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Roll No:
Application No:
Name:
Exam Date: 05-Oct-2020
Exam Time: 09:00-12:00
Examination: 1. Course Code - Ph.D.
2. Field of Study - Physical Science (PHYH)
SECTION 1 - SECTION 1
Case Study - 1 to 3 (Question Id - 53)
Question No.1 (Question Id - 54)
The surface bound charge b is :
(A)
(B)
(C)
(D)
kR (Correct Answer)
Question No.2 (Question Id - 55)
The volume bound charge (b) is :
(A)
(B)
- 3kr
(C)
- 3k (Correct Answer)
(D)
Question No.3 (Question Id - 56)
The electric field outside the sphere is :
(A)
4kR2
(B)
(C)
0 (Correct Answer)
(D)
Question No.4 (Question Id - 7)
(A)
(Correct Answer)
(B)
(C)
(D)
Question No.5 (Question Id - 14)
For an atom with an electronic configuration np2 (where n is the principal quantum number of a shell),
the possible values of total angular momentum L and total spin S in the ground state are :
(A)
L = 2 and S = 0
(B)
L = 2 and S = 1
(C)
L = 1 and S = 1 (Correct Answer)
(D)
L = 1 and S = 0
Question No.6 (Question Id - 2)
(A)
(B)
(C)
(Correct Answer)
(D)
Question No.7 (Question Id - 11)
Electrons are ejected from calcium surface when monochromatic light of wavelength 488 nm falls on it.
The work function of calcium is 2.28 eV. What is the maximum kinetic energy of the emitted electron ?
(Planck's constant, h = 4.14 x 10-15 eV.sec; speed of light, c = 3 x 108 m/sec)
(A)
0.026 eV
(B)
26 eV
(C)
2.6 eV
(D)
0.26 eV (Correct Answer)
Question No.8 (Question Id - 4)
Which one of the following is not true about the superconductors ?
(A)
Type-II superconductors realize a mixed state between the critical magnetic fields Hc1 and Hc2.
(B)
In Type-I superconductors, the penetration depth () is smaller than the coherence length ().
(C)
According to BCS theory, the copper pairs are formed due to electron-phonon interaction.
(D)
Superconductivity is characterized by strongly paramagnetic behavior. (Correct Answer)
Question No.9 (Question Id - 15)
(A)
(B)
(Correct Answer)
(C)
(D)
Question No.10 (Question Id - 5)
Which one of the following expressions is correct for the Helmholtz free energy F(T, V, N) of a
thermodynamic system in canonical ensemble ? Here, P is pressure, V is volume, N is the number of
particles, is chemical potential, and T is temperature.
(A)
F = - PV + N (Correct Answer)
(B)
F = PV + N
(C)
F = - PV - N
(D)
F = N
Question No.11 (Question Id - 1)
Let the angular momentum eigenstates with quantum number j be denoted as |j, m, where m = - j, - j
+ 1, ..., j - 1, j. For a system of two angular momenta j1 and j2, any state can be described as a linear
superposition of their product states j1, m1| j2, m2. For j1 = 1 and j2 = 1/2, which of the following is the
correct expression for the total angular momentum eigenstate with quantum numbers jtotal = 3/2 and
mtotal = 1/2 ?
(A)
(Correct Answer)
(B)
(C)
|jtotal = 3/2, mtotal = 1/2 = |1, 0|1/2, 1/2
(D)
|jtotal = 3/2, mtotal = 1/2 = |1, 1|1/2, - 1/2
Case Study - 12 to 14 (Question Id - 33)
Consider a gas of N free electrons confined in a volume V. (m is the electron mass, is Planck's constant and kB is
Boltzmann's constant.)
Answer the following three questions on the free electron gas problem.
Question No.12 (Question Id - 34)
What is the density of states for the free electrons ?
(A)
(B)
(C)
(Correct Answer)
(D)
Question No.13 (Question Id - 35)
What is the Fermi energy in terms of N and V ?
(A)
(B)
(C)
(Correct Answer)
(D)
Question No.14 (Question Id - 36)
How does the specific heat (CV) of free electron gas vary with temperature (T) at low temperatures ?
(A)
CV T3
(B)
(C)
CV T2
(D)
CV T (Correct Answer)
Case Study - 15 to 17 (Question Id - 45)
Consider the function f (z) = e1/z of a complex variable z = x + iy in a complex plane. Answer the following three
questions on this function.
Question No.15 (Question Id - 46)
The function f (z) = e1/z has :
(A)
no singularity at z = 0
(B)
an essential singularity at z = 0 (Correct Answer)
(C)
a simple pole at z = 0
(D)
a branch point at z = 0
Question No.16 (Question Id - 47)
(A)
(B)
i
(C)
i2 (Correct Answer)
(D)
2
Question No.17 (Question Id - 48)
The equation of the contour corresponding to a fixed value, A, of the amplitude of the function e1/z is :
(A)
(Correct Answer)
(B)
(C)
(D)
Question No.18 (Question Id - 19)
(A)
- cos 2q
(B)
cos 2q
(C)
1 (Correct Answer)
(D)
0
Case Study - 19 to 21 (Question Id - 41)
Answer the following three questions on the relativistic corrections to the hydrogen problem.
Question No.19 (Question Id - 42)
The leading relativistic correction to the kinetic energy term in the hydrogen atom Hamiltonian is :
(A)
(B)
(C)
(Correct Answer)
(D)
Question No.20 (Question Id - 43)
The relativistic correction to the hydrogen atom problem leading to spin-orbit interaction is given by :
(A)
(B)
(Correct Answer)
(C)
(D)
Question No.21 (Question Id - 44)
(A)
Only l = 0 states (Correct Answer)
(B)
Only l = 1 states
(C)
Only l = 2 states
(D)
All l states
Case Study - 22 to 24 (Question Id - 37)
Question No.22 (Question Id - 38)
The tail current is :
(A)
5 mA
(B)
10 mA
(C)
6 mA (Correct Answer)
(D)
8 mA
Question No.23 (Question Id - 39)
The value of emitter current is :
(A)
1 mA
(B)
2 mA
(C)
3 mA (Correct Answer)
(D)
4 mA
Question No.24 (Question Id - 40)
The value of the collector voltage :
(A)
4 V
(B)
6 V (Correct Answer)
(C)
8 V
(D)
10 V
Question No.25 (Question Id - 10)
Which one of the following elements cannot be used as dopants in Silicon to make it n-type
semiconductor ?
(A)
Arsenic
(B)
Phosphorus
(C)
Boron (Correct Answer)
(D)
Antimony
Question No.26 (Question Id - 13)
Consider a particle in a state given by the wavefunction (x, y, z) = (y + iz)2. This wavefunction is an
eigenfunction of the angular momentum operator Lx with eigenvalue.
(A)
- 2
(B)
-
(C)
+
(D)
+ 2 (Correct Answer)
Question No.27 (Question Id - 20)
By doing an elastic scattering experiment with a beam of electrons of momentum p 120 MeV/c, we
can determine :
(Planck's constant, h = 6.63 x 10-34 J.s; speed of light, c = 3 x 108 m/s; electron charge, e = 1.6 x 10-19
C)
(A)
the size of a biomolecule
(B)
the lattice constants of a crystal of gold
(C)
the size of an atomic nucleus (Correct Answer)
(D)
none of the above
Case Study - 28 to 30 (Question Id - 21)
A "two-level" atom is considered to have only two energy levels with energies 0 and . For a system of N non-
interacting two-level atoms with total energy E, answer the following three questions.
Question No.28 (Question Id - 22)
What is the number of microstates (N, E) ?
(A)
(B)
(Correct Answer)
(C)
(D)
Question No.29 (Question Id - 23)
What is the entropy per particle in the limit of large N ?
(A)
(B)
(C)
(Correct Answer)
(D)
Question No.30 (Question Id - 24)
What is the corresponding temperature T ?
(A)
(Correct Answer)
(B)
(C)
(D)
Question No.31 (Question Id - 8)
The decay n p + e- of a neutron (n) into a proton (p) and an electron (e-) is forbidden due to the
violation of conservation of :
(A)
Angular momentum and baryon number
(B)
Energy and lepton number
(C)
Angular momentum and lepton number (Correct Answer)
(D)
Electric charge and baryon number
Case Study - 32 to 34 (Question Id - 49)
Consider a crystalline material which, under ambient conditions, is given to have the FCC (face-centered cubic) lattice
structure with monoatomic basis. Answer the following three questions for this system.
Question No.32 (Question Id - 50)
A primitive unit cell of the monoatomic FCC crystal contains :
(A)
1 atom (Correct Answer)
(B)
2 atoms
(C)
3 atoms
(D)
4 atoms
Question No.33 (Question Id - 51)
The phonon dispersion of a monoatomic FCC crystal has :
(A)
3 branches of acoustic phonons only. (Correct Answer)
(B)
3 branches of acoustic phonons, and 9 branches of optical phonons.
(C)
1 branch of acoustic phonons, and 2 branches of optical phonons.
(D)
3 branches of optical phonons only.
Question No.34 (Question Id - 52)
Suppose by changing the temperature, if the crystal structure of the material changes from the
monoatomic FCC to monoatomic BCC (body-centered cubic), then the number of optical phonon
branches will change by :
(A)
0 (Correct Answer)
(B)
2
(C)
3
(D)
6
Case Study - 35 to 37 (Question Id - 57)
Answer the following three questions on the semi-empirical formula for the binding energy of atomic nuclei in terms of
the nuclear mass number A and the proton number Z.
Question No.35 (Question Id - 58)
In the formula for binding energy per nucleon, the volume energy term is :
(A)
a constant (Correct Answer)
(B)
proportional to Z
(C)
proportional to A
(D)
proportional to A1/3
Question No.36 (Question Id - 59)
In the formula for binding energy per nucleon, the contribution from Coulomb repulsion between protons
is :
(A)
proportional to Z only
(B)
proportional to Z(Z-1) only
(C)
proportional to Z(Z - 1)A-1/3
(D)
proportional to Z(Z - 1)A-4/3 (Correct Answer)
Question No.37 (Question Id - 60)
In the formula for binding energy per nucleon, the pairing energy term is :
(A)
always zero
(B)
zero only when A is an odd integer (Correct Answer)
(C)
non-zero only when A is an odd integer
(D)
always non-zero
Question No.38 (Question Id - 3)
(A)
0
(B)
(Correct Answer)
(C)
(D)
Case Study - 39 to 41 (Question Id - 29)
A body of mass m is thrown up vertically with an initial speed u. The air exerts a drag force - kv upon it, where v is
the instantaneous velocity of the body and k is a constant. The body also experiences gravitational acceleration g.
Answer the following three questions on this problem.
Question No.39 (Question Id - 30)
What is the terminal speed attained by the body ?
(A)
(Correct Answer)
(B)
(C)
(D)
u
Question No.40 (Question Id - 31)
What is the time it will take to attain the maximum height ?
(A)
(B)
(C)
(Correct Answer)
(D)
Question No.41 (Question Id - 32)
What is the maximum height attained by the body ?
(A)
(B)
(Correct Answer)
(C)
(D)
Question No.42 (Question Id - 16)
(A)
(x + y)
(B)
(x - y)
(C)
2(x + y) (Correct Answer)
(D)
2(x - y)
Question No.43 (Question Id - 17)
In spectroscopy, the selection rule for transition between the rotational energy levels of a diatomic
molecule (given by the rotational quantum number J) states that the transition between two rotational
levels is allowed if :
(A)
J = ?1 (Correct Answer)
(B)
J = ?2
(C)
J = 0
(D)
None of the above
Question No.44 (Question Id - 9)
For a classical system described by the Hamiltonian H(q, p) in terms of the generalized coordinates q
and p, the Hamilton's equations of motion (in the standard notation) are :
(A)
(B)
(C)
(Correct Answer)
(D)
Question No.45 (Question Id - 6)
For a thermodynamic system of N particles at temperature T, which of the following relation is correct
for the change in entropy S with respect to volume V ?
(A)
(B)
(Correct Answer)
(C)
(D)
Question No.46 (Question Id - 12)
A spin-1/2 particle in a magnetic field B pointing along y-direction is described by the Hamiltonian H =
BBy, where y is the Pauli matrix corresponding to the y component of the spin-1/2 operator (and B
is the Bohr magneton) . For this system, the time evolution operator e-iHt/ can be written as :
(A)
(B)
(C)
(D)
(Correct Answer)
Case Study - 47 to 49 (Question Id - 25)
Question No.47 (Question Id - 26)
The commutator [aa, aa] is equal to :
(A)
- 2aa
(B)
2aa
(C)
2aa (Correct Answer)
(D)
- 2aa
Question No.48 (Question Id - 27)
(A)
(B)
(Correct Answer)
(C)
0
(D)
Question No.49 (Question Id - 28)
Which of the following is the correct expression for the creation operator ?
(A)
(B)
(Correct Answer)
(C)
(D)
Question No.50 (Question Id - 18)
Consider a rectangular waveguide with a cross-section of dimension 2 cm x 1 cm. If the driving
frequency is 1.7 x 1010 Hz, the Transverse Electric (TE) mode that will propagate in this wave guide is :
(A)
0.53 x 1010 Hz
(B)
0.75 x 1010 Hz (Correct Answer)
(C)
1.9 x 1010 Hz
(D)
1.4 x 109 Hz
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This post was last modified on 21 January 2021