WC6 _ 19 April

What does Boltzmann distribution tell us?

• Energy levels

• Distribution of molecules at different energy levels

• Distribution of electrons in a molecule

• Magnitude of different energy levels of a molecule

Answer explanation

The Boltzmann distribution is a probability distribution of how molecules are at different energy levels.

Six distinguishable particles are distributed over 3 non-degenerate levels, of energies 0, ε and 2ɛ. The most probable value for the total energy is

• 5ɛ

• 7ɛ

• 6ɛ

• 8ɛ

Answer explanation

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

• Parabolic

• Exponential

• Hyperbolic

• Linear

Answer 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 ε_j divided by kT (where k is the Boltzmann constant).

Consider a two-level system in which the excited state, separated from the ground state by energy ε, is doubly degenerate. The fraction of the molecules in the excited state, as T→ ∞, is

• 1/3

• 1/2

• 2/3

• 1

Answer explanation

Entropy associated with a die with all its six faces having equal probability of being on top is

(kb: Boltzmann constant):

• exp(-kb/6)

• exp(-6 kb)

• 6 ln(kb)

• kb ln(6)

Answer explanation