Boltzmann Distribution Peak at Lower Temperature

Steps:

• Identify the curve for the lower temperature: it shifts left with a higher peak at lower energies compared to the higher temperature curve.
• Recall that the most probable energy is the mode, the energy at the curve's maximum probability.
• Locate the peak on the lower temperature curve in the diagram.
• Match the peak position to the labeled point C.

Why C is correct:

• C marks the maximum of the lower temperature distribution, where the probability density function $f(E) \propto E^2 e^{-E/kT}$ peaks, defining the most probable energy by the Boltzmann distribution.

Why the others are wrong:

• A: Marks the peak of the higher temperature curve, which has a lower peak at higher energy.
• B: Lies on the low-energy tail of the lower temperature curve, not the maximum.
• D: Lies on the high-energy tail of the lower temperature curve, beyond the peak.

Final answer: C