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Statistical Physics NAT Level – 2 - IIT JAM MCQ

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10 Questions MCQ Test - Statistical Physics NAT Level – 2

Statistical Physics NAT Level – 2 for IIT JAM 2024 is part of IIT JAM preparation. The Statistical Physics NAT Level – 2 questions and answers have been prepared according to the IIT JAM exam syllabus.The Statistical Physics NAT Level – 2 MCQs are made for IIT JAM 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Statistical Physics NAT Level – 2 below.

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*Answer can only contain numeric values

Statistical Physics NAT Level – 2 - Question 1

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

Detailed Solution for Statistical Physics NAT Level – 2 - Question 1

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

Statistical Physics NAT Level – 2 - Question 2

During compression of a spring, the work done is 10 kJ and 2 kJ escaped to the surrounding as heat. The change in internal energy ∆U (in kJ) is

Detailed Solution for Statistical Physics NAT Level – 2 - Question 2

w = 10 kJ
q = –2 kJ
According to the first law of thermodynamics, ∆U = q + w
= –2 + 10 = 8 kJ

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*Answer can only contain numeric values

Statistical Physics NAT Level – 2 - Question 3

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

Detailed Solution for Statistical Physics NAT Level – 2 - Question 3

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

Statistical Physics NAT Level – 2 - 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)?

Detailed Solution for Statistical Physics NAT Level – 2 - Question 4

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 N₁ , N₂ and N₃ respectively.
where N₁ + N₂ + N₃ = 6
As the particles are distinguishable, the number of microstates i.e. the number of ways of choosing N₁ , N₂ and N₃ particles from 6 particles is

W → thermodynamic probability. It is maximum when N₁ !N₂ !N₃ ! is a minimum
where N₁ = N₂ = N₃ = 2
The corresponding total energy of distribution is

= 6E
The correct answer is: 6

*Answer can only contain numeric values

Statistical Physics NAT Level – 2 - 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?

Detailed Solution for Statistical Physics NAT Level – 2 - Question 5

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

Statistical Physics NAT Level – 2 - Question 6

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

Detailed Solution for Statistical Physics NAT Level – 2 - Question 6

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_fois 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

Statistical Physics NAT Level – 2 - 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?

Detailed Solution for Statistical Physics NAT Level – 2 - Question 7

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

Statistical Physics NAT Level – 2 - Question 8

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

Detailed Solution for Statistical Physics NAT Level – 2 - Question 8

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

Statistical Physics NAT Level – 2 - Question 9

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

Detailed Solution for Statistical Physics NAT Level – 2 - Question 9

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

Statistical Physics NAT Level – 2 - 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.

Detailed Solution for Statistical Physics NAT Level – 2 - Question 10

For B-E statististic, the particles are indistinguishable

So,
The correct answer is: 1

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