IGNOU BPHET-141 June 2025 Previous Year Question Paper

Q1.Answer any five parts : 5x2=10

(a) State the two postulates of special theory of relativity. 141

(b) By what factor does the mass of a relativistic particle increase from its rest mass when it travels at a speed

Q2.8 ८? 2

(c) Calculate the wavelength of a particle of mass 2.0 x 10-9 kg and kinetic energy 40.0 MeV. 2

(d) Can a quantum particle have a well- defined path ? Explain. 2

(e) Determine the eigen value of the operator p, for the wavefunction: 2 w(y,t) = Nei”)

(f) Write the time-independent Schrédinger equation for a particle of energy E in a step potential which has a step Vo for x > 0. 2

(g) An element characterized by A = 238 and Z = 92 loses 8 alpha and 6 beta particles in a decay process. What will the final stable product be ? 2

(h) Define multiplication factor k. For what values of k is a nuclear reactor

(i) critical and

(ii) subcritical ?

Q3.Answer any two parts: 2x5=10

(a) Write the Lorentz transformation equations for a frame S’ travelling parallel to another frame of reference S in the x-direction, with velocity V. Hence, determine the coordinates of an object in S’, given that its coordiantes in S are: 243 x=1.2x10°m, y=0, z=0,t=4.0s and V =0.6c

(b) Derive the relativistic energy- momentum relation for a free massless particle. 5

(c) A particle having rest mass 2.0 kg has an initial speed of 2.4 x 108 ms. A constant relativistic force of magnitude

Q4.0 x 10° N is exerted on the particle for 100 s. Calculate the magnitudes of its initial and final relativistic momenta.

Q5.Answer any two parts: 2x5=10

(a) What observation in the Davisson- Germer experiment confirmed the existence of matter waves ? Suppose, a beam of neutrons is incident on a crystal with an interatomic spacing of ~1.5A. What effect would be observed if the neutron temperature were 300 K ? Explain. 1+4

(b) Determine the normalization constant N for the following wave function : 5 N(c-x)e" , O<x<e (2. ) { 0 ; elsewhere where c is a constant.

(c) Calculate (x) for the wave function: 5 ee nx

Q6.Answer any one part : 1x10=10

(a) Write the time-independent Schrédinger equation for a free particle of mass m confined in a length L. What are the boundary conditions for the problem ? Obtain the solution of the Schrédinger equation for these boundary conditions. Determine the energy eigen values for the particle. 1+1+4+4

(b) Define the potential function for a particle of mass m in the one- dimensional finite potential well of finite energy Vo for x < L and x > L and zero elsewhere. Obtain the general solutions of the time-independent Schrédinger equation in all three regions.

Q7.Answer any two parts: 2x5=10

(a) Define activity of a _ radioactive substance. The half-life of a radioactive substance (200x) is 8 x 104 years. Calculate the decay constant (7 87) and the rate of disintegration of 1 g of the substance. 14+2+2

(b) Draw the schematic diagram of a nuclear fission reactor showing all its constituents. State the functions of moderator and safety rods in a nuclear fission reactor. 3+2

(c) Calculate the atomic number (Z) for the most stable nucleus at a given mass number, from the semi-empirical mass formula. Calculate Zo for A = 60. Take r= 23.7, 8=0.71. 8+2 Values of physical constants : h=6.626x10™J-s h=1.054x10™'J-s leV=1.6x10 "3 m,, =1.675x10~" kg ky =1.88x10° JK* Avogadro’s number Na = 6.02 x 1028 1101-71, x=1.2x10'm, y=0,2=0,t=4.0s और V=0.6c _JN(c-x)e™ , O<x<e w(x) = fPeos{%*}.0 <x<L h=6.626x10'J-s h=1.054x10™'J-s leV=1.6x10°S m,, =1.675x10~" kg ky =1.88x10° JK* c=8x10* ms”