Cooling Sharpens Boltzmann Peak

Steps:

• Boltzmann distribution: fraction of molecules with energy E is proportional to √E exp(-E/kT).
• Total molecules fixed, so curve area stays constant.
• As T decreases, curve narrows and shifts to lower energies.
• Peak height rises, concentrating more molecules at the new most probable energy E_mp = ½ kT.

Why B is correct:

• Peak density scales as T^{-3/2}, so lower T increases molecules at E_mp while total N is fixed.

Why the others are wrong:

• A: Peak molecules increase, do not stay the same.
• C: Area equals total molecules N, remains unchanged.
• D: High-energy tail exp(-E/kT) decays faster at lower T.

Final answer: B