r \)
31.
32. a
33. \( r \)
34. \( e \)
35.
36. \( i \)
37. \( n \)
38.
39. \( o \)
40. \( p \)
41. \( p \)
42. \( o \)
43. \( s \)
44. \( i \)
45. \( t \)
46. \( e \)
47.
48. \( o \)
49. \( r \)
50. \( d \)
51. \( e \)
52. \( r \)
53. \( s \)
54. .

Answer: (d) isobars

Explanation:
1. Both have mass number 14 but different atomic numbers (7 and 6).
2. Nuclides with the same \( A \) and different \( Z \) are isobars.

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

Answer: (b) ¹⁷₈O

Explanation:
1. \( ^{14}_{7}N \) + ⁴₂He → \( X + ^{1}_{1}p \). Mass number: \( 14 + 4 - 1 = 17 \); atomic number: \( 7 + 2 - 1 = 8 \).
2. \( X \) is \( ^{17}_{8}O \) (Rutherford's first artificial transmutation).

Teacher's Note:
1. \( B \)
2. a
3. \( l \)
4. a
5. \( n \)
6. \( c \)
7. \( e \)
8.
9. \( b \)
10. \( o \)
11. \( t \)
12. \( h \)
13.
14. \( t \)
15. \( h \)
16. \( e \)
17.
18. \( m \)
19. a
20. \( s \)
21. \( s \)
22.
23. \( n \)
24. \( u \)
25. \( m \)
26. \( b \)
27. \( e \)
28. \( r \)
29.
30. a
31. \( n \)
32. \( d \)
33.
34. a
35. \( t \)
36. \( o \)
37. \( m \)
38. \( i \)
39. \( c \)
40.
41. \( n \)
42. \( u \)
43. \( m \)
44. \( b \)
45. \( e \)
46. \( r \)
47. .

Answer: (d) boron or cadmium

Explanation:
1. Boron and cadmium absorb neutrons strongly.
2. Graphite and heavy water are moderators that slow neutrons down.

Teacher's Note:
1. \( C \)
2. \( o \)
3. \( n \)
4. \( t \)
5. \( r \)
6. \( o \)
7. \( l \)
8.
9. \( r \)
10. \( o \)
11. \( d \)
12. \( s \)
13.
14. a
15. \( b \)
16. \( s \)
17. \( o \)
18. \( r \)
19. \( b \)
20.
21. \( n \)
22. \( e \)
23. \( u \)
24. \( t \)
25. \( r \)
26. \( o \)
27. \( n \)
28. \( s \)
29. ;
30.
31. \( m \)
32. \( o \)
33. \( d \)
34. \( e \)
35. \( r \)
36. a
37. \( t \)
38. \( o \)
39. \( r \)
40. \( s \)
41.
42. \( s \)
43. \( l \)
44. \( o \)
45. \( w \)
46.
47. \( t \)
48. \( h \)
49. \( e \)
50. \( m \)
51. .

Answer: (b) critical mass

Explanation:
1. Below the critical mass too many neutrons escape.
2. Above it (supercritical) the reaction multiplies rapidly, as in an atomic bomb.

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

Answer: (d) the nuclei must overcome the electrostatic repulsion between them

Explanation:
1. Light nuclei are positively charged and repel each other.
2. Only at very high temperature do they have enough kinetic energy to come close enough to fuse; hence these are called thermonuclear reactions.

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

Answer: (b) 7.1 MeV

Explanation:
1. Mass defect = \( 2(1.0078) + 2(1.0087) - 4.0026 = 0.0304 u \).
2. Binding energy = \( 0.0304 \times 931 = 28.3 \) MeV, so per nucleon \( 28.3/4 = 7.1 \) MeV.

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

Answer: (b) Stable light nuclei have n/p close to 1, and for heavier stable nuclei n/p is greater than 1

Explanation:
1. The belt of stability starts near \( n/p = 1 \) for light nuclei and rises to about 1.5 for heavy nuclei.
2. Nuclei outside this belt are unstable.

Teacher's Note:
1. \( H \)
2. \( e \)
3. a
4. \( v \)
5. \( i \)
6. \( e \)
7. \( r \)
8.
9. \( n \)
10. \( u \)
11. \( c \)
12. \( l \)
13. \( e \)
14. \( i \)
15.
16. \( n \)
17. \( e \)
18. \( e \)
19. \( d \)
20.
21. \( e \)
22. \( x \)
23. \( t \)
24. \( r \)
25. a
26.
27. \( n \)
28. \( e \)
29. \( u \)
30. \( t \)
31. \( r \)
32. \( o \)
33. \( n \)
34. \( s \)
35.
36. \( t \)
37. \( o \)
38.
39. \( o \)
40. \( f \)
41. \( f \)
42. \( s \)
43. \( e \)
44. \( t \)
45.
46. \( p \)
47. \( r \)
48. \( o \)
49. \( t \)
50. \( o \)
51. \( n \)
52. –
53. \( p \)
54. \( r \)
55. \( o \)
56. \( t \)
57. \( o \)
58. \( n \)
59.
60. \( r \)
61. \( e \)
62. \( p \)
63. \( u \)
64. \( l \)
65. \( s \)
66. \( i \)
67. \( o \)
68. \( n \)
69. .

Answer: (c) ²⁰⁸₈₂Pb

Explanation:
1. \( 232 = 4 \times 58 \), so the thorium series is the \( 4n \) series.
2. Its stable end product has \( A = 4n \) as well: 208Pb \( (208 = 4 \times 52) \).

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

Answer: (a) 3 hours

Explanation:
1. \( 2000/250 = 8 = 2^{3} \), so 3 half-lives in 9 hours.
2. Half-life = 3 hours.

Teacher's Note:
1. \( N \)
2. \( u \)
3. \( m \)
4. \( b \)
5. \( e \)
6. \( r \)
7.
8. \( o \)
9. \( f \)
10.
11. \( h \)
12. a
13. \( l \)
14. \( f \)
15. -
16. \( l \)
17. \( i \)
18. \( v \)
19. \( e \)
20. \( s \)
21.
22. =
23.
24. \( l \)
25. \( o \)
26. \( g \)
27. ₂
28.
29. (
30. A
31. ₀
32. /
33. A
34. )
35. .