JEE Chemistry Structure of Atom MCQs Set 19

Answer: (c) \( 7.5\times10^{21} \) s⁻¹

Explanation:
1. Convert: \( 5.0\times10^{-5} \) erg = \( 5.0\times10^{-12} \) J.
2. \( \nu=\dfrac{E}{h}=\dfrac{5.0\times10^{-12}}{6.63\times10^{-34}}\approx7.5\times10^{21} \) s⁻¹.

Teacher's Note:
1. F
2. r
3. e
4. q
5. u
6. e
7. n
8. c
9. y
10.
11. h
12. a
13. s
14.
15. t
16. h
17. e
18.
19. u
20. n
21. i
22. t
23.
24. s
25. ⁻
26. ¹
27.
28. (
29. h
30. e
31. r
32. t
33. z
34. )
35. .
36.
37. C
38. o
39. n
40. v
41. e
42. r
43. t
44.
45. e
46. r
47. g
48.
49. t
50. o
51.
52. j
53. o
54. u
55. l
56. e
57.
58. u
59. s
60. i
61. n
62. g
63.
64. 1
65.
66. J
67.
68. =
69.
70. 1
71. 0
72. ⁷
73.
74. e
75. r
76. g
77. .

Answer: (b) 2 : 1

Explanation:
1. \( E=hc/\lambda \), so the energy is inversely proportional to wavelength.
2. \( \dfrac{E_1}{E_2}=\dfrac{\lambda_2}{\lambda_1}=\dfrac{6000}{3000}=2 \).
3. The ratio is 2 : 1.

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

Answer: (b) (b)

Explanation:
1. (a) is not allowed because the spin quantum number can only be +1/2 or −1/2.
2. (b) n = 2, l = 0, m = 0, ms = −1/2 obeys every rule.
3. (c) l cannot be negative, and (d) is not allowed because m = 1 requires l ≥ 1.

Teacher's Note:
1. R
2. u
3. l
4. e
5. s
6. :
7.
8. l
9.
10. r
11. u
12. n
13. s
14.
15. f
16. r
17. o
18. m
19.
20. 0
21.
22. t
23. o
24.
25. n
26. −
27. 1
28. ,
29.
30. m
31.
32. f
33. r
34. o
35. m
36.
37. −
38. l
39.
40. t
41. o
42.
43. +
44. l
45. ,
46.
47. a
48. n
49. d
50.
51. m
52. s
53.
54. i
55. s
56.
57. ±
58. 1
59. /
60. 2
61. .
62.
63. C
64. h
65. e
66. c
67. k
68.
69. e
70. a
71. c
72. h
73.
74. q
75. u
76. a
77. n
78. t
79. u
80. m
81.
82. n
83. u
84. m
85. b
86. e
87. r
88.
89. i
90. n
91.
92. t
93. h
94. a
95. t
96.
97. o
98. r
99. d
100. e
101. r
102. .

Answer: (c) CO, \( \ce{NO+} \), \( \ce{CN-} \), \( \ce{C2^2-} \)

Explanation:
1. Electrons: CO = 14, \( \ce{NO+} \) = 14, \( \ce{CN-} \) = 14, \( \ce{C2^2-} \) = 14.
2. In (a) \( \ce{O2-} \) has 17 electrons, in (b) NO has 15 and in (d) NO has 15 while \( \ce{CN-} \) and N₂ have 14.
3. So only option (c) is isoelectronic.

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

Answer: (a) (iv) < (ii) < (iii) < (i)

Explanation:
1. Use the (n + l) rule: (i) 4p = 5, (ii) 4s = 4, (iii) 3d = 5, (iv) 3p = 4.
2. A lower (n + l) means lower energy; when equal, the lower n has lower energy.
3. Order: 3p (4, n=3) < 4s (4, n=4) < 3d (5, n=3) < 4p (5, n=4), i.e. (iv) < (ii) < (iii) < (i).

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

Answer: (c) Paschen series

Explanation:
1. The series limit corresponds to n₂ = ∞, so \( \bar\nu=R/n_1^2 \) with \( R=109677.6 \) cm⁻¹.
2. \( n_1^2=109677.6/12186.3=9 \), so n₁ = 3.
3. n₁ = 3 is the Paschen series.

Teacher's Note:
1. S
2. e
3. r
4. i
5. e
6. s
7.
8. l
9. i
10. m
11. i
12. t
13. s
14. :
15.
16. L
17. y
18. m
19. a
20. n
21.
22. 1
23. 0
24. 9
25. 6
26. 7
27. 8
28. ,
29.
30. B
31. a
32. l
33. m
34. e
35. r
36.
37. 2
38. 7
39. 4
40. 1
41. 9
42. ,
43.
44. P
45. a
46. s
47. c
48. h
49. e
50. n
51.
52. 1
53. 2
54. 1
55. 8
56. 6
57. ,
58.
59. B
60. r
61. a
62. c
63. k
64. e
65. t
66. t
67.
68. 6
69. 8
70. 5
71. 5
72.
73. c
74. m
75. ⁻
76. ¹
77. .
78.
79. M
80. e
81. m
82. o
83. r
84. i
85. s
86. e
87.
88. t
89. h
90. e
91.
92. f
93. i
94. r
95. s
96. t
97.
98. f
99. e
100. w
101. .

Answer: (c) For n = 1, the electron has a more negative energy than it does for n = 6, which means that the electron is more loosely bound in the smallest allowed orbit.

Explanation:
1. Radius grows as n², so (a) is correct, and the energy difference between orbits can be calculated, so (b) is correct.
2. (d) correctly explains the negative sign relative to the zero of energy at infinite separation.
3. A more negative energy at n = 1 means the electron is more tightly bound, not more loosely bound, so (c) is incorrect.

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

Answer: (b) \( M_1<10(m_p+m_n) \)

Explanation:
1. Ne-20 has 10 protons and 10 neutrons, so the free nucleons would have mass \( 10(m_p+m_n) \).
2. When nucleons combine, energy is released as binding energy and the nucleus has a smaller mass (mass defect), so \( M_1<10(m_p+m_n) \).
3. Ca-40 has a larger binding energy per nucleon than Ne-20, so \( M_2 \) is slightly less than \( 2M_1 \); options (a), (c) and (d) are false.

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

Answer: (d) n = 2 to n = 1

Explanation:
1. For \( \ce{He+} \) (Z = 2): \( \dfrac1\lambda=4R\left(\dfrac14-\dfrac1{16}\right)=\dfrac{3R}{4} \).
2. For hydrogen: \( \dfrac1\lambda=R\left(\dfrac1{n_1^2}-\dfrac1{n_2^2}\right)=\dfrac{3R}{4} \) is satisfied by n₁ = 1 and n₂ = 2.
3. So the transition is n = 2 to n = 1.

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

Answer: (a) 5 → 2

Explanation:
1. The lines in the visible region form the Balmer series, which ends at n = 2.
2. From the red end the lines are 3→2 (first), 4→2 (second) and 5→2 (third).
3. So the third line is 5 → 2.

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

Answer: (c) A is true, but R is false.

Explanation:
1. An atom has equal numbers of protons and electrons, so it is neutral and the assertion is true.
2. The number of neutrons is not necessarily equal to the number of protons (for example, in \( {}^{23}_{11}\text{Na} \) there are 11 protons and 12 neutrons), so the reason is false.

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

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. Isobars have the same mass number, which is the sum of protons and neutrons, so the assertion is true.
2. The reason gives exactly that definition, so it explains the assertion.

Teacher's Note:
1. I
2. s
3. o
4. b
5. a
6. r
7. s
8. :
9.
10. s
11. a
12. m
13. e
14.
15. m
16. a
17. s
18. s
19.
20. n
21. u
22. m
23. b
24. e
25. r
26.
27. (
28. e
29. .
30. g
31. .
32.
33. A
34. r
35. -
36. 4
37. 0
38.
39. a
40. n
41. d
42.
43. C
44. a
45. -
46. 4
47. 0
48. )
49. .
50.
51. I
52. s
53. o
54. t
55. o
56. p
57. e
58. s
59. :
60.
61. s
62. a
63. m
64. e
65.
66. a
67. t
68. o
69. m
70. i
71. c
72.
73. n
74. u
75. m
76. b
77. e
78. r
79. .
80.
81. I
82. s
83. o
84. t
85. o
86. n
87. e
88. s
89. :
90.
91. s
92. a
93. m
94. e
95.
96. n
97. e
98. u
99. t
100. r
101. o
102. n
103.
104. n
105. u
106. m
107. b
108. e
109. r
110. .

Answer: (d) A is false, but R is true.

Explanation:
1. The energy of a photon is \( E=h\nu=hc/\lambda \), so it depends on frequency and wavelength.
2. Photons of different wavelengths have different energies, so both statements are false.

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

Answer: (d) A is false, but R is true.

Explanation:
1. Atoms are electrically neutral because the number of electrons equals the number of protons.
2. Both the assertion and the reason are false.

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

Answer: (c) A is true, but R is false.

Explanation:
1. In the Balmer series the electron falls to n₁ = 2 from n₂ = 3, 4, 5, ..., so the assertion is true.
2. The longest wavelength means the smallest energy gap, which is the jump from n₂ = 3 to 2, not from 4 or 6, so the reason is false.

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

Answer: (d) A is false, but R is true.

Explanation:
1. An absorption spectrum consists of dark lines on a bright continuous background.
2. An emission spectrum consists of bright lines on a dark background, so both statements are false.

Teacher's Note:
1. T
2. h
3. e
4.
5. a
6. b
7. s
8. o
9. r
10. p
11. t
12. i
13. o
14. n
15.
16. a
17. n
18. d
19.
20. e
21. m
22. i
23. s
24. s
25. i
26. o
27. n
28.
29. p
30. a
31. t
32. t
33. e
34. r
35. n
36. s
37.
38. a
39. r
40. e
41.
42. c
43. o
44. m
45. p
46. l
47. e
48. m
49. e
50. n
51. t
52. a
53. r
54. y
55. .
56.
57. D
58. a
59. r
60. k
61.
62. l
63. i
64. n
65. e
66. s
67.
68. i
69. n
70.
71. t
72. h
73. e
74.
75. a
76. b
77. s
78. o
79. r
80. p
81. t
82. i
83. o
84. n
85.
86. s
87. p
88. e
89. c
90. t
91. r
92. u
93. m
94.
95. a
96. p
97. p
98. e
99. a
100. r
101.
102. a
103. t
104.
105. t
106. h
107. e
108.
109. s
110. a
111. m
112. e
113.
114. w
115. a
116. v
117. e
118. l
119. e
120. n
121. g
122. t
123. h
124. s
125.
126. a
127. s
128.
129. b
130. r
131. i
132. g
133. h
134. t
135.
136. l
137. i
138. n
139. e
140. s
141.
142. i
143. n
144.
145. t
146. h
147. e
148.
149. e
150. m
151. i
152. s
153. s
154. i
155. o
156. n
157.
158. s
159. p
160. e
161. c
162. t
163. r
164. u
165. m
166. .

Answer: (d) A is false, but R is true.

Explanation:
1. Helium-4 is very stable with a binding energy per nucleon of about 7.07 MeV, higher than Li-7 (5.6 MeV) and Be-9 (6.5 MeV). The correct order is He-4 > Li-7 > Be-9, so the assertion is false.
2. Binding energy per nucleon does not increase linearly with the neutron-proton difference, so the reason is false.

Teacher's Note:
1. T
2. h
3. e
4.
5. h
6. i
7. g
8. h
9. e
10. r
11.
12. t
13. h
14. e
15.
16. b
17. i
18. n
19. d
20. i
21. n
22. g
23.
24. e
25. n
26. e
27. r
28. g
29. y
30.
31. p
32. e
33. r
34.
35. n
36. u
37. c
38. l
39. e
40. o
41. n
42. ,
43.
44. t
45. h
46. e
47.
48. m
49. o
50. r
51. e
52.
53. s
54. t
55. a
56. b
57. l
58. e
59.
60. t
61. h
62. e
63.
64. n
65. u
66. c
67. l
68. e
69. u
70. s
71. .
72.
73. M
74. a
75. g
76. i
77. c
78.
79. n
80. u
81. m
82. b
83. e
84. r
85. s
86.
87. a
88. n
89. d
90.
91. s
92. y
93. m
94. m
95. e
96. t
97. r
98. i
99. c
100.
101. N
102.
103. =
104.
105. Z
106.
107. n
108. u
109. c
110. l
111. e
112. i
113.
114. l
115. i
116. k
117. e
118.
119. H
120. e
121. -
122. 4
123.
124. a
125. r
126. e
127.
128. e
129. s
130. p
131. e
132. c
133. i
134. a
135. l
136. l
137. y
138.
139. s
140. t
141. a
142. b
143. l
144. e
145. .

Answer: (d) A is false, but R is true.

Explanation:
1. The 2pₓ and 2p_y orbitals are degenerate, having the same energy.
2. Moving between them involves no energy change, so no light is emitted and no spectral line is seen. Both statements are false.

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

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. l = 1 denotes a p orbital, and p orbitals are dumb-bell shaped, so the assertion is true.
2. The orbital belongs to the 3p subshell, so the reason is true, and the subshell tells us the shape, so it explains the assertion.

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

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. In Bohr's model the angular momentum of the electron in the nth orbit is \( mvr=\dfrac{nh}{2\pi} \), so the assertion is true.
2. The principal quantum number can indeed take any positive integer value, so the reason is true.
3. The permitted values of n do not explain why angular momentum has this form, so it is not the explanation.

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

Answer: (c) A is true, but R is false.

Explanation:
1. The electron spin quantum number has two values, +1/2 and −1/2, so the assertion is true.
2. The signs signify the two opposite orientations of the spin angular momentum, not the sign of a wave function, so the reason is false.

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

Answer: (c) A is true, but R is false.

Explanation:
1. Heisenberg's uncertainty principle forbids simultaneous exact determination of position and momentum, so the assertion is true.
2. Because of this uncertainty the electron has no definite path, so the reason is false.

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

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. For n = 1 and Z = 1 the formula gives \( r_1=0.529 \) Å, so the assertion is true.
2. The formula is correct and the first Bohr radius follows from it, so the reason explains the assertion.

Teacher's Note:
1. T
2. h
3. e
4.
5. B
6. o
7. h
8. r
9.
10. r
11. a
12. d
13. i
14. u
15. s
16.
17. a
18. ₀
19.
20. =
21.
22. 0
23. .
24. 5
25. 2
26. 9
27.
28. Å
29. .
30.
31. O
32. r
33. b
34. i
35. t
36.
37. r
38. a
39. d
40. i
41. i
42.
43. g
44. r
45. o
46. w
47.
48. a
49. s
50.
51. n
52. ²
53.
54. a
55. n
56. d
57.
58. s
59. h
60. r
61. i
62. n
63. k
64.
65. a
66. s
67.
68. Z
69.
70. i
71. n
72. c
73. r
74. e
75. a
76. s
77. e
78. s
79. .