IGNOU BPHET-141 June 2022 Previous Year Question Paper

Q1.Answer any five parts : 5x2=10

(a) An inertial observer moves towards a star at a constant speed V,. Another inertial observer moves away from the star at the same speed. Which of the following quantities would the observers measure to be the same and which would be different :

(i) speed of starlight, and

(ii) wavelength of starlight ? Explain.

(b) An inertial frame S’ is moving at a constant speed of 0-8c with respect to an inertial frame S. The time interval measured between two events at the same position in 8 is 30s. What is the time interval measured by a clock in S ?

(c) A quantum oscillator in the wall of a black body cavity has a frequency of 5-0 x 1014 Hz. Calculate the energy of the first two quantum states.

(d) Calculate the minimum uncertainty in the position of a proton if its measured velocity has an uncertainty of 0-2 x 10-3 ms-1.

(e) Define the Parity Operator. What are its eigen values ?

(f) A particle in a one-dimensional box has an energy of 18 eV in its first excited state. Calculate its ground state energy.

(g) What do you understand by prompt and delayed neutrons ?

(h) With the help of a typical energy level diagram, show the y-decay of 2708 +0 2 81.

Q2.Answer any two parts: 2x5=10

(a) The inertial frame of reference S’ is moving with velocity V,i with respect to another inertial frame S. Write down the Lorentz transformation equations relating (x', y’, z', t') to (x, y, z, t). From these, derive the inverse Lorentz transformation equations. 5

(b) A star emits a blue line of wavelength 450 nm. Suppose the same line has a wavelength of 650 nm on the Earth. What is the “receding” speed of the star ? 5

(c) Show that the relativistic force required to give an acceleration f to a particle in the direction of its motion is : F=rm, f where m, is the rest mass of the particle.

Q3.Answer any two parts: 2x5=10

(a) Write the time-dependent Schrédinger equation. Deduce the time-independent Schrédinger equation from it. 1+4

(b) The wave function of a particle is given by : y(x) = Nxe*7a?, wo cx < 00 Calculate the normalization constant N. 5 AOA A 5

(c) Show that [L,, Ly] =ih Ly.

Q4.Answer any one part: 1x10=10

(a) A free particle is confined in a length segment lying between x = 0 and x = a. Solve the time-independent Schrédinger equation and obtain the eigen functions and eigen energies of the particle. Determine the normalization constant for the eigen function. 7+3

(b) Write down the potential function for a one-dimensional potential barrier of width a. Write down the time-independent. Schrédinger equation for a particle of mass m for this potential and obtain the general solution, when the energy of the particle is less than the barrier height. State the boundary conditions on the wave function.

Q5.Answer any two parts : 2x5=10

(a) The half-life of Zn-71 is 2-4 minutes. If 100 g of Zn was present at the beginning of decay, then how much Zn would be left after 9-6 minutes ? 5

(b) What is meant by secular equilibrium ? Uranium mineral, in which — secular equilibrium is obtained, contains one atom of radium for every 2-5 x 106 atoms of uranium. If the half-life of radium is 1620 years, then calculate the half-life of uranium. 5

(c) Draw a schematic diagram of a nuclear reactor showing its general features. What is the function of a moderator and a reflector in a nuclear reactor ? 3+2 Physical Constants : h = 6626 x 10-94 Js mg = 9:1x 107? kg mp = 16725 x 10-7” kg m,, = 1:6747 x 10-7” kg leV=16x10 J c¢=3x108 ms“! h = 1-054 x 10-34 Js BPHET-141 6 BPHET-141 8 F = rm, ze y(x) = Nxe*7a?, wo cx < 00 BPHET-141 10 h = 6626 x 10-94 Js 76 5 9:1x 107? kg my = 16725 x 10-7” kg m,, = 1:6747 x 10-7” kg leV=16x10 J ¢=3x 10° mst h = 1-054 x 10-34 Js