MCKV Institute of Engineering

Question Bank
Subject: Physics Paper Code: BS-PH101/BS-PH201
Marks Distribution
Group/Module Module-1 Module-2 Module- Module- Module- Module-
3 4 5 6
Group-A 3 3 1 1 1 3
Group-B 5 5 2.5 2.5 5 5
Group-C 15 15 9 6 12 18

Group-A
Module-1

1. The area in which there is no discrepancies between the classical model / theory and
experiments and therefore does not need the concepts of quantum physics is
(a) Blackbody radiation (b) Photoelectric effect (c) Compton Scattering (d) Newton’s
laws of motion.
2. An ideal black body is
(a) an ideal absorber (b) an ideal radiator (c) an ideal reflector (d) both a and b.
3. A black body is something which
(a) does not emit any radiation in any temperature
(b) in room temperature absorbs more energy than it radiates
(c) it absorbs incident radiations of all frequencies completely
(d) absorption coefficient varies with the third power of frequency.
4. The absorptive power of an ideal black body is
(a) 0 (b) 1 (c) 2 (d) .
5. Black body radiation is
(a) longitudinal wave (b) elastic wave (c) electromagnetic wave (d)
mechanical wave.
6. The total emissive power is defined as the total amount of energy radiation emitted by
a blackbody per unit
(a) temperature and time (b) time only (c) area and temperature (d)
area and time.
7. The emissive power of a black body kept at an absolute temperature T is proportional
to
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(a) 𝑻𝟒 (b) 𝑇 3 (c) 𝑇 −1 (d) 𝑇.
8. The wavelength at which a black body at temperature T emits maximum
amount of radiation is proportional to
(a) T (b) 1/T (c) T4 (d) eT.
9. The wavelength at which the radiation is strongest is given by
(a) Stefan-Boltzmann Law (b) Wien’s Radiation Formula
(c) Wien's displacement law (d) Rayleigh Jean’s Formula.
10. The energy of a photon is equal to
ℎ𝑐 ℎ𝑐 ℎ𝜆
(a) (b) (c) (d) infinity.
𝜆2 𝜆 𝑐
11. Number of oscillation modes for the electromagnetic standing waves of frequency γ for
the cavity radiation is proportional to
(a) γ1/2 (b) γ (c) γ4 (d) γ2.
12. Number of oscillation modes for electromagnetic standing waves of frequency between
ν to ν + dν in case of cavity radiation is proportional to
ℎ𝜈
(a) 𝜈 3 (b) 𝝂𝟐 (c) 𝜈 (d) ℎ𝜈 .
𝑒 𝑘𝑇−1
13. According to Rayleigh-Jean’s Law, the energy density of a blackbody radiation is
(a) inversely proportional to the fourth power of wavelength
(b) directly proportional to the fourth power of wavelength
(c) inversely proportional to the fifth power of wavelength
(d) directly proportional to the fifth power of frequency.
14. In the limit of high temperature and large wavelength, Planck’s law of radiation reduces
to
(a) Rayleigh-Jean’s Law (b) Wien’s displacement law (c) Wien’s law (d)
Stephan’s law.
15. Wien’s law and Rayleigh-Jean’s law fail to explain energy distribution of blackbody
radiation in
(a) lower wavelength region (b) higher wavelength region
(c) lower and higher wavelength region respectively (d) higher and lower wavelength
region respectively.
16. According to Wien's displacement law
𝜆𝑚 𝜆𝑚
(a) 𝝀𝒎 𝑻 =Constant (b) =Constant (c) 𝜆𝑚 𝑇 2 =Constant (d) =Constant.
𝑇 𝑇2
17. The wavelength of black body changes with its absolute temperature as
𝟏 1
(a) 𝝀 ∝ (b) 𝜆 ∝ 𝑇 (c) 𝜆 ∝ (d) 𝜆 ∝ 𝑇 2 .
𝑻 𝑇2
18. The maximum energy density of radiations of a black body at absolute temperature 𝑇 =
0K is displaced towards the shorter wavelength. This law is known as

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(a) Wien’s radiation law (b) Wien’s displacement law
(c) Rayleigh-Jeans law (d) Planck’s radiation law.
19. Planck's constant has the dimensions of
(a) linear momentum (b) angular momentum (c) energy (d) torque.
20. If a body emits light be blackbody radiation, there is a unique correspondence between
(a) the temperature of an object and its surface area
(b) the temperature of the object and the wavelength at which it is brightest
(c) the mass of the object and the power radiated
(d) the mass of the object and its surface temperature.

21. You have a black piece of charcoal and a polished metal sphere of identical size. If both
are at the same temperature T, which of the following is true?
(a) The peak of the blackbody radiation from the charcoal is at a longer wavelength than
the peak of the blackbody radiation from the polished metal sphere
(b) The peak of the blackbody radiation from the charcoal is at a shorter wavelength than
the peak of the blackbody radiation from the polished metal sphere
(c) The peak of the blackbody radiation from the charcoal has the same wavelength
as the peak of the blackbody radiation from the polished metal sphere
(d) The polished metal sphere emits more blackbody radiation power than the black
charcoal.
22. The average energy of Planck’s oscillator of frequency 𝜈 is
(a) ℎ𝜈 (b) 𝑒 ℎ𝜈⁄𝑘𝑇 − 1 (c) ℎ𝜈(𝑒 ℎ𝜈⁄𝑘𝑇 − 1) (d) 𝒉𝝂/(𝒆𝒉𝝂⁄𝒌𝑻 −
𝟏)
23. Given that the temperature of a younger star is higher than that of an older one
(a) a blue star is younger than a red star (b) a blue star is older than a red star
(c) both of them are same age (d) colour of the star cannot be correlated to the
age of the star.
24. Two blackbodies A and B have the same size, but A is three times as hot as B. What is
the ratio of the rate of energy emitted by A to the rate of energy emitted by B?
(a) 3 (b) 9 (c) 27 (d) 81.
25. Suppose a black body is brightest at a wavelength of 1µm. If the temperature of the black
body is doubled at what wavelength would it be the brightest
(a) 2 µm (b) 1 µm (c) 0.5 µm (d) 1.2 µm.
26. Mass of a photon of frequency ν is given by
ℎ𝜈 ℎ𝜈 ℎ𝜈2
(a) ℎ𝜈 (b) (c) (d) .
𝑐 𝑐2 𝑐
27. The rest mass of photon is

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(a) p/c (b) hν/c2 (c) E/c2 (d) 0.
28. The relativistic energy momentum relation is
(a)𝑝2 = 𝐸 2 + 𝑚02 𝑐 2 (b) 𝐸 2 = 𝑝2 + 𝑚02 𝑐 4 (c) 𝐸 2 = 𝑝2 𝑐 2 + 𝑚02 𝑐 4 (d) 𝑝2 = 𝐸 2 𝑐 2 +
𝑚02 𝑐 4 .
29. If visible light is used to study Compton scattering, then Compton shift will be
(a) negative (b) more positive than what is observed with X-
rays
(c) zero (d) positive but not detectable in the visible
window.
30. The best suitable rays for the study of Compton effect are
(a) visible rays (b) ultraviolet rays (c) X-rays (d) infrared rays.
31. Compton wavelength of a particle of rest mass m0 is given by
ℎ ℎ ℎ 𝑚0
(a) 𝜆 = (b) 𝜆 = (c) 𝜆 = (d) 𝜆 = .
𝑚0 𝑐2 𝑚0 𝑚0 𝑐 ℎ𝑐
32. The Compton shift is maximum when scattering angle is
(a) 45o (b) 90o (c) 180o (d) 60o.
33. The Compton shift Δλ and Compton wavelength λc of a particle are equal if the angle of
scattering is
(a) 0o (b) 90o (c) 180o (d) 45o.
34. The Compton shift is equal to Compton wavelength when the angle of scattering is
(a) 0o (b) 45o (c) 90o (d) 180o.
35. If the angle of scattering varies from 0 to 180o, the Compton shift varies from 0 to
(a) 0.0121 Å (b) 0.0242 Å (c) 0.0484 Å (d) any value.
36. The change in wavelength of an X-ray photon when it is scattered through an angle of
90o by a free electron is of the order of
(a) 10-9 m (b) 10-10 m (c) 10-12 m (a) 10-15 m.
37. In unmodified Compton line, the wavelength of the scattered photon
(a) increases w.r.t. that of the incident photon (b) decreases w.r.t. that of the incident
photon
(c) remains same as that of the incident photon (d) inversely proportional to that of
the incident photon.
38. In modified Compton line, the wavelength of the scattered photon
(a) increases w.r.t. that of the incident photon (b) decreases w.r.t. that of the incident
photon
(c) remains same as that of the incident photon (d) inversely proportional to that of
the incident photon.
39. The de Broglie wavelength is associated with particles in motion if it is

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(a) charged (b) uncharged (c) both charged or uncharged (d)
none of these.
40. Why don’t ordinary objects like cricket balls readily exhibit a wave nature?
(a) Only objects at the atomic scale in principle can behave as waves
(b) Cricket balls normally have an extremely short de Broglie wavelength
(c) Cricket balls normally have an extremely long de Broglie wavelength
(d) Cricket balls are usually electrically neutral.
41. de Broglie wavelength of a particle of mass m and kinetic energy E is
ℎ 2𝑚𝐸 ℎ √2𝑚𝐸
(a) (b) (c) (d) .
2𝑚𝐸 ℎ √2𝑚𝐸 ℎ
42. The de Broglie wavelength of a moving electron subjected to a potential V is
1.26 12.26 122.6 1226
(a) Å (b) Å (c) Å (d) Å.
√𝑉 √𝑉 √𝑉 √𝑉
43. If -particle, proton, electron and neutron are moving with the same velocity then the
maximum de Broglie wavelength will be of
(a) -particle (b) proton (c) electron (d) neutron.
44. An electron and a proton have the same de Broglie wavelength. Then the kinetic energy
of the electron is
(a) infinity (b) equal to the kinetic energy of the proton

(c) less than the kinetic energy of the proton (d) greater than the kinetic energy of
the proton.
45. A stone is dropped from the top of a building. What happens theoretically to the de
Broglie wavelength of the stone as it falls?
(a) It increases (b) It decreases
(c) It remains constant (d) Cannot be predicted theoretically.
46. A proton, electron and a helium nucleus move with equal velocity. Rank their de Broglie
wavelengths from longest to shortest.
(a) Helium nucleus, proton, electron (b) Proton, electron, helium nucleus
(c) Helium nucleus, electron, proton (d) Electron, proton, helium
nucleus.
47. An electron is accelerated from rest, between two points at which the potentials are 20V
and 50V respectively. The de Broglie wavelength associated with the electron will be
(a) 2.74 Å (b) 2.24 Å (c) 1.94 Å (d) 1.73 Å.
48. An electron (mass = me) and a proton (mass = mp) are accelerated through the same
potential difference. The
ratio of their de Broglie wavelength (λe : λp) will be
(a) 1 (b) mp : me (c) √mp : √me (d) √me : √mp.
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49. Davisson-Germer experiment verifies
(a) photoelectric effect (b) Compton effect (c) wave-particle duality (d) Planck’s
radiation law.
50. Davisson-Germer experiment is related with
(a) interference (b) thermionic emission (c) phosphorescence (d) electron
diffraction.
51. The velocity with which a wave advances in a medium is called
(a) phase velocity (b) group velocity (c) wave velocity (d) critical velocity.
52. The velocity with which energy is transported through a medium is called
(a) phase velocity (b) group velocity (c) drift velocity (d) wave velocity.
53. If vg be the group velocity of the wave group representing a particle moving with
velocity v, then
(a) vg > v (b) v > vg (c) vg = v (d) vg = 1/v.
54. For a non-dispersive medium, the relation between phase velocity vp and group velocity
vg is
(a) vp > vg (b) vp ≤ vg (c) vp = vg (d) vp < vg.
55. If we measure the energy of a particle accurately then the uncertainty of the
measurement of time becomes
(a) 0 (b) π (c) π/2 (d) .
56. Heisenberg’s uncertainty relation is
(a) ∆𝑥∆𝑡 ≥ ℎ/2 (b) ∆𝒙∆𝒑𝒙 ≥ 𝒉/𝟐 (c) ∆𝑥∆𝑝𝑥 ≤ ℎ (d) ∆𝑥∆𝑝𝑥 = 1.
57. Which of the following pairs cannot be simultaneously measured?
(a) px, py (b) y, py (c) px, z (d) px, pz.
58. According to the uncertainty principle, which of the following statements is true?
(a) It is impossible to measure both the position and the velocity of a particle at the
same time
(b) It is impossible to measure both the mass and the velocity of a particle at the same time
(c) It is impossible to measure both the speed and the direction of a particle at the same
time
(d) It is impossible for science to make any meaningful predictions about nature
whatsoever.
59. Which of the following is NOT a correct consequence of the Heisenberg uncertainty
principle:
(a) The shorter the lifetime of an excited state of an atom, the less accurately can its energy
be measured
(b) An electron in an atom cannot be described by a well-defined orbit
(c) The momentum of an electron cannot be measured exactly
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(d) A harmonic oscillator possesses a zero-point energy.
60. Why doesn't the uncertainty principle affect our ability to follow the path of a baseball?
(a) The uncertainty principle applies only to subatomic particles
(b) The uncertainties in all the individual atoms within the baseball cancel each other out
(c) The uncertainties in the position and momentum of the baseball are so small in
comparison to its size and total momentum that they are unnoticeable
(d) The exclusion principle says that large objects are excluded from the consequences of
the uncertainty principle.
Module-2
61. The probability of finding a particle in space at time t is
(a) 0 (b) 1 (c) 1/2 (d) ∞.
62. The value of probability of an event cannot be
(a) 1 (b) negative (c) zero (d) positive.
63. If 𝜓(𝑥, 𝑡)is a normalized one dimensional wave function, then
∞ ∞ 1 ∞
(a) ∫−∞ 𝝍∗ 𝝍 𝒅𝒙 = 𝟏 (b) ∫−∞ 𝜓 ∗ 𝜓 𝑑𝑥 = (c) ∫−∞ 𝜓 ∗ 𝜓 𝑑𝑥 = 0 (d)
2
∞
∫−∞ 𝜓 ∗ 𝜓 𝑑𝑥 = ∞.
𝑑
64. For the function 𝛹 = √−5. 𝑒 −𝑘𝑥 ; The Eigen value corresponding to the operator is
𝑑𝑥
(a) −5𝑖𝑘 (b) −√5 𝑖𝑘 (c) √5 𝑘 (d) − 𝒌
65. The wave function of a moving particle for all values of x, y, z must be
(a) single-valued (b) multi-valued (c) infinite (d) zero.
66. Choose the function which can be a physically acceptable wave function:
𝟐 𝟐 2
(a) 𝜓 = 𝑎𝑥 (b) 𝜓 = √𝑥 (c) 𝝍 = 𝒆−𝒂 𝒙 (d) 𝜓 = 𝑒 𝑎 𝑥 .
67. Which of the following functions is acceptable as a wave-function of a one-
dimensional quantum mechanical system?
𝐴 𝟐
(a) 𝜓 = (b) 𝝍 = 𝑨𝒆−𝒙 (c) 𝜓 = 𝐴𝑥 2 (d) 𝜓 = 𝐴 𝑠𝑒𝑐(𝑥).
𝑥
68. Which one of the following is not an acceptable wave function of a quantum particle?
(a) 𝝍 = 𝒆𝒙 (b) 𝜓 = 𝑒 −𝑥 (c) 𝝍 = 𝒙𝒏 (d) 𝜓 = 𝑠𝑖𝑛 𝑥.
69. Schrödinger time independent wave equation is
̂ 𝜓 = 𝐸𝜓 2
(a) 𝐻 ̂ 𝜓 2 = 𝐸𝜓 2
(b) 𝐻 ̂1 =𝐸1
(c) 𝐻 ̂ 𝝍 = 𝑬𝝍.
(d) 𝑯
𝜓 𝜓
70. The 3-dimensional momentum operator is
ℏ 𝑖 𝑖 −1
(a) 𝛻⃗ (b) 𝛻⃗ (c) − 𝛻⃗ (d) (𝑖ℏ𝛻⃗) .
𝑖 ℏ ℏ
71. The eigenvalues of Hermitian operator are always
(a) imaginary (b) real (c) dependent upon the eigenvectors (d)
zero.

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72. When the Hamiltonian operator operates on a wave function
𝜓(𝑟), then the corresponding eigenvalue is
(a) potential energy of the system (b) kinetic energy of the system
(c) total energy of the system (d) none of these.
73. The wave functions of a one-dimensional box represent
(a) progressive waves (b) standing waves (c) progressive and standing waves (d)
mechanical waves.
74. The expected average of the momentum of a particle trapped in a box of length l is
ℎ ℎ
(a) (b) (c) 1 (d) 0.
𝑙 2𝜋𝑙
75. For a free particle in a cubical box, the degeneracy of the first excited state is
(a) two-fold (b) three-fold (c) six-fold (d) nine-fold.
76. The ground state energy of a particle moving in a one dimensional potential box of
length L is given by
2ℏ2 ℏ2 𝒉𝟐
(a) (b) (c) (d) 0.
8𝑚𝐿2 8𝑚𝐿2 𝟖𝒎𝑳𝟐
77. In a 1D potential box with ground state energy value 𝐸𝑔 , the energy difference between
two consecutive energy states 𝑛 and (𝑛 + 1) is
(a) 2𝑛𝐸𝑔 + 1 (b) (2𝑛 + 1) (c) (𝟐𝒏 + 𝟏)𝑬𝒈 (d) (𝑛 + 1)𝐸𝑔 .
78. A system with time independent potential is in an
energy state E. The wave function of this state is
(a) independent of time
(b) an exponentially decaying function of time
(c) a periodic function of time with time period proportional to E
(d) a periodic function of time with time period inversely proportional to E.
𝑑2
79. Which of the following functions are eigen functions of the operator ?
𝑑𝑥 2
𝑐
(a) 𝑐 𝑙𝑜𝑔 𝑥 (b) 𝑐𝑥 2 (c) (d) 𝒄𝒆−𝒎𝒙 .
𝑥
𝑑2
80. The eigen value of the eigen function 𝑒 𝑖𝑥 for the operator is
𝑑𝑥 2
(a) 1 (b) 0 (c) -1 (d) √1 + 𝑖.
81. The value of [𝑥̂, 𝑝̂𝑥 ] is
(a) 𝒊𝒉⁄𝟐𝝅 (b) 0 (c) -𝑖ℎ⁄2𝜋 (d) 1.
82. The communication bracket [𝑝̂𝑦 , 𝑦̂] is equal to
𝑖
(a) 𝑖ℏ (b) −𝒊ℏ (c) 𝑖ℏ2 (d) .
ℏ

𝜕𝑦
83. The value of [𝑥, ] is
𝜕𝑥
(a) -1 (b) 0 (c) 1 (d) 2.
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84. If the ground state energy of a particle moving in 1D potential box is 1eV, what would
be the energy of its 2nd excited state?
(a) 1 eV (b) 2 eV (c) 4 eV (d) 9 eV.
85. A particle moving in a 1D potential box. If the energy of its 1st excited state is 6 eV, what
is the value of its ground state energy?
(a) 6 eV (b) 3 eV (c) 1.5 eV (d) 0.67 eV.
86. If E1 is the energy of the ground state of an 1D potential box of length l and E2 be the
energy of the ground state when the length of the box is halved, then
(a) E2 = E1 (b) E2 = 2E1 (c) E2 = E1/4 (d) E2 = 4E1.
87. For a free particle in a cubical box, the degree of degeneracy of the state having
quantum number (1,2,3) is
(a) 1 (b) 3 (c) 6 (d) 9.
88. For a free particle in a cubical box, the degree of degeneracy of the state having
quantum number (2,2,3) is
(a) 1 (b) 3 (c) 6 (d) 12.
ℎ2
89. The eigen value of the energy of a particle in a cubical box of dimension a is [11 ( )].
8𝑚𝑎2
The quantum number of the state are
(a) (3, 1, 1) (b) (3, 0, 1) (c) (2, 2, 2) (d) (1, 1, 1).

Module-3
90. Dielectrics are substances which are
(a) semiconductor (b) conductor (c) insulator (d)
none of these.
91. Which of the following cannot be considered as polar molecule?
(a) H2O (b) O2 (c) CO2 (d) HCl.
92. Which of the following cannot be considered as nonpolar molecule?
(a) H2 (b) HCl (c) O2 (d) Cl2.
93. If 𝐸⃗ be the applied electric field, 𝑃⃗ be the polarization vector, 𝛼 be the atomic
polarizability, N be the number of polarized molecules per unit volume and 𝑝 be the
dipole moment of each molecule, then which of the following relation is not true?
(a) 𝑝 = 𝛼𝐸⃗ (b) 𝑃⃗ = 𝑁𝛼𝐸⃗ (c) 𝐸⃗ = 𝛼𝑃⃗. (d) ⃗𝑷
⃗ = 𝜶𝑬
⃗⃗ .
94. If 𝑃⃗ represents the polarization vector then 𝛻⃗ . 𝑃⃗ = −𝜌, where 𝜌 is the density of
(a) free charge (b) bound charge
(c) free charge at the boundary of the dielectric (d) sum of free and bound charge.
95. The electric dipole moment of a particle (atom or
molecule) per unit polarizing electric field is termed as

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(a) polarization (b) polarizability (c) net dipole moment (d)
susceptibility.
96. The electrical conductivity of an insulator is zero due to the absence of
(a) bound electrons (b) free electrons (c) protons (d) neutrons.
97. The change in the total charge inside a dielectric before and after polarization remains
(a) negative (b) positive (c) unchanged (d) unity.
98. The electronic polarizability (𝛼𝑒 ) of an atom is related to its radius (R) as
(a) 𝜶𝒆 ∝ 𝑹𝟑 (b) 𝛼𝑒 ∝ 𝑅2 (c) 𝛼𝑒 ∝ 𝑅 (d) 𝛼𝑒 ∝ 𝑅0 .
99. The susceptibility (𝜒𝑒 ) and the dielectric constant (k) are related by the expression
(a) 𝑘 = 1 − 𝜒𝑒 (b) 𝒌 = 𝟏 + 𝝌𝒆 (c) 𝜒𝑒 = 1 + 𝑘 (d) 𝜒𝑒 = 1 − 𝑘.
100. The electronic polarizability for a rare gas atom is
𝜀𝑟 −1 (𝜺𝒓 −𝟏) 𝑁
(a) 𝛼𝑒 = (b) 𝜶𝒆 = 𝜺𝟎 (c) 𝛼𝑒 = 𝑁(𝜀𝑟 − 1) (d) 𝛼𝑒 = (𝜀 .
𝜀0 𝑁 𝑵 𝑟 −1)

101. The ionic polarizability is

(a) dependent on temperature (b) independent on temperature
(c) dependent on current density (d) dependent on the concentration of ions.
102. Which of the following statement is true?
(a) Orientational polarization decreases with rise in temperature
(b) Orientational polarization increases with rise in temperature
(c) Orientational polarization does not depend on temperature
(d) Orientational polarization occurs for nonpolar molecules.
103. The total polarization of a polyatomic gas is
𝜇
(a) 𝑃⃗ = 𝑁(𝛼𝑒 + 𝛼𝑖 )𝐸⃗ (b) 𝑃⃗ = 𝑁 (𝛼𝑒 + 𝛼𝑖 + ) 𝐸⃗
𝑘𝑇
𝝁𝟐 𝑁𝜇𝐸⃗
⃗⃗ = 𝑵 (𝜶𝒆 + 𝜶𝒊 +
(c) 𝑷 ⃗⃗
)𝑬 (d) 𝑃⃗ =
𝟑𝒌𝑻 𝑘𝑇
104. Local electric field is calculated by using the method suggested by
(a) Weiss (b) Curie (c) Lorentz (d) Coulomb.
105. On placing a dielectric in an electric field, the field strength
(a) increases (b) decreases (c) remains constant (d) reduces
to zero.
106. The dielectric constant of air is practically taken as
(a) zero (b) unity (c) more than unity (d) less than unity.
107. To make a good capacitor, it is wise to select a dielectric material with
(a) low permittivity (b) high permittivity
(c) permittivity same as that of air (d) permittivity slightly higher than that of air.
108. In absence of any battery, when a dielectric slab is introduced between two plates of
a parallel-plate capacitor, the potential difference between the plates

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(a) increases (b) decreases (c) remains unchanged (d)
becomes zero.
109. The unit of the relative permittivity is
(a) F/m (b) Fm2 (c)C/m2 (d) no unit.
110. In absence of any applied electric field, the positive and negative charges of a polar
molecule
(a) coincide with each other (b) are slightly separated from each other
(c) exchange charge with each other (d) have different amount of charges.
111. At moderate temperature T, the electronic polarizability is
(a) directly proportional to T (b) inversely proportional to T
(c) directly proportional to T2 (d) independent of T.
112. Select the correct relation.
⃗ = 𝜀0 (𝜀𝑟 − 1)𝐸⃗
(a) 𝐷 (b) 𝐸⃗ = 𝜀0 (𝜀𝑟 − 1)𝑃⃗
(c) ⃗𝑷
⃗ = 𝜺𝟎 (𝜺𝒓 − 𝟏)𝑬⃗⃗ ⃗ = 𝜀0 (𝜀𝑟 − 1)𝑃⃗.
(d) 𝐷
113. In presence of an applied electric field, monoatomic gases exhibit only
(a) electronic polarization (b) ionic polarization
(c) orientational polarization (d) space-charge polarization.
114. In presence of high amount of electric field, the dielectric breakdown of a material
occurs when
(a) the atoms get ionized
(b) positive and negative charges are slightly separated from each other
(c) the torque due to the field rotates the intrinsic dipoles
(d) intrinsic dipoles are randomly oriented.
115. Which of the following statement is not correct?
(a) Electronic polarizability is proportional to atomic volume
(b) Orientational polarization depends on the temperature
(c) Electronic polarization occurs for both polar and nonpolar molecules
(d) Torque due to applied electric field is developed for each dipole in case of Orientational
polarization.
116. The dielectric constant of an ideal conductor is
(a) 0 (b) 1 (c) -1 (d) infinity.
117. The electronic polarizability of Ar atom having radius 2 × 10-10 m is
(a) 8.9 × 10-32 F.m2 (b) 2.8 × 10-40 F.m2
(c) 8.9 × 10-40 F.m2 (d) 2.8 × 10-32 F.m2.

Module-4
118. In electromagnetic induction
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(a) heat energy is converted into electrical energy
(b) electrical energy is converted into magnetic energy
(c) magnetic energy is converted into electrical energy
(d) mechanical energy is converted into magnetic energy.
119. Steady current in a conductor produces
(a) static electric field (b) static magnetic field
(c) time varying electric field (d) time varying magnetic field.
120. The equation of continuity in a steady charge distribution is
(a) ⃗𝜵
⃗ .𝑱 = 𝟎 (b) 𝛻⃗ × 𝐽 = 0 (c) 𝛻⃗ . 𝐽 = 𝜌 (d) 𝛻⃗ × 𝐽 = 𝜌.
121. The total number of magnetic field lines passing through an area is termed as
(a) voltage (b) e.m.f. (c) magnetic flux density (d) magnetic flux.
122. The magnitude of the induced e.m.f. in a conductor depends on the
(a) flux density of the magnetic field only (b) area of the coil only
(c) amount of flux linkages (d) rate of change of flux-linkages.
123. The direction of induced e.m.f. can be found by
(a) Laplace’s law (b) Newmann’s law (c) Lenz’s law (d) Fleming’s right
hand rule.
124. The law that the induced e.m.f. and current always oppose the cause producing them
is due to
(a) Coulomb’s law(b) Newmann’s law (c) Lenz’s law (d) Ampere’s law.
125. Lenz’s law of electromagnetic induction is as per law of conservation of
(a) angular momentum (b) electromotive force (c) charge (d) energy.
126. Which of the following statements is not correct?
(a) Whenever the amount of magnetic flux linked with a circuit changes, an emf is induced
in circuit.
(b) The induced emf lasts so long as the change in magnetic flux continues.
(c) The direction of induced emf is given by Lenz’s law.
(d) Lenz’s law is a consequence of the law of conservation of charges.
127. The north pole of a bar magnet is rapidly introduced into a solenoid at one end (say
A). Which of the following statements correctly depicts the phenomenon taking place?
(a) No induced emf is developed.
(b) The end A of the solenoid behaves like a south pole.
(c) The end A of the solenoid behaves like north pole.
(d)The end A of the solenoid acquires positive potential.
128. An e.m.f is produced in a coil, which is not connected to an external voltage source.
This is not due to
(a) the coil being in a time varying magnetic field.
Page 12 of 36
(b) the coil moving in a time varying magnetic field.
(c) the coil moving in a constant magnetic field.
(d) the coil is stationary in external spatially varying magnetic field, which does not
change with time.
129. Which of the following can be treated as integral form of Faraday’s law?
𝑑
(a) ∮ 𝐸⃗ . 𝑑𝑙 = − ∫𝑆 𝐵
⃗ . 𝑑𝑆 (b) ∮ 𝐸⃗ . 𝑑𝑙 = ⃗ . 𝑑𝑆
∫ 𝐵
𝑑𝑡 𝑆
𝒅 𝑑
⃗⃗ . 𝒅𝒍 = −
(c) ∮ 𝑬 ∫ 𝑩 ⃗
⃗⃗ . 𝒅𝑺 ⃗ . 𝑑𝑆 =
(d) ∫𝑆 𝐵 ∮ 𝐸⃗ . 𝑑𝑙 .
𝒅𝒕 𝑺 𝑑𝑡
130. Which of the following can be treated as differential form of Faraday’s law?
⃗
𝜕𝐵 ⃗⃗
𝝏𝑩 𝜕𝐸⃗ 𝜕𝐸⃗
⃗ × 𝐸⃗ =
(a) ∇ ⃗ ×𝑬
(b) 𝛁 ⃗⃗ = − ⃗ ×𝐵
(c) ∇ ⃗ =− ⃗ ×𝐵
(d) ∇ ⃗ = .
𝜕𝑡 𝝏𝒕 𝜕𝑡 𝜕𝑡
131. Which of the following cannot be treated as Faraday’s law?
⃗
𝜕𝐵 ⃗
𝜕𝐵 𝑑𝜑𝐵
⃗ × 𝐸⃗ = −
(a) ∇ (b) ∮ 𝐸⃗ . ⃗⃗⃗
𝑑𝑙 = − ∫𝑆 . 𝑑𝑆 (c) ℇ = − (d) ⃗ ×𝑬
∫𝑺 (𝛁 ⃗ =
⃗⃗ ). 𝒅𝑺
𝜕𝑡 𝜕𝑡 𝑑𝑡
⃗⃗
𝝏𝑩
∫𝑺 ⃗.
. 𝒅𝑺
𝝏𝒕
132. The equation of continuity essentially represents
(a) conservation of mass (b) conservation of charge
(c) conservation of potential (d)conservation of force.
133. The inconsistency in Ampere’s law was removed by
(a) Coulomb (b) Maxwell (c) Faraday (d) Lenz.
134. Which of the following is not true for displacement current?
(a) Displacement current is a current only in the sense that it produces a magnetic field.
(b) Displacement current obeys Ohm’s law.
(c) Displacement current serves the purpose to make the total current continuous across
the discontinuity in conduction current.
(d) Displacement current exists even in the free space between the plates of a capacitor.
135. The concept of displacement current was introduced by
(a) Ampere (b) Maxwell (c) Faraday (d) Lenz.
136. Ampere’s circuital law is valid when
𝜕𝜌 𝝏𝝆 𝜕𝜌 𝜕𝜌
(a) = 𝑘𝑡 (b) =𝟎 (c) = constant (d) = ∞.
𝜕𝑡 𝝏𝒕 𝜕𝑡 𝜕𝑡
137. Magnetic field in vacuum can be created by
(a) steady current(b) conduction current (c) transient current (d) displacement
current.
138. Displacement current can produce
(a) chemical effect (b) magnetic field (c) Joule heating (d) Peltier effect.
139. Displacement current appears due to
(a) positive charges (b) negative charges

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(c) time varying electric field (d) time varying magnetic field.
140. The north pole of a long bar magnet was pushed slowly into a short solenoid
connected to a short galvanometer. The magnet was held stationary for a few seconds
with the north pole in the middle of the solenoid and then withdrawn rapidly. The
maximum deflection of the galvanometer was observed when the magnet was
(a) moving towards the solenoid (b) moving into the solenoid
(c) at rest inside the solenoid (d) moving out of the solenoid.

Module-5
141. Which of the following equations indicates the non-existence of magnetic monopole?
⃗ . 𝐸⃗ = 𝜌 ,
(a) ∇ ⃗ . ⃗𝑩
(b) 𝛁 ⃗ = 𝟎,
𝜀0
⃗
𝜕𝐵 𝜕𝐸⃗
⃗ × 𝐸⃗ = −
(c) ∇ , ⃗ ×𝐵
(d) ∇ ⃗ = 𝜇0 𝐽 + 𝜇0 𝜀0 .
𝜕𝑡 𝜕𝑡
⃗
⃗ = 𝐽𝑐 + 𝜕𝐷 represents
142. The equation 𝛻⃗ × 𝐻
𝜕𝑡
(a) Gauss’s law (b) Faraday’s law
(c) Ampere’s law (d) Modified Ampere’s law.
143. In a perfect insulator, Maxwell’s fourth equation becomes
⃗ ⃗
(a) ∇ ⃗ = 𝜇0 𝐽 + 𝜕𝐷
⃗ ×𝐻 ⃗ = 𝐽 + 𝜇0 𝜕𝐷
⃗ ×𝐻
(b) ∇
𝜕𝑡 𝜕𝑡
⃗
𝜕𝐷 ⃗⃗
𝝏𝑫
⃗ ×𝐵
(c) ∇ ⃗ = ⃗ × ⃗𝑯
(d) 𝛁 ⃗⃗ = .
𝜕𝑡 𝝏𝒕
144. In a perfect conductor, Maxwell’s fourth equation becomes
⃗
(a) ∇ ⃗ = 𝐽 + 𝜇0 𝜕𝐷
⃗ ×𝐻 ⃗ × ⃗𝑯
(b) 𝛁 ⃗⃗ = 𝑱
𝜕𝑡
⃗ ×𝐻
(c) ∇ ⃗ = 𝜇0 𝐽 ⃗ ×𝐵
(d) ∇ ⃗ = 𝐽.

145. Which of the following cannot be considered as Maxwell’s fourth equation?

⃗ ⃗
(a) 𝛁 ⃗ = 𝝁𝟎 𝑱 + 𝜺𝟎 𝝏𝑬
⃗ × ⃗𝑩 ⃗ = 𝐽 + 𝜀0 𝜕𝐸
⃗ ×𝐻
(b) ∇
𝝏𝒕 𝜕𝑡
𝜕𝐸⃗ 𝜕𝐸⃗
⃗ . 𝑑𝑙 = 𝜇0 ∫ 𝐽. 𝑑𝑆 + 𝜇0 𝜀0 ∫
(c) ∮ 𝐵 ⃗ . 𝑑𝑙 = ∫ 𝐽. 𝑑𝑆 + 𝜀0 ∫
. 𝑑𝑆 (d) ∮ 𝐻 . 𝑑𝑆.
𝑆 𝑆 𝜕𝑡 𝑆 𝑆 𝜕𝑡
146. In case of time invariant fields, Maxwell’s fourth equation becomes
𝜕𝐸⃗ 𝜕𝐸⃗
⃗ ×𝐵
(a) ∇ ⃗ = 𝜇0 𝐽 + 𝜇0 𝜀0 ⃗ ×𝐵
(b) ∇ ⃗ = 𝜇0 𝜀0
𝜕𝑡 𝜕𝑡
⃗ × ⃗𝑩
(c) 𝛁 ⃗ = 𝝁𝟎 𝑱 ⃗ ×𝐵
(d) ∇ ⃗ =𝐽
147. Example of electromagnetic wave is
(a) sound wave (b) -wave
(c) matter wave (d) stationary wave in stretched string.
148. Electromagnetic wave is produced due to simultaneous action of

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(a) steady 𝐸⃗ and 𝐻⃗ (b) time varying 𝐸⃗ and steady 𝐻⃗
(c) steady 𝐸⃗ and time varying 𝐻
⃗ (d) time varying 𝑬 ⃗⃗ and 𝑯
⃗⃗⃗ .
149. The velocity of electromagnetic wave in free space is
(a) equal to velocity of light (b) greater than the velocity of light
(c) less than the velocity of light (d) zero.
150. The velocity of plane electromagnetic wave in free space is given by
1 𝟏 𝜇0
(a) (b) (c) (d) 𝜇0 𝜀0 .
𝜇 0 𝜀0 √ 𝝁𝟎 𝜺𝟎 𝜀0

151. The direction of propagation of electromagnetic wave is

(a) along the direction of 𝐸⃗ ⃗
(b) along the direction of 𝐵
⃗⃗ × 𝑩
(c) along the direction of 𝑬 ⃗⃗ ⃗⃗ × 𝑬
(d) along the direction of 𝑩 ⃗⃗ .
152. Which of the following is true in a plane electromagnetic wave?
(a) 𝐸⃗ × 𝐵
⃗ =0 (b) 𝐸⃗ ∥ 𝐵⃗ ⃗⃗ ⊥ 𝑩
(c) 𝑬 ⃗⃗ ⃗ ×𝐵
(d) 𝑘 ⃗ = 0.
153. The relation between the electric field and the magnetic field is
⃗ ×𝑬
(a) 𝒌 ⃗⃗ = 𝝁𝟎 𝝎𝑯
⃗⃗⃗ ⃗ ×𝐻
(b) 𝑘 ⃗ = 𝜀0 𝜔𝐸⃗ ⃗ × 𝐸⃗ = 𝜀0 𝜔𝐻
(c) 𝑘 ⃗ (d) ⃗ ×𝐻
𝑘 ⃗ =
−𝜇0 𝜔𝐸⃗ .
154. In an electromagnetic wave in free space, the electric and magnetic fields are
(a) parallel to each other (b) perpendicular to each other
(c) inclined at an angle (d) inclined at an obtuse angle.
155. The relation between the amplitudes of electric field E0 and the magnetic field H0 in
a medium through which the electromagnetic wave propagates with a speed v is given
by
𝐸0 𝐻0 𝑬𝟎 𝐻0
(a) 𝐻0 = (b) 𝐸0 = (c) 𝑯𝟎 = (d) 𝐸0 = .
𝑣 𝑣 𝝁𝒗 𝜇𝑣

156. The value of a for which 𝐴 = 𝑖̂2𝑎𝑥 + 𝑗̂2𝑦 + 𝑘̂4𝑧 is solenoidal is equal to
(a) 2 (b) 3 (c) -3 (d) 1.
157. A vector space is represented by 𝐴 = 𝑎2 𝑥 ̂𝑖 + 𝑎𝑦 𝑗̂ − 6𝑧𝑘̂ , for what value(s) of 𝑎, it
may represent Magnetic fields.
158. (a) 1, 6 (b) -2, 3 (c) 2, -3 (d) -2, -3
159. An EM wave is propagating in free space. If the electric field is represented by 𝐸⃗ =
𝐸0 𝑒 𝑖(𝑘𝑦−𝜔𝑡) 𝑘̂, then the magnetic field is along
(a) X-direction (b) Y-direction (c) Z-direction (d) negative X-
direction.
160. An electromagnetic wave is propagating through a region of vacuum, which does not
contain any charge or current. If the electric vector is given by 𝐸⃗ = 𝐸0 𝑒 𝑖(𝑘𝑥−𝜔𝑡) 𝑗̂, then
the magnetic vector is
(a) in the X-direction (b) in the Y-direction
Page 15 of 36
(c) in the Z-direction (d) rotating uniformly in the XY plane.

Module-6
161. Spontaneous emission rate depends on
(a) the number of atoms in ground state
(b) the number of atoms in excited state
(c) energy density 𝑢(𝜈) of excited state
(d) both (b) and (c).
162. Which of the following relation is correct?
(a) atom* + photon → atom + photon (b)atom* → atom + photon
(c) atom* → atom + 2 photons (d) atom* + 2 photons → atom + photon.
163. In lasing action, the spontaneous emission does not depend on
(a) the number of atoms present in the excited state
(b) the intensity of the incident light
(c) both of (a) and (b)
(d) none of these.
164. Einstein theoretically proved the existence of
(a) spontaneous emission (b) thermal emission
(c) stimulated emission (d) stimulated absorption.
165. Emission of photon due to transition of an electron from higher to lower energy level
caused by an external energy is known as
(a) stimulated absorption (b) spontaneous emission
(c) stimulated emission (d) population inversion.
𝐴21
166. The ratio of Einstein’s A and B co-efficients, i.e. is proportional to
𝐵21
(a) ν (b) ν2 (c) ν3 (d) ν4.
167. If𝑁1 ,𝑁2 and𝑁3 be the number of atoms per unit volume in the energy states𝐸1 ,𝐸2 and
E3 (𝐸3 > 𝐸2 > 𝐸1 ) respectively, then the condition for population inversion between𝐸2

and 𝐸3 is
(a)𝑁2 = 𝑁3 (b)𝑁3 > 𝑁1 (c)𝑁3 > 𝑁2 (d)𝑁2 > 𝑁1 .
168. The population inversion process is observed due to the existence of
(a) ground state (b) any excited state (c) first excited state (d) metastable
state.
169. For Laser action to occur, the medium used must have at least
(a) 2 energy levels (b) 4 energy levels (c) 3 energy levels (d) one energy
level.
170. Which of the following schemes does not produce lasing action?

Page 16 of 36
(a) Two level scheme (b) There level scheme (c) Four level scheme (d) Five level
scheme.
171. Two different laser sources can produce sustained interference because laser is
(a) highly coherent (b) incoherent (c) highly intense (d) highly
directional.
172. A laser requires mirrors because they
(a) invert the population density of atoms (b) provide optical feedback
(c) initiate the pumping process (d) determine the wavelength at which
lasing occurs.
173. The first laser invented by Maiman was
(a) Ruby laser (b) He-Ne laser (c) CO2 laser (d) Nd-YAG laser.
174. An example of pulsed laser is
(a) Ruby laser (b) He-Ne laser (c) Argon ion laser (d) Nitrogen
laser.
175. In Ruby Laser, the host crystal is
(a) Al2O3 ` (b) MnO2 (c) CaCO3 (d) Al2SO4.
176. In Ruby laser the active medium is
(a) solid (b) liquid (c) gas (d) a solid and gas mixture.
177. The colour of the laser output in case of ruby laser is
(a) violet (b) blue (c) red (d) green.
178. In a ruby laser population inversion is achieved by
(a) chemical reactions (b) inelastic collision between atoms
(c) optical pumping (d) applying strong electric field.
179. The activator action in Ruby laser is
(a) Aluminium (b) Oxygen (c) Gron (d) Chromium.
180. The wavelength of ruby laser is
(a) 694.3 nm (b) 632.8 nm (c) 600 nm (d) 550 nm.
181. The wavelength of He-Ne laser is
(a) 694.3 nm (b) 632.8 nm (c) 600 nm (d) 550 nm.
182. In He-Ne laser, Ne atom obtains energy
(a) on collision with He atom (b) from chemical reaction
(c) from optical pumping (d) from electrical pumping.
183. In He-Ne laser, the laser light emits due to the transition from
(a) 3s → 2p (b) 3s → 3p (c) 2s → 2p (d) 4s → 3p.
184. The Nd:YAG laser is an example of
(a) three-level solid-state laser (b) four-level solid-state laser
(c) three-level gas laser. (d) four-level gas laser.
Page 17 of 36
185. Multimode step index fiber has ___________
(a) large core diameter & large numerical aperture
(b) large core diameter and small numerical aperture
(c) small core diameter and large numerical aperture
(d) small core diameter & small numerical aperture.
186. The performance characteristics of multimode graded index fibers are ___________
(a) better than multimode step index fibers (b) same as multimode step index
fibers
(c) lesser than multimode step index fibers (d) negligible.
187. The fibers mostly not used nowadays for optical fiber communication system are
___________
(a) single mode fibers (b) the intensity of the incident light
(c) coaxial cables (d) multimode graded index fibers.
188. Which type of dispersion occurs due to difference in the propagation times of light
rays that take different paths down a fiber?
(a) Inter-modal dispersion (b) Delay dispersion
(c) Material dispersion (d) Waveguide dispersion.
189. Which type of fiber has the highest amount of intermodal dispersion?
(a) Step-index single mode fiber (b) Step-index multimode fiber
(c) Graded-index single mode fiber (d) Graded-index multimode fiber.
190. Which one of the following is not a guided medium of transmission?
(a) Fiber–Optic cable (b) Coaxial cable (c) Twisted-pair cable (d) The
atmosphere.
191. In optical fiber, the inner layer is _________ and the outer layer is ________________ .
(a) core, cladding (b) cladding, core (c) laser, detector (d) detector, laser.
192. Optical fibers are highly immune to electromagnetic interference because
information is carried by
(a) light (b) electrical signal (c) magnetic signal (d) acoustic signal.
193. In an optical fiber, the fiber core ________ the cladding.
(a) is less dense than (b) is denser than
(c) has the same density as (d) is another name for.
194. The light is propagated within the fiber core by the phenomenon of
(a) total internal reflection at core-cladding interface
(b) refraction at core-cladding interface
(c) total internal reflection at the outer surface of the cladding
(d) total internal reflection at air-core interface.
195. The spreading of pulse width in optical fiber is due to
Page 18 of 36
(a) scattering (b) total internal reflection (c) dispersion (d)
diffraction.
196. Dispersion is maximum in _______ optical fibers.
(a) step-index single mode (b) step-index multimode
(c) graded-index single mode (d) graded-index multimode.
197. In an optical fiber, the concept of numerical aperture is applicable in describing the
ability of
(a) light collection (b) light scattering
(c) light dispersion (d) light polarization.

Group-B
Module-1
1. Show graphically how the energy density varies with wavelength of black body
radiation. What would be the effect of temperature of the body on this characteristic?
State Wien’s displacement law on the basis of the temperature dependence of the
energy density. [Module 1/CO1/ Remember- LOCQ] 2+1+2
2. (a) State Kirchoff’s law of blackbody radiation. Prove that good absorbers are good
radiators too [Module 1/CO1/ Remember- IOCQ] 1+2
3. Show graphically how the energy density versus frequency plot of blackbody radiation
is changed if the temperature is increased. State Wien’s displacement theory in this
context. [Module 1/CO1/ Understand, Remember- LOCQ] 3+2
4. State clearly, explaining all the terms, Planck’s law, Rayleigh Jeans law and Wien’s law
for radiation. Select the two limits at which Planck’s formula reduces to the other two.
[Module 1/CO1/ Remember, Understand- IOCQ] 3+2
5. Write down Planck’s law of frequency distribution of Black body radiation. Convert the
expression into the wavelength distribution and find out the limiting form of this
distribution at very small wavelengths. 1+2+2
[Module 1/CO1/ Remember, Understand- IOCQ]
6. A wire of length 1 m and radius 1 mm is heated by electric current to produce 1 kW of
radiant power. Treating the wire as a perfect blackbody and ignoring any end effect,
estimate the temperature of the wire. [Given: 𝜎 = 5.67 × 10−8 Wm−2 k −4 ] 5
[Module 1/CO1/ Apply- HOCQ]
7. Estimating the average human body to have a total surface area of 1.5 m2 and skin
temperature of 30˚C, find the energy that one would lose in space in 30 sec (Assume the
emissivity of the skin surface to be 0.9). [Given: 𝜎 = 5.67 × 10−8 Wm−2 k −4 ] 5
[Module 1/CO1/ Apply- HOCQ]

Page 19 of 36
8. Compute the wavelength at which a room temperature (T = 27˚C) object emits the
maximum thermal radiation. Find the temperature to what we must heat the object
until its peak thermal radiation is in the red region of the spectrum (λ = 650 nm)? How
many times more thermal radiation will the body at the higher temperature emit with
respect to the one at the lower temperature? [Given: Wien’s constant = 2.9 × 10−3 mK]
[Module 1/CO1/ Apply- IOCQ] 2+2+1
9. In converting electrical energy to light energy, a 50W incandescent bulb operates at
about 70% efficiency. Assuming that all light is green (555 nm), determine the number
of photons emitted per second by the bulb. [Module 1/CO1/ Apply- IOCQ] 5
10. (b) Explain why Compton Effect cannot be observed with visible light but can be
observed due to X-rays. [Module 1/CO1/ Understand-LOCQ, IOCQ] 2
11. Explain why the Compton Effect cannot be observed with (i) visible light, (ii)
macroscopic bodies. [Module 1/CO1/ Understand-LOCQ, IOCQ] 2+3
12. X-ray of wavelength 0.2 Å is scattered by a stationary particle of Compton wavelength
of 2.43 pm at an angle 45o. Calculate the wavelength of the scattered ray and the kinetic
energy of the recoiled particle. [Module 1/CO1/ Apply- IOCQ] 2+3
13. A monochromatic radiation of wavelength 2.5 × 10−12 m is incident on free stationary
electron. Compute the wavelength of the beam which is scattered directly backwards.
Also estimate the energy gained by the scattered electron. 2+3
[Module 1/CO1/ Apply- IOCQ]
14. Molybdenum K X-rays of wavelength 0.711 Å are allowed to suffer Compton scattering
from a carbon target. Calculate the wavelength of the photon scattered at an angle 45o.
Also estimate the kinetic energy and the direction of the recoil electron.
[Module 1/CO1/ Apply- IOCQ] 2+3
15. Define phase velocity of a wave and show that a particle in motion cannot be
represented by a single wave. Hence define group velocity. 1+2+2
[Module 1/CO1/ Apply- IOCQ]
16. Calculate the de Broglie wavelength of a baseball of mass 1 kg moving at a speed of 10
m/s. Discuss the reason why its wave nature cannot be observed. 3+2
[Module 1/CO1/ Apply, Analyse- IOCQ]
17. A free electron has de Broglie wavelength 2 pm. Find the phase and group velocities of
its de Broglie wave. [Module 1/CO1/ Apply- IOCQ] 3+2
Module-2
18. A particle is in a cubic box with infinitely hard walls whose edges are L units long. The
𝑛𝜋𝑥 𝑛𝜋𝑦 𝑛𝜋𝑧
wave function is given by 𝜓(𝑥, 𝑦, 𝑧) = 𝐴 𝑠𝑖𝑛 ( ) 𝑠𝑖𝑛 ( ) 𝑠𝑖𝑛 ( ). Find the value of
𝐿 𝐿 𝐿
the ground state and first excited energy eigenvalues. Explain if they are non-
degenerate. [Module 2/CO2/ Apply, Analyse- IOCQ] 3+2
Page 20 of 36
 𝑞𝑥
19. (a) Show that the wave function 𝛹(𝑥) = 𝐴 𝑐𝑜𝑠 ( ) is an eigenfunction of kinetic energy.
ℎ
2
b) What is the corresponding eigenvalue? 3
[Module 2/CO2/Understand, Apply-IOCQ]
20. A particle is moving along Y-axis has the wave function
𝜓(𝑦) = 𝛽𝑦 2 between y = 0 and y = 2, and 𝜓(𝑦) = 0 elsewhere.
Find the expectation value 〈𝑦〉 of the particle’s position. 5
[Module 1/CO1/ Apply- IOCQ]
21. Find out the energy difference between the ground state and first excited state of an
electron moving in one dimensional potential box of length 1.5Å. Also find the frequency
of the emitted radiation due to the transition of electron in between the two states.
[Module 2/CO2/ Apply- IOCQ] 2+3
22. An electron is constrained to move in a one-dimensional box of length 1.0 Å. Calculate
the first three energy eigen values and the corresponding deBroglie wavelengths.
[Module 2/CO2/ Apply- IOCQ] 2+3
23. An electron is constrained to move within a one-dimensional box of length 2 Å,
(a) Find out the minimum energy that the electron can possess
(b) Calculate the wavelength of emitted radiation due to the transition of electrons from
its 2nd excited state to the ground state. 2+3
[Module 1/CO1/Understand, Apply-LOCQ, IOCQ]
24. Show that 𝜓(𝑥) = 𝐴𝑒 2𝑖𝑥 and 𝜓(𝑥) = 𝐴𝑒 −2𝑖𝑥 are degenerate wave functions for a free
particle. Find out the energy eigenvalue. [Module 2/CO2/ Apply- IOCQ] 2+3
25. The energy of an electron constrained to move in a one-dimensional box of length 4.0 Å
is 9.664×10-17 J. Calculate the order of the excited state. 5
[Module 2/CO2/ Apply- IOCQ]

Module-3
26. Discuss the various types of polarization. 2.5
[Module 3/CO3/Understand-LOCQ]
27. Define the atomic polarizability of a dielectric material. State its unit in SI system. 2.5
[Module 3/CO3/Remember-LOCQ]
28. Explain polarization within a dielectric medium. 2.5
[Module 3/CO3/ Understand-LOCQ]
29. The atomic polarizability of He is 0.18×10-40 F.m2 and density is 2.6×1025 atoms/m3.
Calculate the induced dipole moment per unit volume of He gas if it is placed in a field
of 6000 V/cm. (b) Also calculate the separation between the centers of positive and
negative charges. [Module 3/CO3/ Apply- IOCQ] 2.5+2.5
Page 21 of 36
30. Establish a relation between electric displacement vector, polarization and electric field
for a dielectric. [Module 3/CO3/ Understand-LOCQ] 2.5
31. If an electric field of 105 V/m is applied on a dielectric material of electrical
susceptibility 0.4, calculate the polarization vector and hence the electric displacement
vector for the material. [Module 3/CO3/ Understand-LOCQ] 2.5
32. (a) Define the atomic polarizability of a dielectric material. State its unit in SI system.
1+1
(b) Calculate the bound volume charge density at the point (2,1,3) in a dielectric
material given the polarization vector 𝑃⃗ = 2𝑥 2 𝑖̂ + 3𝑦 3 𝑗̂ − 4𝑧 2 𝑘̂ (SI unit) 3
[Module 3/CO3/ Remember, Apply- LOCQ, IOCQ]
33. Define orientational polarization. How does it depend on the temperature of the
dielectric? [Module 3/CO3/ Remember, Understand-LOCQ] 1.5+1
34. Which types of polarization occurs in case of polyatomic gases? Write down the total
polarizability in this case. [Module 3/CO3/ Remember-LOCQ] 1+1.5
Module-4
35. State and explain one application of Faraday’s law in practical life. 2.5
[Module 4/CO4/Remember-LOCQ]
36. Explain the significance of negative sign in Faraday-Lenz law. 2.5
37. Write down Ampere’s law. Discuss the inconsistency of Ampere’s law. How Maxwell
modified this law? and write down the Modified Ampere’s law. 1+2+(1+1)
[Module 4/CO4/Remember, Understand-IOCQ]
38. “Ampere’s Circuital Law is bound to fail for non-steady current” – Justify this statement.
[Module 4/CO4/ Analyse-IOCQ] 2.5
39. The magnetic flux (𝜑 in Weber) in a closed circuit of resistance 10 Ω varies with time (t
in sec) as 𝜑 = 5𝑡 2 − 7𝑡 + 3. Calculate the induced current at t = 0.2 sec. 2.5
[Module 4/CO4/ Apply-IOCQ]
40. A parallel-plate capacitor with circular plates of radius 5 cm is charged at such a uniform
rate that the rate of change of the electric field 𝑑𝐸⁄𝑑𝑡 is 4×1012 V/ms. Compute the
displacement current in that capacitor. [Module 4/CO4/ Apply-IOCQ] 2.5
41. In free space, the electric field intensity is given by 𝐸 = 10 cos(108 𝑡 − 20𝑥) V/m.
Calculate the displacement current density. [Module 4/CO4/ Apply-IOCQ] 2.5
Module-5
42. Show that in a charge free, current free region the electric field vector satisfies a wave
equation. Identify the velocity of this wave. 4+1
[Module 5/CO5/ Understand-IOCQ]

Page 22 of 36
43. A plane electromagnetic wave whose electric field is given by 𝐸 = 24 sin(107 𝜋𝑡 −
0.5𝜋𝑧) V/m travels in a perfect dielectric. Find its velocity and the corresponding
magnetic field. [Module 5/CO5/ Apply-IOCQ] 2+3
44. (a) Define ‘skin depth’. What is its physical significance? On what parameters does
it depend on? What do you mean by electromagnetic shielding? 2+1+1+1
[Module 5/CO5/Remember, Understand-LOCQ]
45. State Poynting theorem. Find the dimension of Poynting vector. Write down its
conventional unit. [Module 5/CO5/Remember-LOCQ] 2+2+1
46. Write down Maxwell’s equations for (i) time varying fields and (ii) time invariant fields
separately. [Module 5/CO5/Remember, Understand-LOCQ] 2+3
Module-6
47. Calculate the ratio of stimulated to the spontaneous emission at a temperature 300K for
sodium D-line (λ = 5890 Å). Given, Boltzmann constant 𝑘𝐵 = 1.38 × 10−23 J/K, Planck’s
constant ℎ = 6.625 × 10−34 J.s. [Module 5/CO5/Apply-LOCQ] 5
48. Assuming the wavelength of laser light to be emission with the rate of stimulated
absorption and the rate of spontaneous emission and hence find out the fundamental
conditions needed for lasing action. 5
[Module 6/CO6/Understand-LOCQ, IOCQ]
49. Assuming the wavelength of laser light to be 6500 Å, compute the temperature at
which the rates of stimulated and spontaneous emission are equal. Given, Boltzmann
constant 𝑘𝐵 = 1.38 × 10−23 J/K, Planck’s constant ℎ = 6.625 × 10−34 J.s. 5
[Module 6/CO6/Apply-IOCQ]
50. Consider an atomic system in a radiation field of energy density 𝑢(𝜈)𝑑𝜈under
equilibrium condition at temperature T. Determine the relation between the
spontaneous emission probability and stimulated emission probability between two
energy states 𝐸1 and E2 (𝐸2 > 𝐸1 ) having 𝑁1 and 𝑁2 number of atoms respectively per
unit volume. If the energy difference between the energy states is small enough with
respect to 𝑘𝑇 (k being the Boltzmann constant), compare the emission rate with the
𝑁2
absorption rate and hence show that their ratio can be expressed as . 2+3
𝑁1
[Module 6/CO6/Understand- IOCQ]
51. Find the energy difference between two energy levels of neon atom if the transition
between these levels gives a photon of wavelength 632.8 nm. Also calculate the number
of photons emitted per second to give a power output of 2 mW. Given, ℎ =
6.626 × 10−34 J.s. [Module 6/CO6/Understand, Apply-LOCQ, IOCQ] 2+3
52. Discuss the construction of an optical fiber. Define step-index and graded-index fibers
with diagram. [Module 6/CO6/Remember-LOCQ] 2+3

Page 23 of 36
53. If an optical fiber placed in air has core refractive index of 1.52 and cladding refractive
index of 1.44, compute: (i) critical angle at the core-cladding interface, (ii) numerical
aperture and (iii) acceptance angle. [Module 6/CO6/Apply- IOCQ] 1+2+2

Group-C
Module-1
1. Define Black-Body. How a black body is made in practical life? 2+3
[Module 1/CO1/ Remember-IOCQ]
2. What do you mean by black body? State Kirchoff’s law of blackbody radiation. Prove
that good absorbers are good radiators too. [Module 1/CO1/ Understand-LOCQ] 2+2+2
3. (A) In converting electrical energy to light energy, a 75W incandescent bulb operates at
56% efficiency. Assuming that all light is green 4729.7 Å, determine the number of
photons emitted per second by the bulb. [Module 1/CO1/Apply, IOCQ] 5
4. State the characteristics of black body radiations. How Wien’s radiation formula and
Rayleigh-Jeans law failed to explain the characteristic of the energy density of black
body radiation? [Module 1/CO1/ Understand-IOCQ] 3+(2+2)
5. Show graphically, how the energy density varies with the wavelength of black body
radiation for different temperatures and interpret the reason for the shift of the entire
spectrum with temperature. [Module 1/CO1/ Understand-IOCQ] 3+3
6. State Wien’s law of black body radiation. Discuss the limitation of the law. 2+1
[Module 1/CO1/Remember, Understand-LOCQ]
7. State Rayleigh Jeans’s law of black body radiation and explain the limitation of the law.
Describe ultraviolet catastrophe? [Module 1/CO1/Remember, Understand-LOCQ] 2+1+2
8. (a) Write down Planck’s law of Black body radiation in the wavelength domain. 1
(b) Hence, clearly mention the limits and arrive at Rayleigh-Jeans Law of Black Body
Radiation. How does this law, lead to ultraviolet catastrophe? 3+1
[Module 1/CO1/Remember, Understand-LOCQ, IOCQ]
9. Write down the expression of the number of possible modes of cavity waves of
frequency ν to ν+dν. Using Planck’s hypothesis about the energy quantization of the
cavity oscillation, find out the average energy of an oscillator at a temperature T and
hence the energy density within the frequency range ν to ν+dν. 1+6
[Module 1/CO1/Remember, Understand-LOCQ, IOCQ]
10. (i) State Planck’s hypothesis.
(ii) If 𝑛 number of Planck’s oscillators with the total energy 𝐸 is distributed in accordance
to Maxwell’s distribution formula such that the number of oscillators with energy 𝑟𝜀 is
𝑁0 𝑒𝑥𝑝(− 𝑟𝜀⁄𝑘𝑇), where 𝑁0 is the number of oscillators in the ground state, find out the
average energy of the oscillators.
Page 24 of 36
(iii) If the number of oscillators per unit volume within the frequency range 𝜈 and 𝜈 + 𝑑𝜈
is 𝑛𝜈 𝑑𝜈 = 8𝜋𝜈 2 ⁄𝑐 3 𝑑𝜈, then find the radiant energy density within the frequency range
𝜈 and 𝜈 + 𝑑𝜈.
(iv) Convert this energy density between the wavelength range 𝜆 and 𝜆 + 𝑑𝜆.
(v) Show that Planck’s radiation law reduces to Wien’s radiation law and Rayleigh-Jeans
law in the low and high wavelength limits respectively. 2+3+2+2+(3+3)
[Module 1/CO1/Remember, Understand-LOCQ, IOCQ]
11. Taking Sun’s temperature to be 6000 K, calculate the wavelength corresponding to the
maximum emission from the sun. [Given: Wien’s constant = 2.9 × 10−3 mK] 3
[Module 1/CO1/Apply-IOCQ]
12. A 10 kilowatt radio transmitter operates at a frequency of 600 kHz. Find the number of
photon it emits per second. [Module 1/CO1/Apply-IOCQ] 3
13. Calculate the number of photons emitted per second by a 50 watt sodium lamp if the
wavelength of sodium lamp is 5893 Å. [Module 1/CO1/Apply-IOCQ] 3
14. An electric heater emits 2000W of thermal radiation. Assuming that the coils of the
heater radiates like black body, determine its temperature. (Surface area of coil = 0.05
m2 and  = 5.6710-8 Wm-2K-4) [Module 1/CO1/Apply-IOCQ] 4
15. What is Compton Effect? Write down the momentum conservation and energy
conservation equations for Compton Effect. Derive an expression for Compton shift in
wavelength for a photon scattered from a free electron at an angle 𝜃. Define Compton
wavelength. [Module 1/CO1/Remember, Understand-LOCQ] 2+1+4+1
16. Describe Compton wavelength of a particle. Calculate the Compton wavelength for an
electron. [Module 1/CO1/Understand, Apply-LOCQ, IOCQ] 1+2
17. Explain why Compton Effect cannot be observed with visible light but can be observed
due to X-rays. [Module 1/CO1/Understand- IOCQ] 2
18. (a) A monochromatic x-ray radiation suffers a Compton scattering in Carbon, and it is
observed that the longer wavelength presents in the scattered rays at an angle 60° is
0.02426 Å.. At an angle 60°, calculate the wavelength of
(i) Modified x-rays, and 1
(ii) Un-modified x-rays 2
(b) If the detector is now placed at an angle of 90° position, calculate and identify the
difference between the longest and shortest wavelength, observed by the detector.
[Module 1/CO1/Apply, HOCQ] 1+1
19. State the reason for modified and unmodified lines appearing in Compton Effect.
[Module 1/CO1/Analyse-IOCQ] 4
20. When photon strikes an electron tightly bound to the nucleus, explain what would be
its effect on the Compton shift. 2
Page 25 of 36
 or
Explain why the Compton Effect cannot be observed with macroscopic bodies. 2
[Module 1/CO1/ Analyse -IOCQ]
21. A photon of frequency 𝜈 is scattered through an angle of 90o in Compton scattering.
Show that the scattered frequency is
𝑚0 𝑐 2
𝜈′ = 𝜈 3
ℎ𝜈+𝑚0 𝑐 2
[Module 1/CO1/Understand-IOCQ]
22. X-rays of wavelength 15.0 pm are scattered from a target.
(i) Find the wavelength of X-rays scattered through 45o.
(ii) Find the maximum wavelength present in the scattered X-rays.
(iii) Find the maximum kinetic energy of the recoil electrons. 2+2+3
[Module 1/CO1/Apply-IOCQ]
23. An X-ray photon found to have its wavelength doubled on being scattered through 90°.
Find the wavelength of the incident photon. [Module 1/CO1/Apply-IOCQ] 3
24. (a) An X-ray photon found to have its wavelength doubled on being scattered through
90°, find the wavelength of the incident photon. What is the origin of unmodified
wavelength observed at any non-zero angle scattering. 3+2
[Module 1/CO1/Analyse-IOCQ]
25. X-ray of frequency 4.221019 Hz is scattered by a free electron through 90o. Calculate
the frequency of the scattered X-ray. [Module 1/CO1/Apply-IOCQ] 3
26. In Compton scattering, the incident photons have wavelength equal to 2.5×10-10 m.
After scattering the photons make an angle of 60° with the incident direction. Find the
wavelength of photons after scattering and the kinetic energy of the electron.
[Module 1/CO1/Apply-IOCQ] 2+3
27. A radiation of wavelength 𝜆 = 0.712 Å suffers a Compton scattering in Carbon. Find the
wavelength shift of the photon scattered at 90o if it is scattered by the whole Carbon
atom (Take the mass of proton to be 1836 times the mass of an electron, also assume
that the number of neutrons and protons to be same). 4
[Module 1/CO1/Apply-IOCQ]
28. What do you mean by matter waves? State and explain de Broglie’s hypothesis of matter
waves. Write down the characteristics of this type of waves. 1+2+2
[Module 1/CO1/Remember, Understand-LOCQ, IOCQ]
29. If an electron is subjected to a potential difference of 𝑉 volt, then show that the
corresponding de Broglie wavelength is 𝜆 = 12.26⁄√𝑉 Å. 4
[Module 1/CO1/Apply-IOCQ]

Page 26 of 36
30. If a particle of charge 𝑒 and rest mass 𝑚0 is accelerated by a potential 𝑉 then find the de
Broglie wavelength of the particle viewing the relativistic energy momentum relation.
[Module 1/CO1/Apply-LOCQ] 4
31. State de Broglie hypothesis. Show that the relativistic de Broglie wavelength is given by
ℎ𝑐
𝜆=
√𝐸𝑘 (𝐸𝑘 + 2𝑚0 𝑐 2 )
Where the notations used have their usual meanings. 4
[Module 1/CO1/Understand-LOCQ]
32. Distinguish between phase velocity and group velocity. Show that the relation between
𝑑𝑣𝑝
group velocity (vg) and phase velocity (vp) is given by 𝑣𝑔 = 𝑣𝑝 − 𝜆 . 2+4
𝑑𝜆
[Module 1/CO1/Understand-IOCQ]
33. Prove that the product of phase velocity and group velocity for a de Broglie wave is
constant for relativistic cases. [Module 1/CO1/Understand-LOCQ] 3
34. Show that the group velocity of the wave packet representing a particle is equal to the
velocity of the particle itself. [Module 1/CO1/Understand-IOCQ] 3
35. State and explain Heisenberg’s uncertainty principle regarding the canonically
conjugated pair of position and momentum. The maximum uncertainty in the position
of an electron in a nucleus is 2×10-14 m. Find the minimum momentum, given h =
6.626×10-34 Js. [Module 1/CO1/Apply-IOCQ] 2+3
36. Explain the non-existence of electrons within the nucleus of an atom from the
Heisenberg’s uncertainty relation. [Module 1/CO1/Apply-IOCQ] 5
37. Compute the velocity of a particle so that its Compton wavelength equals to its de
Broglie wavelength. [Module 1/CO1/Apply-IOCQ] 3
38. Compute the smallest possible uncertainty in the position of an electron moving with
velocity 3×107 m/s. The rest mass of electron is 9.1×10-31 kg. 3
[Module 1/CO1/Apply-IOCQ]
39. Calculate the minimum uncertainty in the energy state of an atom if an electron remains
in this state for 2×10-8 s. [Module 1/CO1/Apply-IOCQ] 3
40. The maximum uncertainty in the position of an electron in a nucleus is 2×10-14 m. Find
the minimum momentum, given h = 6.626×10-34 Js. 3
[Module 1/CO1/Apply-IOCQ]
41. Assuming that an electron is inside a nucleus of radius 10-15 m, estimate from the
uncertainty principle the minimum kinetic energy of the electron. 5
[Module 1/CO1/Apply-IOCQ]

Page 27 of 36
Module-2
42. Write down the one-dimensional Schrödinger’s time-dependent equation of motion.
Obtain the time-independent form of Schrödinger’s equation by the method of
separation of variable. [Module 2/CO2/Understand-IOCQ] 1+4
43. (a) Derive the expression for (i) the momentum operator, (ii) the kinetic energy
operator and hence (iii) the total energy operator in quantum mechanics, starting with
𝑖
(𝑝 𝑥−𝐸𝑡)
the wave function 𝜓(𝑥, 𝑡) = 𝐴𝑒 ℏ 𝑥 2+2+1
[Module 2/CO2/Understand-LOCQ]
44. What do you mean by commutator brackets? Prove that [𝑥̂, 𝑝̂𝑥 ] = 𝑖ℏ. 2+3
[Module 2/CO2/Remember, Understand-LOCQ]
45. Explain the physical significance of a wave-function. 3
[Module 2/CO2/Understand-LOCQ]
46. State the basic postulates of quantum mechanics. 4
[Module 2/CO2/Remember-LOCQ]
47. If we consider a free particle moving in a one-dimensional space inside a box of length
L,
(i) Write down Schrödinger time-independent equation for such a system.
(ii) Solve Schrödinger equation to find out the normalized Eigen function.
(iii) Find out the expression of energy Eigen value and draw different energy states and
hence show that the energy Eigen values of a free particle enclosed in a potential box is
quantized.
(iv) Show that the solution of the Schrödinger wave equation for a free particle moving
along X-axis in an enclosure represents a standing wave. Draw the waves bounded
between the lengths of the box corresponding to first three quantum numbers.
(v) Obtain & draw probability density corresponding to ground, first-excited & second-
excited states. 1+5+(2+2+1)+(1+3)+3
[Module 2/CO2/ Remember, Understand, Apply- LOCQ, IOCQ]
48. The wave function of a particle in one dimensional box of length L is given by
2 𝑛𝜋𝑥
𝜑𝑛 = √ 𝑠𝑖𝑛 (
𝐿 𝐿
). Find the expectation value of (i) position and (ii) momentum of the

particle. [Module 2/CO2/ Apply- IOCQ] 4+3

49. If the wave function 𝜓(𝑥) of quantum mechanical particle is given by
𝜋𝑥
𝜓(𝑥) = 𝑎 𝑠𝑖𝑛 ( ) , for 0 < x < L
𝐿
= 0, otherwise,
then determine the value of a. Also determine the value of x where probability of
finding the particle is maximum. [Module 2/CO2/ Apply- IOCQ] 3+3

Page 28 of 36
50. Show that the energy difference between two consecutive energy levels of a one-
ℏ2 𝜋 2
dimensional potential box with rigid walls is given by 𝛥𝐸 = (2𝑛 + 1). 3
2𝑚𝑙 2
[Module 2/CO2/ Apply- IOCQ]
51. Find out the energy Eigen function and energy Eigen values for a particle in one
dimensional potential box with rigid walls and side L characterized by 𝑉(𝑥) = 0, for 0 <
𝑥 < 𝐿 and 𝑉(𝑥) = ∞, otherwise. Compute the energy difference between two
consecutive energy levels. [Module 2/CO2/ Apply- IOCQ] 5+2+2
52. Obtain the expression for stationary energy levels for a particle of mass m which is free
to move in a region of zero potential between two rigid walls at x = 0 and x = L. Explain
whether the energy levels are degenerate. [Module 2/CO2/ Apply- IOCQ] 4+2
53. Starting from the time independent Schrödinger equation for 1-D motion of a free
particle in 1-D potential box, find out the energy Eigen values. Show that the energy
Eigen values of the free particle enclosed in a potential box are quantized. Draw the
wave functions of that free particle for ground state and 1st excited state. 5+3+2
[Module 2/CO2/Remember, Apply- IOCQ]
54. Write down the wave function of a free particle confined to move inside a box of
dimensions L×L×L. Give its corresponding energy. Find the degree of degeneracy in the
following cases: (i) n(111), (ii) n(123), (iii) n(121). 1+1+(2+2+2)
[Module 2/CO2/Remember, Apply- LOCQ, IOCQ]
55. Write down the mathematical expression of the wave function of a free particle
confined to move inside a box of dimensions L×L×L. Find the degree of degeneracy for
the energy states with quantum numbers: (i) n(111), (ii) n(123), &(iii) n(223).
[Module 2/CO2/Remember, Apply- LOCQ, IOCQ] 2+3
56. Define degeneracy and non-degeneracy of energy state. Show that the lowest energy
state of a free particle in a cubical box is not degenerate. Compute the degeneracy of the
second excited state. [Module 2/CO2/ Understand, Apply- LOCQ, IOCQ] 3+1+2
57. Consider a free particle in a cubical box. Calculate the degeneracy of the levels that has
three times that of the lowest level. [Module 2/CO2/Understand, Apply- IOCQ] 3
58. Show that the first excited state of a free particle enclosed in a three-dimensional box is
three-fold degenerate. Express corresponding Eigen energy value and the three Eigen
functions. [Module 2/CO2/Understand- IOCQ] 2+1+3
𝑑
59. The operator (𝑥 + ) has the Eigen value μ. Derive the corresponding Eigen function.
𝑑𝑥
[Module 2/CO2/Apply- LOCQ, IOCQ] 4
60. Find out if the following wave-functions satisfy the Schrödinger wave equation: 12

Page 29 of 36
 1 1 1
(𝑖) , (𝑖𝑖) , (𝑖𝑖𝑖) , (𝑖𝑣) 𝑥 𝑛 , (𝑣) sin 𝑥 ,
𝑥 1+𝑥 1 + 𝑥2
(𝑣𝑖) 𝐴 sec 𝑥 , (𝑣𝑖𝑖) 𝐴 tan 𝑥,
(𝑣𝑖𝑖𝑖) 𝐴 cos(𝑘𝑥 − 𝜔𝑡) , (𝑖𝑥) 𝑒 𝑥 , (𝑥) 𝑒 −𝑥 , (𝑥𝑖) 𝐴 exp 𝑥 2 , (𝑥𝑖𝑖) 𝐴 exp(−𝑥 2 ).
[Module 2/CO2/Apply- IOCQ]
61. Evaluate the following operators: 3+3
2
𝜕2
(𝑖) [(𝑥̂) , 2 ] , (𝑖𝑖)[𝑝̂𝑥 , 𝑝̂𝑦 ].
𝜕𝑥
[Module 2/CO2/Apply- IOCQ]
𝑑 2 𝑑 𝑑2
62. Show that (1 + ) = 1 + 2 𝑑𝑥 + 𝑑𝑥 2 . 3
𝑑𝑥
[Module 2/CO2/Apply- LOCQ]
𝜕 𝜕2
63. Show that the operators and are commutative. 2
𝜕𝑥 𝜕𝑥 2
[Module 2/CO2/ Apply- IOCQ]
64. Show that the function 𝜓(𝑥) = 𝐴𝑒 𝑖𝑘𝑥 + 𝐵𝑒 −𝑖𝑘𝑥 is an Eigen function of the kinetic energy
operator 𝐸̂𝑘 . [Module 2/CO2/Apply- IOCQ] 3
𝑥2
− 𝑑2
65. Show that the function 𝛹(𝑥) = 𝐶𝑥𝑒 2 is an Eigen function of the operator (𝑥 2 − ).
𝑑𝑥 2
Also find the corresponding Eigen value. 2+1
[Module 2/CO2/Apply- LOCQ, IOCQ]
𝜎2 2
(− 𝑥 +𝑖𝑘𝑥)
66. (a) Determine the probability density for the wave function 𝜑(𝑥) = 𝐴𝑒 2 .
[Module 2/CO2/ Apply-LOCQ]
(b) A particle confined to move along the x-axis has a wave function 𝜓(𝑥) = √3 𝑥. Find
the probability of finding the particle between 𝑥 = 0.35 to 𝑥 = 0.45. 2+3
[Module 2/CO2/Understand, Apply-LOCQ, IOCQ]
67. A particle confined to move along the x-axis has a wave function 𝜓(𝑥) = √3 𝑥. Find the
probability of finding the particle between 𝑥 = 0.35 to 𝑥 = 0.45. 3
[Module 2/CO2/ Apply- IOCQ]
68. A particle is moving along X-axis has the wave function
𝜓(𝑥) = 𝑘𝑥 Between x = 0 and x = 1, and 𝜓(𝑥) = 0, otherwise.
Find the expectation value 〈𝑥〉 of the particle’s position. 4
[Module 2/CO2/ Apply- IOCQ]
69. The wave function associated with a particle is given by
𝜓(𝑦) = 𝑏𝑦 for 0 ≤ 𝑦 ≤ 1 and 𝜓(𝑦) = 0 elsewhere.
Find the probability that the particle can be found between 𝑦 = 0.30 and 𝑦 = 0.70. 4
[Module 2/CO2/ Apply- IOCQ]

Page 30 of 36
70. An electron is trapped in 1-D infinite well of width 1.0 Å. Calculate the wavelength of
the photon emitted when the electron makes a transition from the second excited state
to the ground state. [Module 2/CO2/ Apply- IOCQ] 4
71. Considering an electron is confined between two rigid walls 0.50 nm apart, calculate
the energy levels for the states n = 1, 2 and 3. [Module 2/CO2/ Apply- IOCQ] 3
72. Find the energy of the ground state of an electron moving in a cubical box having each
side equal to 1.2 Å. (Mass of electron = 9.1×10-31 kg, h = 6.626×10-34Js) 3
[Module 2/CO2/ Apply- IOCQ]

Module-3
73. Distinguish between nonpolar and polar molecules with examples. 2+1
[Module 3/CO3/ Understand- LOCQ]
74. Show that 𝐷 ⃗ = 𝑃⃗ + 𝜀0 𝐸⃗ where symbols have their usual meaning. Rewrite the
differential form of Gauss’s Law in terms of displacement vector. 3+1
[Module 3/CO3/ Understand- IOCQ]
75. Establish the relation between dielectric constant and electric susceptibility of a
dielectric material. [Module 3/CO3/ Understand- IOCQ] 4
or
Show that 𝐾 = 1 + 𝜒𝑒 , where 𝐾 and 𝜒𝑒 are the dielectric constant and electric
susceptibility of the medium respectively. [Module 3/CO3/ Understand- IOCQ] 4
76. Discuss on how the polar and non-polar molecules get influenced by the applied
external electric field. [Module 3/CO3/ Understand- LOCQ] 3+3
77. Define polarization vector. State how is it related to the atomic polarizability of a
dielectric material. [Module 3/CO3/ Remember- LOCQ] 2+2
78. Define dielectric constant. Find out the relation between dielectric constant and
electrical susceptibility. [Module 3/CO3/ Remember, Understand- LOCQ] 2+3
𝜀0 (𝜀𝑟 −1)
79. Explain the phenomena of polarization. Show that electronic polarizability𝛼𝑒 = ,
𝑁
where the symbols have their usual meanings. [Module 3/CO3/Understand- LOCQ] 2+3
80. Define dielectric constant and atomic polarizability. Establish the relation between
them. [Module 3/CO3/ Remember, Understand- LOCQ, IOCQ] (2+2)+3
81. If the number density of argon is 2.689 × 10 m and its dielectric constant is
25 −3

1.00044, calculate its polarizability (and free-space permittivity (𝜀0 ) is 8.854 × 10−12
F/m) [Module 3/CO3/ Apply- IOCQ] 4
82. Assuming that the electric polarizability of an Argon atom is 1.43×10 -40 F.m2, estimate
the dielectric constant of solid Argon. Given concentration of Argon is 2.7137 ×
1028 m−3 and free-space permittivity (𝜀0 ) is 8.854 × 10−12 F/m. 4
[Module 3/CO3/ Apply- IOCQ]
Page 31 of 36
83. Define electronic polarizability. Discuss how monoatomic gases can be polarized. 2+4
[Module 3/CO3/ Remember, Understand- LOCQ]
84. Define electronic polarizability. Show that the electronic polarizability is proportional
to the atomic volume. [Module 3/CO3/ Understand- IOCQ] 1+5
85. What is meant by electronic polarization? Find out the expression of electronic
polarizability on the basis of the classical theory. How does it depend on the
temperature? [Module 3/CO3/ Understand- IOCQ] 2+4+1
86. Calculate the electronic polarizability of Ar atom having radius 10−10 m. 3
[Module 3/CO3/ Apply- LOCQ]
87. Discuss the dependence of the electronic polarizability of an atom on the radius of the
atom. [Module 3/CO3/ Understand- HOCQ] 5
88. Estimate the polarizability of CO2 if its susceptibility is 0.985 × 10−3 and the number of
molecules per unit volume is 2.706 × 1025 m−3 . [Given: free-space permittivity (𝜀0 ) =
8.854 × 10−12 F/m] [Module 3/CO3/ Apply- LOCQ] 3
89. Discuss on dielectric loss of a material. [Module 3/CO3/ Understand- LOCQ] 2
90. Discuss on dielectric breakdown and dielectric strength of a material. 2+2
[Module 3/CO3/ Understand- LOCQ]
Module-4
91. What do you mean by electromagnetic induction? State Faraday’s laws of
electromagnetic induction. Express it in differential form. 2+2+1
[Module 4/CO4/ Understand- IOCQ]
92. Establish the (i) integral form and hence (ii) differential form of Faraday's law of
electromagnetic induction. [Module 4/CO4/ Understand- IOCQ] 4+2
93. Discuss that the Lenz’s law is in accordance with the conservation of energy. 3
[Module 4/CO4/ Understand- IOCQ]
94. A single turn coil having an area 10 m2 for each turn is held in a uniform and
perpendicular to field of 5×10-3 Tesla. Calculate the induced e.m.f. in the coil, if the field
is removed in 0.5 sec. [Module 4/CO4/ Apply- IOCQ] 3
95. Give an example of an electrical circuit carrying non-steady current where Ampere’s
law is not possible to be used. [Module 4/CO4/Understand- IOCQ] 2
96. Show how Ampere’s law was modified by Maxwell to make it valid for a time varying
field. [Module 4/CO4/Understand- LOCQ] 4
97. Define displacement current. Distinguish between conduction current and
displacement current. [Module 4/CO4/ Remember, Understand- LOCQ] 2+3
98. A parallel-plate capacitor has a capacitance of 2 μF. Calculate the rate at which the
potential difference between the two plates must change to obtain a displacement
current of 0.5 A. [Module 4/CO4/Apply- IOCQ] 3
Page 32 of 36
Module-5
99. Write down Maxwell’s field equations and explain the terms used. Also write down the
physical significance of each equation. [Module 5/CO5/ Remember- LOCQ] 4+4
100. Write down Maxwell’s equation in the differential form and state the name of each.
Convert them into the integral form. [Module 5/CO5/ Understand- IOCQ] (4+2)+4
101. Write down Maxwell’s field equations in free space for (i) time varying fields (ii)
static field. [Module 5/CO5/ Understand- LOCQ] 2+2
102. (a) Write down Maxwell’s field equations in case of (i) dielectric medium (perfect
insulator) and (ii) good conductor. 4+4
[Module 5/CO5/ Remember, Understand- LOCQ]
103. Starting from Maxwell’s equations in free space, show that both electric and magnetic
fields obey wave equation. [Module 5/CO5/ Understand- LOCQ] 4+3
104. Write down Maxwell’s equations for free space. Show that in a charge free, current free
region the Electric/Magnetic field vector satisfies a wave equation. Identify the
velocity of this wave. [Module 5/CO5/ Remember, Understand- LOCQ] 2+2+1
105. Prove that electromagnetic wave moves with the speed of light in free space. 6
[Module 5/CO5/ Understand- IOCQ]
106. State how the velocity of light depends on the properties of the medium. 2
[Module 5/CO5/ Understand- IOCQ]
107. An electromagnetic wave is represented by 𝐸 = 𝐸0 cos(1000𝑥 − 5000𝑡). Calculate
the wavelength and speed of propagation of the wave. 2+2
[Module 5/CO5/ Apply- IOCQ]
108. Explain why an electromagnetic wave is called transverse wave. 2
[Module 5/CO5/ Understand- HOCQ]
109. An electromagnetic wave is propagating in free space in z-direction. If the magnetic
field is given by 𝐵⃗ = 𝐴 cos(𝜔𝑡 − 𝑘𝑧) 𝑖̂, then find out the corresponding electric field. 4
[Module 5/CO5/ Apply- IOCQ]
110. The electric vector component of a plane electromagnetic wave propagating in a non-
magnetic medium is given by 𝐸⃗ = 50 cos(108 𝑡 + 2𝑧) 𝑖̂ V/m. Find the relative
permittivity of the medium and the magnetic vector component of the wave. 3+4
[Module 5/CO5/ Apply- IOCQ]
111. Obtain the Equation of Continuity from Maxwell’s equations. 3
[Module 5/CO5/ Understand- IOCQ]
112. Show that 𝐵 ⃗ = 𝑎(𝑥𝑖̂ + 2𝑦𝑗̂), where 𝑎 is a constant is not consistent with Maxwell’s
electromagnetic field equations. [Module 5/CO5/ Apply- IOCQ] 3
113. Obtain the wave equation in terms of the electric field (𝐸⃗ ) in non-conducting medium
and find out the speed of electromagnetic wave in this medium. 5+2
Page 33 of 36
 [Module 5/CO5/ Apply- IOCQ]
114. Calculate the skin depth at a frequency 1.5 MHz in aluminium where 𝜎 = 38.2 × 106
mho/m and 𝜇 = 4𝜋 × 10−7 Henry/m. [Module 5/CO5/ Apply- IOCQ] 3
115. Compute the depth of penetration of 2 MHz wave into Copper which has a conductivity
𝜎 = 5.8 × 107 mhos/m and permeability approximately equal to that of free space.
Given, 𝜇0 = 4𝜋 × 10−7 Henry/m. [Module 5/CO5/ Apply- IOCQ] 4
Module-6
116. Write down the differences between LASER and normal visible light. 4
[Module 6/CO6/ Understand- LOCQ]
117. State the characteristics and applications of a laser beam. 2+2
118. Explain with neat diagram, spontaneous emission, stimulated absorption and
stimulated emission of radiation. Hence distinguish between spontaneous and
stimulated emission of radiation. [Module 6/CO6/ Understand- LOCQ] 6+2
119. Define Einstein’s A, B coefficients for absorption and emission of radiation. Relate
spontaneous and stimulated emission probabilities and hence find out the relation
between field energy and Einstein’s A, B coefficients. 2+6
[Module 6/CO6/ Understand- IOCQ]
120. Show that the ratio of spontaneous to stimulated emission is proportional to the cube
of the frequency. [Module 6/CO6/ Understand- IOCQ] 3
121. Calculate the ratio of spontaneous emission rate to stimulated emission rate at T =
1000 K for visible light of frequency 5 × 1014 Hz and microwave of frequency 109 Hz.
Hence explain which type of source would be easy to construct: LASER or MASER.
Given, Boltzmann constant 𝑘𝐵 = 1.38 × 10−23 J/K, ℎ = 6.625 × 10−34 J.s. 3+3+1
[Module 6/CO6/ Apply- IOCQ]
1
122. A relative population (Boltzmann ratio) of is representative of the ratio of
𝑒
populations in two energy states at room temperature (T = 27 oC). Determine the
wavelength of the radiation emitted at the temperature. Given, Boltzmann constant
𝑘𝐵 = 1.38 × 10−23 J/K, ℎ = 6.625 × 10−34 J.s. [Module 6/CO6/ Apply- IOCQ] 5
123. In an active medium the separation between two atomic levels is 2.3 eV. Compute the
temperature at which the population ratio (N2/N1) would be 1/2. Given, Boltzmann
constant 𝑘𝐵 = 1.38 × 10−23 J/K. [Module 6/CO6/ Apply- IOCQ] 5
124. Describe briefly the working principle of laser action. 4
[Module 6/CO6/ Understand- IOCQ]
125. Explain why a laser beam shows a high degree of monochromaticity, coherence and
directionality. [Module 6/CO6/ Understand- IOCQ] 3
126. Discuss on population inversion in the context of LASER. Why is it needed for lasing
action? [Module 6/CO6/ Understand- IOCQ] 2+2
Page 34 of 36
127. Explain why population inversion cannot be achieved by direct pumping in a two-
level system. [Module 6/CO6/ Understand- IOCQ] 3
128. Discuss on pumping in the context of laser. State four types of pumping used in lasers.
Which of these methods can be implemented in Ruby laser and He-Ne gas laser? 2+2+2
[Module 6/CO6/ Understand- IOCQ]
129. What do you mean by ‘metastable state’? How can it be achieved? 2+1
[Module 6/CO6/ Understand- IOCQ]
130. Discuss the construction of an optical resonator and explain its function in a Laser
device. [Module 6/CO6/ Understand- LOCQ] 2+3
131. Describe the construction of a ruby laser. Also discuss how population inversion is
achieved in ruby laser with clearly drawing the energy diagrams and hence the working
principle of that laser. Discuss whether this result is suitable for continuous or pulse
mode operation. [Module 6/CO6/ Understand- IOCQ] 3+(2+3)+1
132. Discuss the operation of ruby laser with the help of energy level diagram. If the
wavelength of radiation of ruby laser is 6943 Å, find the energy of a photon emitted.
Given, ℎ = 6.625 × 10−34 J.s. [Module 6/CO6/ Apply- IOCQ] 4+2
133. A pulsed laser is constructed with a ruby crystal as the active element. The ruby rod
contains typically a total of 3 × 1019 Cr3+ ions. If the laser emits light at 6943Å
wavelength, then find the energy of the emitted photon in eV and the total energy
available per pulse, assuming the total population inversion to occur.
Given, ℎ = 6.625 × 10−34 J.s. [Module 6/CO6/ Apply- IOCQ] 2+2
134. A ruby laser emits light of 693.95 nm wavelength. If 1 mole of Cr3+ ions are involved
in population inversion process in a pulse, calculate pulse energy in eV. Given, ℎ =
6.625 × 10−34 J.s. [Module 6/CO6/ Apply- IOCQ] 4
135. Explain the working principle of He-Ne laser with energy level diagram. 3+2
[Module 6/CO6/ Understand- IOCQ]
136. A He-Ne laser produces light of wavelength 6328 Å. If the laser radiates energy at the
rate of 1mW, calculate the intensity of the focused beam. (A laser beam can be focused
on an area equal to the square of its wavelength) [Module 6/CO6/ Apply- IOCQ] 3
137. In a He-Ne laser transition from 3s to 2p level gives a laser beam of wavelength 632.8
nm. If the 2p level has energy equal to 15.2×10-19 J, calculate the required pumping
energy (assuming no loss of energy). Given, ℎ = 6.625 × 10−34 J.s. 4
[Module 6/CO6/ Apply- IOCQ]
138. Briefly describe the construction of an optical fiber. Define step-index and graded-
index fibers with diagram. [Module 6/CO6/ Understand- LOCQ] 2+3
139. Describe how an optical pulse is propagated through an optical fiber? Write down the
advantages of using optical fibers in the telecommunication system. 2+3
Page 35 of 36
 [Module 6/CO6/ Understand- IOCQ]
140. Define numerical aperture of a fiber. Derive the expression of numerical aperture
(NA) for a step-index optical fiber. [Module 6/CO6/ Understand- IOCQ] 1+4
141. Define acceptance angle of a fiber. Express acceptance angle in terms of numerical
aperture of a fiber. [Module 6/CO6/ Understand- IOCQ] 1+1
142. How many 8-bit audio speech signals can be sent simultaneously through an 8 𝐺𝐻𝑧
bandwidth analogue communication system? [Module 6/CO6/ Apply- IOCQ] 4
143. How many simultaneous voice channels can be used in a 128 Mb/s digital
communication system? [Module 6/CO6/ Apply- IOCQ] 3
144. When the mean optical power launched into an 8 km length of fiber is 120 μW, the
mean optical power at the fiber output is 3 μW. Determine (i) the overall signal
attenuation in decibels through the fiber assuming there are no connectors or splices;
(ii) the signal attenuation per kilometer for the fiber, (iii) the overall signal attenuation
for a 10 km link using the same fiber with splices at 1 km intervals, each giving an
attenuation of 1 dB. [Module 6/CO6/ Apply- IOCQ] 2+2+2

Page 36 of 36