IGNOU BPHET-141 December 2024 Previous Year Question Paper

Q1.Answer any five parts : 5x2=10

(a) What is relativity of simultaneity ? 2

(b) The kinetic energy of a relativistic particle is 100 MeV. What is its total energy (in MeV) if its rest mass is 938 MeV/c? ? 2

(c) Calculate the energy (in eV) of a photon that has wavelength 3 nm. 2

(d) The uncertainty in the position of a microscopic particle is 0.1 m. What is the uncertainty in its momentum ? 2

(e) Determine the eigen value of the operator P, for the wave function : 2 y = Aelod

(f) Write the time-independent Schrédinger equation for a free particle confined in the length L and the expression for its energy. 141

(g) An element characterised by A = 232 and Z = 90 loses 6 alpha and 4 beta particles in a decay process. What will the final stable product be ? 2

(h) State the condition for a nuclear fission chain reaction to be self-sustained.

Q2.Answer any two parts: 2x5=10

(a) What is length contraction ? Calculate the length of an object as measured by an observer moving at the speed 0.8 ¢

(6) parallel and

(ii) perpendicular with respect to the frame in which the object is at rest and of length 2.0 m. 2+2+1

(b) Derive the relativistic velocity addition formulae. 5

(c) Write the relativistic energy-momentum relation for a free particle. Hence, explain the concept of a massless particle. Give two examples of a massless particle. 14+3+1

Q3.Answer any two parts: 2x5=10

(a) What are matter waves ? Determine the phase velocity and group velocity of matter waves associated with a free particle having velocity v. 243

(b) Write the one-dimensional time-dependent Schrédinger equation for a particle of mass m moving in a potential V (x, t). Deduce the time-independent Schrédinger equation from it for a particle having constant energy E and subject to a potential V (x). 1+4

(c) Calculate the commutator : 5 [० +qk4 cok” By | where ¢),¢; and cy are constants.

Q4.Answer any one part : 1x10=10

(a) Write the expression for a one-dimensional step potential having a non-zero value V) in the region x > 0. Obtain the general solution of the time-independent Schrédinger equation for a particle of mass m in this step potential given that its energy is less than Vo. 248

(b) Define the one-dimensional potential barrier of height V, in the region O<x<R. Solve the time-independent Schrédinger equation for this potential and obtain the general solution for a particle of mass m when its energy E> Vj.

Q5.Answer any two parts : 2x5=10

(a) Calculate the disintegration rate of 1 g of 1171 (in curies), given that its half life is

Q6.05 days. What is the safe dose of 1°!I used for medical treatment and the corresponding disintegration rate ? 4+1

(b) Calculate the binding energy (in MeV) of $He based on

(i) mass defect and

(ii) semi- empirical mass formula and compare the two. It is given that : m, =1.008665 u, M

(H) =1.007825 u, M(‘He) = 4.002604 u and 1 w= 931.5 MeV/c”. 24241

(c) What is the source of energy in the Sun ? Give the relevant reactions and state the Q value. 14+3+1 Values of Physical constants : h=6.626x10™ J-s h=1.054x10 J-s leV =1.6x10 1° c=3x108mst Avogadro’s constant N, = 6.022107? mol y = Agi(kxtot)

(3) A=232 SR Z=90 Tea WH WH 2+8 #% +1.008665७,.._ (प्र) -1.007825 ७, M({He) = 4.002604u और 1 & = 931.5 MeV/c? | h =6.626x 10-4 J-s h=1.054x10-*4J-s leV =1.6x10 93 c=3x108ms! ararmst Frais N, = 6.02210 mol