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indian Forest Service (Main)
Examination, 2024
PHYSICS
PAPER—II
JBNV-B-PHYS
Maximum Marks : 200
Time Allowed : Three Hours
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.
Question Nos. 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.
Answers must be written in ENGLISH only.
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.
Useful Constants :
Mass of proton = 1-673x1072" kg
Mass of neutron = 1-675x10~27 kg
Mass of electron = 9-11x1073! kg
Planck constant
Boltzmann constant
Bohr magneton (1g)
Nuclear magneton (Ly)
Electronic charge
Atomic mass unit (u)
gf? = 5-5855 py
m(n) = 1-00866u
m(2C) = 12-00000u
m(2H) = 2-014022u
m(80) = 15-999u
h = 1:05x104 Js
he = 197eVnm
JBNV-B-PHYS/49
6-626x10754 Js
1-380 x10773 yK7!
9-273 x1072* A m?
5-051x10°?7 JT"! (A m?)
1-602x107!9 c
1-660 x10~?” kg
931 MeV
m(p) = 1-00727u
m($He) = 4-002603u
87Sr) = 86-908893u
m(3H) = 3-0160500u
& = 8-85x107!2 Fm"!
[P.T.O.
SECTION—A
1. (a) Determine the size of the hydrogen atom using uncertainty principle. Given
2
that the potential energy of electron V = , where a is the distance of the
4m& oa
electron from the nucleus.
(b) Calculate the group and phase velocities for the wave packet corresponding to
a relativistic particle.
(c) Calculate [J2, Jy], [J?, Jy] and [J?, Jy], and then show that
(J, m|J2|J, m) =(J,mlJglJ, m)
(ad) Calculate the possible angles between L and § for a d-electron in one-electron
atom.
(e) The force constant of the bond in CO molecule is 1900 Nm7?. Calculate the
energy of the lowest vibrational level. The reduced mass of CO molecule is
1-14x10776 kg. Given h =6-63x107°4 Js and 1 eV =1-6x107!9 J.
2. (a) Consider a particle of mass m and charge q moving under the influence of
a one-dimensional harmonic oscillator potential. Assume that it is placed in a
constant electric field E. The Hamiltonian of this particle is therefore given by
2
H=P2_ 41 mex? —qEx
2m 2
Derive the energy expression and wave function of the nth excited state.
(b) Find the energy levels of a spin S = 3 particle whose Hamiltonian is given by
a
H= a2 Se +S? -28?) -Fs,
where a, B are constants. Are these levels degenerate?
(c) Explain the formation of molecular hydrogen in the interstellar medium.
3. (a) A beam of hydrogen atoms in a Stern-Gerlach experiment obtained from
an oven heated to a temperature of 400 K passes through a magnetic field
of length 1 m and having a gradient of 10 T/m perpendicular to the beam.
Calculate the transverse deflection of an atom of the beam at a point where the
beam leaves the field. The value of Bohr magneton pp is 9-27x1077* A m?
and the Boltzmann constant k is 1:38x10~79 J/K.
JBNV-B-PHYS/49 2
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(b) (i) Describe in brief the Raman effect.
(ii) In the vibrational Raman spectrum of HF, the Raman lines are observed
at wavelengths 2670 A and 3430A. Find the fundamental vibrational
frequency of the molecule.
(c) Discuss the rotational fine structure of electronic bands of molecule.
4. (a) Consider a particle of mass m moving in the potential
+00 ; xsO
V(x) = 1 nw? x? ; x>0O
3 ;
10
10
Estimate the ground state energy of this particle using the WKB method. 15
(b) Consider a particle of mass m moving freely between x =O and x =a inside
an infinite square well potential. Calculate the expectation values (X) n> (P) n>
(x?) and (Pp?) » and compare them with their classical counterparts.
(c) Derive the degeneracy of a harmonic oscillator g, =—(n+1)(n+2).
die
SECTION—B
10
5. (a) Asample contains 4 mg of 7!°Bi. If the half-life of radioactive 21° Bi is 5 days
and the average energy of the B-particles emitted is 0-34 MeV, then at what rate
does the sample emit energy?
(b) In the case of deuterons, answer the following :
(i) What percentage of the time do the nucleons of a deuteron spend within
the range of the nuclear forces?
(i) From a study of the radial part of the Schrédinger equation of a deuteron
for any angular momentum J, what do we conclude?
(c) Write the decay reactions of the neutral pions (n°) and the charged pions
(x*, 2°).
(d) Consider the planes with indices (1 0 0) and (0 0 1); the lattice is f.c.c., and the
indices refer to the conventional cubic cell. What are the indices of these
planes when referred to the primitive axes : d =F (t+ i), a, =S0+9 and
> ay “A
a, =—(Z+x)?
3 5! )
JBNV-B-PHYS/49 3
[P.T.O.
(e)
6. (a)
(b)
()
(b)
(¢)
(b)
(i) Prove that AB+A+AB =O.
(i) Draw a simplified logic circuit for the following Boolean expression :
Y =(A+B)AB
A radionuclide (N,) decays to a radioactive daughter (N,) that subsequently
decays to a third daughter (N3). If at t =O, the initial concentrations of N,, No
and Nz are Ne , O and O respectively, and the decay constants are A, (from
N, > N2) and A, (from Nz > N3), then derive the expression for N2 at time t.
Given that the daughter N3 is stable.
() Apply the meson theory of nuclear forces to write the interaction between
protons, neutrons, proton to neutron and neutron to proton.
(ti) Assume that the range of the interaction of nuclear force and of meson is
2x107'5 m. Estimate the mass of the meson.
State the characteristics of an ideal Op-Amp. Explain the use of an Op-Amp
as a summing amplifier and a differentiator.
Calculate the speed and radius of a-particles of energy 5998 MeV emitted into
a magnetic field B=107Wbm™. Given that the mass of proton is
1-673 x107?” kg.
Given that for intrinsic Si at T= 300 K, the band gap is 1-1 eV and the intrinsic
carrier concentration is nj =1-5x10!° cm.
(i) Calculate the intrinsic carrier concentration at T= 450 K. Assume that the
band gap at T=450 K is 1-08 eV.
(ii) Recalculate the intrinsic carrier concentration at T=450 K by assuming
that the effective electron and hole masses in the respective bands
decrease by 0:5%.
State the Barkhausen criterion for sustained oscillations of a feedback circuit.
Explain the operation of a Hartley oscillator using proper circuit diagram.
What were the difficulties faced by the initial theory of B-decay? How did Pauli
eliminate the difficulties? What were the expected properties of the new particle
proposed by Pauli?
The density of a liquid monovalent metal near absolute zero temperature is given
to be 0-081 g cm. Calculate the Fermi energy €y, the electron velocity vp at
the Fermi surface and the Fermi temperature Ty.
JBNV-B-PHYS/49 “
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( The n-p-n transistor given below has B=100, 100 = 12 nA and 8% =0-8 .
Determine the transistor currents and the region of operation of the transistor.
What happens if 7 is indefinitely increased?
=o]
Rpp=5V --
15
kkk
JBNV-B-PHYS/49 5 25SS—192
