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(B) In the absence of an external electric field,the free electrons in a metallic block are in random thermal motion.According to the kinetic theory o

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Proportional to $\sqrt{T}$

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(B) In the absence of an external electric field,the free electrons in a metallic block are in random thermal motion.According to the kinetic theory of gases,the root mean square velocity $(V_{rms})$ of these electrons is given by the formula $V_{rms} = \sqrt{\frac{3KT}{m}}$,where $K$ is the Boltzmann constant,$T$ is the absolute temperature,and $m$ is the mass of an electron.From this expression,it is clear that $V_{rms} \propto \sqrt{T}$.Therefore,the mean velocity (specifically the root mean square thermal velocity) is proportional to $\sqrt{T}$.

$A$ metallic block has no potential difference applied across it. What is the mean velocity of free electrons in terms of $T$ (absolute temperature of the block)?

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