IGNOU BPHET-141 December 2022 Previous Year Question Paper

Q1.Answer any five parts : 5x2=10

(a) In an inertial frame of reference S, one of Maxwell’s equations is written as : ce at Write this equation in another inertial frame S" moving uniformly with respect to S. State the postulate of special relativity that explains this.

(b) The length of a scale is measured to be

Q3.What is its length as measured by an observer moving at the speed of 0.8 ¢ with respect to the frame S ?

(c) The average life time of an excited atom is

Q4.0x10%s. Calculate the minimum uncertainty in the energy of the emitted photon.

(d) Calculate the average energy of a Planck oscillator which has an energy of Av = 0.20kgT at temperature T.

(e) Explain why the wavelength of light emitted by a quantum dot changes with the size of the dot.

(f) Define parity operator and state its eigen values.

(g) Explain multiplication factor. When is reactor said to be critical ?

(h) What is beta decay process ? Give one example of a beta decay process.

Q5.Answer any two parts: 2x5=10

(a) An object moves with a uniform velocity ए (०.५ Vy, v,) with respect to an inertial frame S which is at rest. Derive the expression for the velocity of the object u' (U;,,U,,U,) relative to the inertial frame S' which is moving with a constant speed V in the positive x-direction with respect to S.

(b) Light takes 4.8 years to travel from a star to the earth. If an astronaut travelled from earth to this star at a speed of 0.80 c, how long would it take, according to the astronaut’s clock, to reach there ?

(c) Calculate the linear momentum, total energy (in MeV) and kinetic energy (in MeV) of a proton travelling with a speed of

Q6.6 c, given that its rest energy is 938 MeV.

Q7.Answer any two parts :

(a) The wave function of a particle is given by : e*, forx <0 e*, forx >0 @)_ Is the wave function normalized? 2

(ii) Calculate the probability of finding the particle between 0 < x < 2. 3

(b) Use the uncertainty principle to estimate the approximate size of an atom. 5

(c) Define a Hermitian operator. Show that Hermitian operators have real eigen values.

Q8.Answer any one part:

(a) A particle is confined within a length segment lying between x = 0 and x = L. Solve the time independent Schrédinger equation for the particle and obtain the eigen functions and energy eigen values. Show that the eigen functions are orthogonal. 7+3

(b) A particle of mass m is moving in a step potential defined by : va) 0 , forx <0 Vo >0, forx >0 Obtain the general solution of the Schrédinger equation for this system when the energy of the particle E < Vy. State the boundary conditions. Write down the reflected and transmitted probability densities. 5+2+3

Q9.Answer any two parts :

(a) Plot a graph between binding energy per nucleon as a function of mass number. Write the main features of the curve. 3+2

(b) Define mean life of a radioactive element. The mean life of a radioactive element is