IGNOU BPHET-141 June 2023 Previous Year Question Paper

Q1.Answer any five parts : 5x2=10

(a) What is the difference between the Galilean principle of relativity and the principle of relativity stated by Einstein ?

(b) Explain why we do not observe the effects of time dilation in everyday phenomena ?

(c) Calculate the wavelength of a photon which has an energy of 8.0 MeV.

(d) The uncertainty in the energy of a short lived particle is 0.6 MeV. What is the smallest life time the particle can have ?

(e) Determine the eigen value of the operator H=in o for the wave function : y = Nel(kx-o0)

(f) Write the Schrédinger equation for a free particle and the expression for its energy.

(g) An element characterised by A = 238 and Z = 92, loses 8 alpha

(a) and 6 beta

(f) particles in a decay process. What will the final stable product be ?

(h) Calculate the mass defect (in u) of Fe given that : Mn = 1.008665 u, m (iA) = 1.007825 u, M (Fe) = 55.934932 u.

Q2.Answer any two parts: 2x5=10

(a) Two spaceships of proper length Lo approach the earth from _ opposite directions at velocities कु What is the length of one of the spaceships with respect to the other ?

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

(c)

(i) A spaceship is receding from earth at a speed of 0.40 c. The wavelength of light emitted by a source in the spaceship is measured to _ be 2 =450nm on the spaceship. What would the wavelength of this light be as measured by an observer on earth ? Gi) Show that for v c, the expression for the relativistic kinetic energy approaches that of the classical kinetic energy.

Q3.Answer any two parts : 5x2=10

(a)

(i) State the probabilistic interpretation of the wave function. 2 Gi) List the conditions that a wave function y(x,t) must satisfy to be an acceptable solution of the Schrédinger equation. 3

(b) A particle of mass m has the following wave function : _ JNxe® forx>0 ve={ 0 forx <0 If the total energy of the particle is zero, determine its potential energy function.

(c) Calculate the commutator : as ~ pe a

Q4.Answer any one part : 10x1=10

(a) The potential function for a symmetric infinite potential well is given by : «© for x<-L ४०- for -L<x<L o for x>L Solve the time-independent Schrédinger equation for a particle of mass m in this potential. Obtain the even and odd parity eigen-functions and energy eigen values. 5+3+2

(b) Obtain the general solution of the time- independent Schrédinger equation for a particle of mass m for a potential function defined by : 0 for x<0O V(x) =4Vy for O<x<a 0 for x>a when the energy of the particle is E < Vo. Write down the boundary conditions. Define the reflection and transmission coefficients and the tunnelling length. 5+2+3

Q5.Answer any two parts : 5x2=10

(a) Calculate the energy of reaction (Q — Value) in MeV in the fusion reaction involving two deuterons to form a tritium and a proton : Qry , 2 3p 1 jH+;H>)H+)H Take m(?H) = 2.0141029 u, m

(H) = 3.016049 u and m({H) = 1.008665 u lu = 931.5 MeV/c?.

(b) Explain why electrons cannot reside inside the nucleus.

(c) Plot number of neutrons versus the number of protons for naturally occurring nuclei. Explain the features of this plot. 243 Physical constants : h = 6.626 x 10-84 J-s m, = 9.1x 1031 kg m, = 1.6725 x 10°" ke m, = 1.6747 x 10-°7 kg c= 383x108 mst h = 1.054 x 104 J-s leV=16x1019J