States of Matter and Gaseous StatehardCOMPREHENSIVE

At what speed of the molecules, the value of the Maxwell distribution function f(c) for the temperatStates of Matter and Gaseous State Chemistry Question

Question

At what speed of the molecules, the value of the Maxwell distribution function f(c) for the temperature $T$ will be the same as that of the temperature $n$ times higher?

Answer: B

💡 Solution & Explanation

Equating $f(C, T) = f(C, nT)$ simplifies to $n^{3/2} = e^{MC^2(n-1)/(2RTn)}$. Taking natural log gives $C = \sqrt{3RTn \ln n / M(n-1)}$. Therefore, correct answer is B.

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