BPHET-141 EM 2025 SOLVED ASSIGNMENT

Description

Tutor Marked Assignment
ELEMENTS OF MODERN PHYSICS
Course Code: BPHET-141
Assignment Code: BPHET-141//TMA/2025
Max. Marks: 100

Note: Attempt all questions. The marks for each question are indicated against it.
PART A
1. a) A spacecraft A has a speed 0.80c with respect to the Earth. If the speed of another
spacecraft B with respect to spacecraft A is 0.50c, what is the speed of B with
respect to the Earth (5)
b) A particle is travelling through the Earth’s atmosphere at a speed of 0.6c. To an
Earth-bound observer, the distance it travels is 4.0 km. How far does the particle
travel in its own frame of reference? (5)
c) A particle of rest mass 2.0 kg has an initial speed of 8 10 2 ms-1 . A constant
relativistic force of magnitude 6 10 5 . 1  N is exerted on the particle in the same
direction as the initial relativistic momentum for 1000 s. Calculate the magnitudes
of the initial and final relativistic linear momentum and its final speed. (10)
d) A star emits light with wavelength 420 nm. An observer on earth measures the
wavelength of the light received from the star to be 600 nm. Calculate the speed
with which the star is moving. (5)
2. a) Determine the wavelengths of the photons scattered at (i) 60 and (ii) 90 when X
rays of wavelength 4.5 pm are scattered from a target. (5)
b) Calculate the de Broglie wavelength of a 87Rb atom that has been laser cooled to
200 µK. (Assume that the kinetic energy is ). 2
3 T kB (5)
c) Using Heisenberg’s Uncertainty Principle explain whether a particle trapped inside a one
dimensional box of finite length can be at rest.
(5)
d) The quantum mechanical wave function for a particle is given by

 
 


   
0 , 0
0 , ) ( 2 2
3
x
x e x N x x
Determine (i) the normalization constant N and(ii) the most probable position of the particle.
(10)

4

PART B
3. a) The eigenfunction of a particle confined in a box of length L ( L x  0 ) is
 
  
    L
x
L x 3 sin 2 ) (
Calculate 2 ˆx p and the probability of finding the particle between 0  x and
4 / L x . (5+5)
b) A particle encounters a step potential of height . 0 V What is the reflection and
transmission coefficient if ? 5 . 1 0 V E Show that 1  T R . (5)
c) Show that, for a symmetric potential function  ) ( ) ( x V x V   , the parity operator
commutes with the Hamiltonian. What is the parity of the of the following eigenfunctions
of a symmetric potential well of width 2a: (i)  
  
    a
x A x 2
3 cos ) ( and (ii)


 

   a
x A x sin ) ( . (10)
4. a) The half life of 51Cr is 27.70 days. After how many days will only 10% of the
element be left over? (5)
b) Establish the relation for binding energy per nucleon for X A
Z nuclei. Calculate the
value of binding energy per nucleon for . Ni 68
28 Given:
Mass of Ni : 63.9280 u
Mass of proton : 1.007825 u
Mass of neutron : 1.008665 u
Is this nucleus stable? (10)
c) A piece of wood from the ruins of an ancient dwelling was found to have a 14C
activity of 14 disintegrations per minute per gram of its carbon content. The 14C
activity of living wood is 16 disintegrations per minute per gram. How long ago did
the tree die from which the wood sample came? Take half-life of radiocarbon as
5760 years. (5)
d) Calculate Q-Value of the reaction:
H Si He Al 1 1 30 14 4 2 27 13   
Take
  u 9815 26 Al 27 13 . m  ,
  u 0078 . 1 H 1 1  m ,
  u 0026 4 He 4 2 . = m and
u 29.9738 Si 30
14  .