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INDIAN FOREd 1 SERVICE (MAIN)EXAM- 2023 B/KE-B-PHY
PHYSICS
Paper - II
Time Allowed : Three Hours Maximum Marks : 200
Question Paper Specific Instructions
Please read each of the following instructions carefully before attempting
questions:
There are EIGHT questions in all, out of which FIVE are to be attempted.
Questions no. 1 and 5 are compulsory. Out of the remaining SIX questions, THREE are
to be attempted selecting at least ONE question from each of the two Sections A and B.
Attempts of questions shall be counted in sequential order. Unless struck off, attempt of a
question shall be counted even if attempted partly. Any page or portion of the page left
blank in the Question-cum-Answer Booklet must be clearly struck off.
All questions carry equal marks. The number of marks carried by a question/part is
indicated against it.
Unless otherwise mentioned, symbols and notations have their usual standard meanings.
Assume suitable data, if necessary and indicate the same clearly.
Neat sketches may be drawn, wherever required.
Answers must be written in ENGLISH only.
Useful Constants :
Mass of proton = 1-673 x 10-2" kg
Mass of neutron = 1675 x 10-27 kg
Mass of electron = 9-11x 10lkg
Planck constant = 6626 x 104 Js
Boltzmann constant = 1-380 x 10-23 JK-1
Bohr magneton (ip) = 9-273 x 10-24 A m2
Nuclear magneton (jy) = 5-051 x 10-27 JT-1(A m?)
Electronic charge = 1-602 x10-9C
Atomic mass unit (u) = 1-660 x 10-27 kg
= 931 MeV
ri = 5-5855 uy m(p) = 1:00727u
m(n) = 100866 u m(5He) = 4-002603 u
m(1ZC) = 12-00000u m(5,Sr) = 86:908893 u
m(7H) = 2-:014022u m(?7H) = 3:0160500u
m($0) = 15:999u
h = 1:05 x 10-34 Js
he = 197eVnm
BIKE-B-PHY 1
Ql. (a)
(b)
(c)
(d)
(e)
Q2. (a)
(b)
(c)
Q3. (a)
(b)
(c)
SECTION A
Find the condition at which de Broglie wavelength equals the Compton
wavelength for a particle.
The time independent wave function of a system is w(x) = A exp (ikx),
where k is a constant.
(i) Is this wave function normalizable in the domain — « < x < «?
Gi) Calculate the probability current density for this function.
The components of arbitrary vectors A and B commute with those of
a. Show that(o. A)(0.B)=A.B+io.(A xB).
An atomic state is denoted by ‘Dep. What should be the minimum
number of electrons involved for this state ? Give a possible electron
configuration.
Often the intensity of rotational transition J = 0 — J = 1 is not the most
intense. Explain.
2
Evaluate the commutator lS. | and hence show that [p”, x] = — 2 itp.
For the n‘ state of linear harmonic oscillator, evaluate the uncertainty
product (Ax) . (Ap).
The raising (J,,) and lowering (J_) operators of total angular momentum
are defined by J, = J, + iJy and J_ = J, — id,. Find the values of the
following :
(i) [Jx, J+]
(i) = Wy, Jz]
(ii) J_J,
What is vector model of the atom ? On the basis of it, explain the L-S
and j-j coupling under external magnetic field.
How does the Stern-Gerlach experiment explain the concept of electron
spin and its angular momentum quantization ?
Evaluate the Landé g-factor for the °P, level in the 2p 3s configuration
of the ®C atom, and then calculate the splitting of the level in eV, when
the atom is in an external magnetic field of 0-2 tesla.
BIKE-B-PHY >
10
15
15
15
15
10
Q4. (a) The rotational and centrifugal distortion constants of a diatomic
molecule are 10-59 cm™! and 5-3 x 10-4 cm“, respectively. Obtain an
estimate each for the vibrational frequency and force constant of the
molecule. [Given : The reduced mass of the molecule is 1-626 x 10-27 kg] 10
(b) Discuss the influence of anharmonicity on the vibrational spectra of
diatomic molecules with necessary diagrams. 15
(c) (i) Homonuclear diatomic molecules do not give any pure rotational
or vibrational spectra, whereas they do give a rotational Raman
spectra. Comment.
(ii) The separation between the adjacent rotational Raman lines is
4B in hydrogen molecule, whereas in oxygen molecule it is 8B.
Why ? 7+8=15
BIKE-B-PHY 3
Q5. (a)
(b)
(c)
(d)
(e)
Q6. (a)
(b)
(ce)
SECTION B
The nature of curves of binding energy and packing fraction are
complementary to each other. Explain. 8
Derive an expression for o-disintegration energy for a nucleus in a
radioactive decay process. 8
Why can Electron-Positron pair production through a high energy
photon not take place in vacuum ? 8
What will be the frequency of Josephson current, if a d.c. voltage of
4-0 nV is applied across a Josephson junction ? 8
(i) Using the logic gates, draw the circuit diagram representing the
Boolean expression AB + A(B + C) + B(B + C).
(ii) | Simplify the following Boolean expression :
[AB(C + BD) + AB] CD 44+-4=8
What do you understand by the critical size of a nuclear reactor ? Write
down the common features of nuclear reactors used for the production of
electricity. 20
On the basis of conservation laws, explain whether the following
reactions are allowed or forbidden : 10
(i) 1m +p—> Yt+K
(ii) K +p ——> Q +K*t+K?
(iii) = Q”> ——» 29400
(iv) mt+p—>pt+pin
(v) St ——> Ad+ Kt
Justify the fact that the electrons are emitted from nuclei in B-decay but
they cannot be contained inside the nuclei. 10
BIKE-B-PHY 4
(a)
(b)
(c)
(a)
(b)
(c)
Explain Gell-Mann and Ne’eman SU(3) symmetry for the classification
of elementary particles — baryons and mesons. 10
Draw the crystal structure of CaF, indicating the positions of cations
and anions. What are their respective coordination numbers ? 10
Gi) Derive an expression for the period of Bloch oscillation for a
one-dimensional crystal having lattice period a and electric
field e.
Gi) Consider an electron in a perfectly periodic lattice, wherein the
energy-wavenumber relationship in the first Brillouin zone is
21,2
k
expressed as E = ; where m, is the mass of an electron in
e
free space. Find the effective mass of the electron and hence write
down the time-independent Schrodinger equation for the electron.
Also determine the velocity of the electron. Ignore all interactions
except between the electron and the lattice. 10+10=20
With the help of a schematic diagram, describe the structure of
n-depletion MOSFET. Draw and describe its drain and transfer
characteristics. 25
Consider the BJT amplifier circuit given below with the following
parameters :
d.c. current gain Bg, = a.c. current gain Ba, = 100
Ip =20uA for Vp =0-7 V, and
ip=+2wuA for v;=+10 mV.
Determine the values of Vcr, input impedance and voltage gain A,. Vis
Vp =0-7V 7
WHT
Consider an n-channel JFET which has Ipgg = 15 mA and pinch-off
voltage V, = — 5 V. If Vgg = — 1:5 V, how much will the drain current Ip
be ? What will be the minimum value of Vpg for pinch-off to occur at
Veg =-15V? 10
B/KE-B-PHY Ss
