CSS past paper

CSS Physics Paper II Past Paper 2023

CSS Physics Paper II 2023 carries 100 marks over 3 hours. It has 7 questions.

Marks: 100
Time: 3 hours
Questions: 7

Years

How to attempt: Attempt ONLY FOUR questions from PART-II. ALL questions carry EQUAL marks.

Questions

Question 1 (Part I) is the paper's MCQs, which are not reproduced here.

Q. 2
A particle of mass m is in the state
(20)
$\psi(x,t) = A\, e^{-a\left[\left(\frac{mx^{2}}{h}\right)+it\right]}$
Where A and a are positive constants.
- (a)
  Find A.
  (5)
- (b)
  For what potential energy function V(x) does $\psi(x,t)$ satisfy the Schrodinger equation?
  (5)
- (c)
  Calculate the expectation values of x, x $^{2}$ , p, and p $^{2}$
  (5)
- (d)
  Find $\sigma_{x}$ and $\sigma_{y}$ . Is their product consistent with the uncertainty principle?
  Printed 'σy'; the uncertainty product is presumably σx σp.
  (5)
Q. 3
(20)
- (a)
  Consider a pair of copper wires 1 mm in diameter and 5 cm apart. In copper the number of conduction electrons per cubic meter is 8.45 x10 $^{28}$ . Suppose their mean drift velocity v is 0.3 cm / s, calculate current in each wire.
  (8)
- (b)
  If the wires are 20 cm apart, calculate the magnetic force on the wires.
  (8)
- (c)
  Define electric current in a wire with respect to number of charges and their drift velocity.
  (4)
Q. 4
Give expressions for the following quantities in terms of $e$ , $h$ , $c$ , $k$ , $m_{e}$ and $m_{p}$ .
(20)
- (a)
  The energy needed to ionize a hydrogen atom.
  (5)
- (b)
  The difference in frequency of the Lyman alpha line in hydrogen and deuterium atoms.
  (5)
- (c)
  The magnetic moment of the electron.
  (5)
- (d)
  The spread in measurement of the $\pi^{0}$ mass, given that the $\pi^{0}$ lifetime is $\tau$ .
  (5)
Q. 5
(20)
- (a)
  An atom is capable of existing in two states: a ground state of mass M and an excited state of mass M + Δ. If the transition from ground to excited state proceeds by the absorption of a photon, what must be the photon frequency in the laboratory where the atom is initially at rest?
  (7)
- (b)
  Derive the energy levels of the hydrogen atom, from Coulomb’s law and the simple quantization of angular momentum.
  (7)
- (c)
  In radio astronomy, hydrogen atoms are observed in which, for example, radiative transitions from n = 109 to n = 108 occur. What are the frequency and wavelength of the radiation emitted in this transition?
  (6)
Q. 6
(20)
- (a)
  Consider the elastic vibrations of a crystal with one atom in the primitive cell and calculate the frequency of an elastic wave in terms of the wavevector that describes the wave and in terms of the elastic constants.
  (12)
- (b)
  Describe vibrations of crystal.
  (8)
Q. 7
(20)
- (a)
  Discuss density of states in Three Dimension
  (8)
- (b)
  Describe Debye Model for Density of States
  (8)
- (c)
  Define phonon heat capacity.
  (4)
Q. 8
Write Notes on any TWO of the following: (10 each)
(20)
- (a)
  Maxwell’s Equations
- (b)
  Magnetic Materials: (Ferro-Dia-Para)
- (c)
  Black Body Radiation

Part-II is to be attempted on the separate Answer Book.
Attempt ONLY FOUR questions from PART-II. ALL questions carry EQUAL marks.
All the parts (if any) of each Question must be attempted at one place instead of at different places.
Write Q. No. in the Answer Book in accordance with Q. No. in the Q.Paper.
No Page/Space be left blank between the answers. All the blank pages of Answer Book must be crossed.
Extra attempt of any question or any part of the question will not be considered.
Use of Calculator is allowed.