Module -6
For theory descriptive type questions please refer “A textbook of Integrated Engineering Physics” by Dr. Amal Kr.
Chakrabarty
1
2
3
4
5
What do you mean by (a) macro state
Refer Page 280, 281, 282
(b) microstate (c) ensemble (d) micro
canonical ensemble (e) canonical
ensemble (f) grand canonical ensemble
(g) thermodynamic probability (h) phase
space.
a. Calculate the total no. of
a. Refer Page 309
macrostate and microstate of a
b. Refer Page 309
system consisting of ε, 2ε and 3ε
energy states with total energy
4ε and two distinguishable
particles.
b. Calculate the total no. of
macrostate and microstate of a
system consisting of ε, 2ε and 3ε
energy states with total energy
4ε and two indistinguishable
particles
a. Distribute three particles in two
a. Refer Page 306
different states according to (i)
b. Refer Page 309
MB (ii) BE (iii) FD statistics.
b. Three distinguishable particles
each of which can be
accommodated in energy states
E, 2E, 3E. 4E with total energy
6E. Find all the possible number
of distributions. Also find total
microstates in each case.
a. Write down basic postulates of
a. Refer Page 285, 289, 300 and 310
MB, BE and FD statistics.
b. Refer Page 285, 290, 300
Compare MB, BE and FD
statistics according to their
particle nature, no. of particles
in a state, energy distribution
and spin.
b. Give examples of boltzons,
bosons and fermions.
a. Discuss Fermi distribution
a. Refer Page 293
function with graphical
b. Refer Page 295, 296
representation at zero and non
zero temperature.
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7
8
b. Show that at absolute zero
temperature the no of fermions
per unit volume within energy
range ε to ε + dε is proportional
1
to 𝜀 ⁄2 .
a. Show that the average electron
energy is equal to 3/5 th of the
Fermi energy at absolute zero.
b. Calculate the value of Average
velocity, Fermi velocity and
Fermi temperature.
a. Use BE statistics to obtain
Planck’s radiation formula for
black body radiation.
b. Calculate the Fermi energy in
copper. Consider density of
copper as 8.94 x 103 kg/m3 with
atomic mass 63.5 amu.
a. The Fermi energy for sodium at
T=0K is 3.1 eV. Find its value for
aluminium. Given that the free
electron density in aluminium is
approximately 7 times that in
sodium.
b. If the Fermi energy of a metal at
thermal equilibrium is 15 eV ,
then find the average energy of
the electron.
a. Refer Page 298, 299
2
 3 2 N  3 1 2
Ef 

  mv f
2m  V 
2
2
b.
a. Refer Page 304
2
b.
a.
b.
2
 3 2 N  3
N N 
n   A and E f 


V
W
2m  V 
nNa  E f  Na

nAl  E f  Al
3
Eav  E f
5



3
2
9
a. Find the electron concentration
of silver atom with atomic
weight 108 and number of free
electron per atom as one and
Fermi energy 4.5 eV at 0 K.
b. Calculate Fermi energy at 0K of
metallic silver containing one
free electron per atom. The
density and atomic weight of
silver is 10.5 g/cm3 and 108
g/mol respectively.
a.
b.
2
 3 2 N  3
N N 
n   A and E f 


V
W
2m  V 
a.
 3 2 N  3
Ef 


2m  V 
2
2
10
a. There are about 25 x 1028 free
electrons/m3 in sodium.
Calculate its Fermi energy, Fermi
velocity and Fermi temperature.
b. A system with non-degenerate
single particle state with 0,1,2,3
energy units. Three particles are
3
N 8  2mE f 
n 


V
3  h2 
2
2
1 2
mv f
2
E f  kT f
Ef 
b. Refer Page 309
to be distributed in three states
so that the total energy of the
system is 3 units. Find the
number of microstates if
particles obey (i) MB statistics
(ii) FD statistics.
11
a. Show that at T=0, the average
energy E of an electron in a
metal is given by E 
3
E f (0)
5
where Ef(0) is Fermi energy at
absolute zero.
b. If the Fermi energy of any metal
is 10 eV. What is the
corresponding classical
temperature?
a. Refer Page 298, 299
b.
E
3
3
kT  E f
2
5