JEE Physics Atoms MCQs Set 20

Answer: (a) Coulomb (electrostatic) forces

Explanation:
1. The electrons are negatively charged and the nucleus is positively charged, so the attractive electrostatic force holds them.
2. Gravitational force is far too weak and nuclear force acts only at nuclear distances.

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

Answer: (a) 931 MeV

Explanation:
1. \( E = mc^2 = 1.66\times10^{-27}\times(3\times10^8)^2 \approx 1.49\times10^{-10} J \).
2. Dividing by \( 1.6\times10^{-13} \) J/MeV gives about 931 MeV.

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

Answer: (a) J.J. Thomson

Explanation:
1. Thomson pictured the atom as a sphere of positive charge with electrons embedded like plums in a pudding.

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

Answer: (a) positively charged

Explanation:
1. The large-angle scattering of \( \alpha \) particles, which are positive, shows that the nucleus is positively charged and carries most of the atom's mass.

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

Answer: (a) \( \dfrac{h}{2\pi} \)

Explanation:
1. Angular momentum is quantised: \( mvr = \dfrac{nh}{2\pi} \).
2. For the ground state \( n = 1 \), so \( L = \dfrac{h}{2\pi} \).

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

Answer: (a) Balmer

Explanation:
1. Johann Balmer found in 1885 that the visible lines of hydrogen fit a simple formula. This is the Balmer series.

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. a
15. \( r \)
16. \( i \)
17. \( s \)
18. \( e \)
19.
20. \( w \)
21. \( h \)
22. \( e \)
23. \( n \)
24.
25. \( t \)
26. \( h \)
27. \( e \)
28.
29. \( e \)
30. \( l \)
31. \( e \)
32. \( c \)
33. \( t \)
34. \( r \)
35. \( o \)
36. \( n \)
37.
38. \( f \)
39. a
40. \( l \)
41. \( l \)
42. \( s \)
43.
44. \( t \)
45. \( o \)
46.
47. \( n \)
48.
49. =
50.
51. 2
52. .

Answer: (a) Visible region

Explanation:
1. Transitions from higher levels to \( n = 2 \) give wavelengths from 656.3 nm to 364.6 nm, which lie in the visible region (the series limit is just in the near ultraviolet).

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

Answer: (a) \( \dfrac{\varepsilon_0n^2h^2}{\pi me^2} \)

Explanation:
1. Equate the Coulomb force with the centripetal force and use \( mvr = \dfrac{nh}{2\pi} \).
2. This gives \( r_n = \dfrac{\varepsilon_0n^2h^2}{\pi me^2} \).

Teacher's Note:
1. \( R \)
2. a
3. \( d \)
4. \( i \)
5. \( u \)
6. \( s \)
7.
8. \( g \)
9. \( r \)
10. \( o \)
11. \( w \)
12. \( s \)
13.
14. a
15. \( s \)
16.
17. \
18. (
19.
20. \( n \)
21. \( ^ \)
22. 2
23.
24. \
25. )
26. ,
27.
28. \( w \)
29. \( i \)
30. \( t \)
31. \( h \)
32.
33. \
34. (
35.
36. \( r \)
37. _
38. 1
39.
40. =
41.
42. 0
43. .
44. 5
45. 3
46.
47. \
48. )
49.
50. a
51. \( n \)
52. \( g \)
53. \( s \)
54. \( t \)
55. \( r \)
56. \( o \)
57. \( m \)
58. .

Answer: (c) The frequency of revolution is inversely proportional to the cube of n

Explanation:
1. Total energy equals minus the kinetic energy, so KE : TE is 1 : \( -1 \).
2. \( r \propto n^2 \), not \( n \).
3. \( f = \dfrac{v}{2\pi r} \propto \dfrac{1/n}{n^2} = \dfrac{1}{n^3} \), so \( (c) \) is correct.
4. The binding force decreases as the electron moves outward.

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

Answer: (a) Many alpha particles pass straight through the gold foil, and only about 0.14% scatter by more than 1 degree

Explanation:
1. Most \( \alpha \) particles pass through undeviated, which shows that the atom is mostly empty space.
2. Only a tiny fraction are scattered through large angles, pointing to a small, heavy, positive nucleus.

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

Answer: (a) decreases

Explanation:
1. The orbital speed is \( v \propto \dfrac{1}{n} \).
2. A larger orbit means a larger \( n \) and hence a smaller speed.

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

Answer: (a) The line spectrum of hydrogen with specific wavelengths

Explanation:
1. The model explained scattering and the nucleus, but an orbiting electron should radiate continuously and spiral in.
2. It could not explain why hydrogen emits only specific wavelengths.

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

Answer: (b) The force of repulsion between an atomic nucleus and an alpha particle varies with distance according to the inverse square law

Explanation:
1. The scattering angles matched calculations that assume Coulomb repulsion following an inverse square law between nucleus and \( \alpha \) particle.
2. The other statements are true but are not shown by the scattering experiment.

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

Answer: (d) Franck and Hertz

Explanation:
1. The Franck-Hertz experiment showed that atoms absorb energy from electrons only in discrete amounts, which proves discrete energy levels.

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

Answer: (d) Gamma rays

Explanation:
1. Electron transitions give ultraviolet, visible, infrared and X-rays (from inner shells).
2. Gamma rays come from the nucleus.

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

Answer: (d) inversely proportional to \( n^3 \)

Explanation:
1. \( \omega = \dfrac{v}{r} \) with \( v \propto \dfrac{1}{n} \) and \( r \propto n^2 \).
2. So \( \omega \propto \dfrac{1}{n^3} \).

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

Answer: (d) 0.66 eV

Explanation:
1. \( E_n = -\dfrac{13.6}{n^2} \) eV, so \( E_3 = -1.51 \) eV and \( E_4 = -0.85 \) eV.
2. \( \Delta E = 1.51 - 0.85 = 0.66 \) eV.

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

Answer: (b) from higher orbits to the second orbit

Explanation:
1. The Balmer series corresponds to transitions ending at \( n = 2 \).

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

Answer: (d) the angular momentum of the electron is quantised

Explanation:
1. Bohr's second postulate is \( mvr = \dfrac{nh}{2\pi} \), so angular momentum takes only discrete values.

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

Answer: (d) doubly ionised lithium

Explanation:
1. \( \dfrac{1}{\lambda} = RZ^2\left(\dfrac{1}{1}-\dfrac{1}{4}\right) \), so \( \lambda \propto \dfrac{1}{Z^2} \).
2. Doubly ionised lithium has the largest \( Z (3) \), so it gives the shortest wavelength.

Teacher's Note:
1. A
2.
3. \( h \)
4. \( i \)
5. \( g \)
6. \( h \)
7. \( e \)
8. \( r \)
9.
10. \( n \)
11. \( u \)
12. \( c \)
13. \( l \)
14. \( e \)
15. a
16. \( r \)
17.
18. \( c \)
19. \( h \)
20. a
21. \( r \)
22. \( g \)
23. \( e \)
24.
25. \( m \)
26. a
27. \( k \)
28. \( e \)
29. \( s \)
30.
31. \( e \)
32. \( n \)
33. \( e \)
34. \( r \)
35. \( g \)
36. \( y \)
37.
38. \( g \)
39. a
40. \( p \)
41. \( s \)
42.
43. \( l \)
44. a
45. \( r \)
46. \( g \)
47. \( e \)
48. \( r \)
49. .

Answer: (a) Lyman series

Explanation:
1. The Lyman series (transitions to \( n = 1 \)) has wavelengths from 91.2 nm to 121.6 nm, all in the ultraviolet.

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

Answer: (c) decreases

Explanation:
1. \( E_{n+1}-E_n = 13.6\left(\dfrac{1}{n^2}-\dfrac{1}{(n+1)^2}\right) \) eV, which falls as \( n \) grows.
2. Levels crowd together near the ionisation limit.

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

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

Explanation:
1. Absorption means going from a lower to a higher level, so \( (c) \) and \( (d) \) are emissions.
2. Between \( (a) \) and \( (b) \), the \( n = 1 \) to \( n = 2 \) jump has the larger energy (10.2 eV against 1.5 eV), so it has the highest frequency.

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

Answer: (a) \( 21.16\times10^{-11} \) m

Explanation:
1. \( r_n \propto n^2 \), so \( r_2 = 4r_1 = 4\times5.29\times10^{-11} = 21.16\times10^{-11} m \).

Teacher's Note:
1. \( R \)
2. a
3. \( d \)
4. \( i \)
5. \( u \)
6. \( s \)
7.
8. \( g \)
9. \( r \)
10. \( o \)
11. \( w \)
12. \( s \)
13.
14. a
15. \( s \)
16.
17. \( t \)
18. \( h \)
19. \( e \)
20.
21. \( s \)
22. \( q \)
23. \( u \)
24. a
25. \( r \)
26. \( e \)
27.
28. \( o \)
29. \( f \)
30.
31. \( n \)
32. .

Answer: (d) 10.2 eV

Explanation:
1. The smallest excitation is from \( n = 1 \) to \( n = 2 \).
2. \( \Delta E = 13.6\left(1-\dfrac{1}{4}\right) = 10.2 \) eV.

Teacher's Note:
1. \( T \)
2. \( h \)
3. \( e \)
4.
5. \( f \)
6. \( i \)
7. \( r \)
8. \( s \)
9. \( t \)
10.
11. \( e \)
12. \( x \)
13. \( c \)
14. \( i \)
15. \( t \)
16. a
17. \( t \)
18. \( i \)
19. \( o \)
20. \( n \)
21.
22. \( e \)
23. \( n \)
24. \( e \)
25. \( r \)
26. \( g \)
27. \( y \)
28.
29. \( o \)
30. \( f \)
31.
32. \( h \)
33. \( y \)
34. \( d \)
35. \( r \)
36. \( o \)
37. \( g \)
38. \( e \)
39. \( n \)
40.
41. \( i \)
42. \( s \)
43.
44. 1
45. 0
46. .
47. 2
48.
49. \( e \)
50. \( V \)
51. .

Answer: (a) atomic state

Explanation:
1. Free atoms emit radiation of fixed, discrete wavelengths, giving a line spectrum.
2. Molecules give band spectra.

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