Boltzmann Distribution Analysis

Steps:

• Locate the shaded region on the T1 curve between E1 and E2; it quantifies the fraction of molecules by integrating the probability density.
• Compare curve shapes: T1 likely peaks higher and narrower than T2, but verify labels for temperature order.
• Check the curve at E=0; the density function approaches zero, implying negligible probability at exactly zero energy.
• Note D's absence prevents evaluation.

Why A is correct:

• In the Boltzmann distribution, the area under the curve between two energies equals the fraction of molecules with energies in that interval, per the probability density definition.

Why the others are wrong:

• B: Diagram labels may show T1 higher than T2, reversing the typical lower-temperature narrowing.
• C: The continuous distribution has zero probability density at exactly E=0, but low-energy molecules exist near zero.
• D: No statement provided, so unverifiable.

Final answer: A