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This mock test of Statistical Physics NAT Level - 1 for IIT JAM helps you for every IIT JAM entrance exam.
This contains 10 Multiple Choice Questions for IIT JAM Statistical Physics NAT Level - 1 (mcq) to study with solutions a complete question bank.
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*Answer can only contain numeric values

QUESTION: 1

A system of non-interacting Fermi particles with Fermi energy E_{F} , has the density of states proportional to √E where E is the energy of a particles. The ratio of average energy per particle at T = 0 to the Fermi energy is.

Solution:

We know that E = U/N

and

and

The correct answer is: 0.6

*Answer can only contain numeric values

QUESTION: 2

In a Maxwellian gas, if V_{rms }is the root means square velocity, then the most probable velocity v_{mp} in terms of v_{rms} is.

Solution:

We know that

and

v_{mp} = 0.8165 v_{rms}

The correct answer is: 0.8165

*Answer can only contain numeric values

QUESTION: 3

A system has energy level E_{0}, 2E_{0}, 3E_{0},....., where the excited states are triply degenerated. Three non-interacting bosons are placed in the system. The total energy of these bosons is 5E_{0}, the number of microstates is.

Solution:

*Answer can only contain numeric values

QUESTION: 4

The total number of accessible states of non-interacting particles of spin 1/2 is given that N = 20.

Solution:

Since the particles which exhibit odd integral spins are fermions and hence they obey Pauli’s exclusion principles. According to Pauli’s exclusion principle, not more than one particle can exist in the one quantum state. Hence, the number of assessible states N = 20.

The correct answer is: 20

*Answer can only contain numeric values

QUESTION: 5

The number of coordinates in the phase space of a single particle is.

Solution:

For a single particle, these are 3 degrees of position coordinates x, y, z and 3 degrees of momentum coordinates p_{x}, p_{y}, p_{z}, hence total coordinates = 6.

The correct answer is: 6

*Answer can only contain numeric values

QUESTION: 6

The total energy per particle of a collection of free fermions is 3eV. The Fermi energy of the system (in eV) is?

Solution:

= 5eV

The correct answer is: 5

*Answer can only contain numeric values

QUESTION: 7

An ensemble of N three level systems with energies in thermal equilibrium at temperature T. Let If βε = 2, the probability of finding the system in level ε = 0 is given as (1 + 2cosh 2)^{α }. Find value of α?

Solution:

The probability of finding the system in the energy state with energy ε may be defined

But hence probability of finding the sytem with ε = 0 is

In question, βε_{0} = 2 so

P(0) = (1 + 2cosh 2)^{-1}

⇒ α = 0.

The correct answer is: -1

*Answer can only contain numeric values

QUESTION: 8

The dimension of phase space of ten rigid diatomic molecule is

Solution:

For a rigid diatomic molecule, there is no rotation possible along the inter-nuclear axis. That remove one angle from 3 Euler angles needed to describe the orientation of the molecules, and hence also removes an angular momentum component. That leaves 4 angular degrees of freedom plus 3 coordinate and 3 momenta for the center of mass motions.

∴ One diatomic molecule has phase space of dimension 10, so the number ofphase space for10 diatomic molecule = 10 ×10 = 100.

The correct answer is: 100

*Answer can only contain numeric values

QUESTION: 9

For a particle moving in a circle of fixed radius with constant speed, dimension of phase space is.

Solution:

For a 2D moving in a plane as in case of a circular motion, we have two degrees of freedom for the q i.e. for x – y plane, q_{1} = x and q_{2} = y, and two degrees of freedom for the velocity given by u_{x} and v_{y} and thus p_{x} and p_{y}.

⇒ dimension of phase space = 2 + 2 = 4.

The correct answer is: 4

*Answer can only contain numeric values

QUESTION: 10

A system of N non-interacting classical point particles is constrained to move on the two-dimensional surface of a sphere. The internal energy of the system is in units of Nk_{B}T?

Solution:

Since the particle is moving on two dimensional surface, its degree of freedom = 2.

Hence, for N non-interacting particles total degree of freedom = 2N

The energy per degree of freedom = 1/2 k_{B}T

Hence, total energy

U = Nk_{B}T

The correct answer is: 1

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