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This mock test of Statistical Physics NAT Level – 2 for IIT JAM helps you for every IIT JAM entrance exam.
This contains 10 Multiple Choice Questions for IIT JAM Statistical Physics NAT Level – 2 (mcq) to study with solutions a complete question bank.
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*Answer can only contain numeric values

QUESTION: 1

The pressure for a non-interacting Fermi gas with internal energy U at temperature T is given as . Find value of x?

Solution:

The mean pressure of the perfect Fermi gas can be written as

The average energy of the system is

For an ideal fermion is a cubical box, the energy of single particle states are given by

If there is no interaction

E_{i} = energy of i^{th} microstate of the system.

The correct answer is: 0.667

*Answer can only contain numeric values

QUESTION: 2

Boltzmann distribution of particles between different states under equilibrium at temperature T is given

Vibrational states have equal spacing hv as a first approximation. For a particular case Out of N molecules, a number N_{0} is in the ground state. Then is nearest to?

Solution:

= N_{0} (1 + 0.4 + 0.4^{2} + ...)

N = N_{0} (1.68) nearly

⇒

The correct answer is: 0.595

*Answer can only contain numeric values

QUESTION: 3

According to Fermi-Dirac statistic the number of particles in a phase cell is.

Solution:

Systems following Fermi-Dirac statistics obey Pauli’s exclusion principal and each phase cell corresponding to one energy level which can be occupied by only 1 particle.

The correct answer is: 1

*Answer can only contain numeric values

QUESTION: 4

Six distinguishable particles are distributed over three non-degenerate levels of energies 0, E and 2E. The total energy of the distribution for which the probability is a maximum is (in terms of E)?

Solution:

Since, the levels are non-degenerate there is only one state associated with each energy.

Let the number of particles is 3 energy state be N_{1} , N_{2} and N_{3} respectively.

where N_{1} + N_{2} + N_{3} = 6

As the particles are distinguishable, the number of microstates i.e. the number of ways of choosing N_{1} , N_{2} and N_{3} particles from 6 particles is

W → thermodynamic probability. It is maximum when N_{1} !N_{2} !N_{3} ! is a minimum

where N_{1} = N_{2} = N_{3} = 2

The corresponding total energy of distribution is

= 6E

The correct answer is: 6

*Answer can only contain numeric values

QUESTION: 5

Consider a radiation cavity of volume V at temperature T. The average number of photons in equilibrium is proportional to T^{α} , Find α?

Solution:

For photons, B-E statistics is applicable

For photons,

the density of states for photons between p and p + dp is

Since two independent direction of polarization

hv = dE

⇒ hdv = dE

Average number of photons

The correct answer is: 3

*Answer can only contain numeric values

QUESTION: 6

Ratio is average energy of an electron in a metal at T = 0 to the Fermi energy at T = 0 is.

Solution:

The total number of cells upto energy level

Thus, the number of cells corresponding to energy interval E and E + dE is given by

The total number of cells between energy level 0 and E_{F} at T = 0, are equal to the total number of particles i.e.

Thus,

E_{fo }is value of E_{F} at T = 0.

The average kinetic energy of the particle at T = 0 is given by

The correct answer is: 0.6

*Answer can only contain numeric values

QUESTION: 7

Consider a system of 2 identical particles each of which can be in any one of the 3 single particles states. The number states of the systems are possible in B-E statistics?

Solution:

The total number of way W, of distributing 2 identical particles in the given system is

n_{i} = 2, g_{i} = 2

The correct answer is: 6

*Answer can only contain numeric values

QUESTION: 8

The probability that a state which is 0.2eV above the Fermi energy in metal atom at 700K is.

Solution:

Probability of occupancy of a given state with energy E is given by the FermiDirac distribution formula which is

f(E) = 0.035

The correct answer is: 0.035

*Answer can only contain numeric values

QUESTION: 9

The Fermi energy of a free electron gas depends on the electron density ρ as Find the value of α?

Solution:

The Fermi energy of the electron gas is given by

with g_{s} = 2

The correct answer is: 0.667

*Answer can only contain numeric values

QUESTION: 10

In a system of particles, each particles can be in any one of three possible quantum states. The ratio of the probability that the two particles occupy the same state to the probability that the two particle occupy different state for B-E statistics is.

Solution:

For B-E statististic, the particles are indistinguishable

So,

The correct answer is: 1

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