In the Maxwell-Boltzmann equation for the distribution of molecular speeds, , the exponential term is known as the Boltzmann factor. What specific physical feature of the distribution curve does this

Question

In the Maxwell-Boltzmann equation for the distribution of molecular speeds, $\frac{1}{N}\frac{dN}{du} = 4\pi \left(\frac{M}{2\pi RT}\right)^{3/2} u^2 e^{-Mu^2/2RT}$, the exponential term $e^{-Mu^2/2RT}$ is known as the Boltzmann factor. What specific physical feature of the distribution curve does this term primarily dictate?

Prashant Kotian · Accepted Answer

Correct answer: C. The distribution curve is a product of a term (which dominates at low speeds, causing the initial parabolic rise) and the exponential term. At very high speeds (), the negative exponential term dominates and decays rapidly towards zero, dictating the steep drop-off in the fraction of molecules with extremely high speeds.

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