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# MCQs on Boltzmann Distribution

At low temperature, low – lying states close to the ground energy levels are overly populated.

a) True

b) False

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a

Explanation: At higher temperatures, the molecules are spread over different states in several energy levels but the same trend is not observed at lower temperatures. At temperatures below 5K, molecules are near or at the ground state thus making it overly populated.

What does Boltzmann distribution tell us?

a) Energy levels

b) Distribution of molecules at different energy levels

c) Distribution of electrons in a molecule

d) Magnitude of different energy levels of a molecule

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b

Explanation: The Boltzmann distribution is a probability distribution of how molecules are at different energy levels. It is given by:

N∗j = Ngje−ε‘jkT∑jgje–ε‘jkT

Where, ε‘j is total energy

gj are the degenerate states

N are the number of molecules

What is a partition function Q a function of?

a) Volume

b) Temperature

c) Temperature and volume

d) Volume and mass

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c

Explanation: The partition function Q is also known as the state sum. It is defined by the formula:

Q = ∑jgje−ε‘jkT

This partition function has its use in statistical thermodynamics and is a function of both temperature and volume.

Boltzmann distribution tells us the distribution of molecules in an unsteady system.

a) True

b) False

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b

Explanation: Boltzmann distribution helps in analyzing the energy state εj in which the molecule or atom lies within a system of N – molecules. This distribution is provided for a system of molecules/atoms which is in thermodynamic equilibrium.

How does the probability of finding molecule in an energy state vary?

a) Parabolic

b) Exponential

c) Hyperbolic

d) Linear

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b

Explanation: On observing the equation of finding the molecule in a particular energy state as given by Boltzmann distribution law, we see that the graph varies exponentially as energy εj divided by kT (where k is the Boltzmann constant).