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Relating Translational KE and T

For a monoato...

Question

For a monoatomic gas kinetic energy = E. The relation with R.M.S velocity is

A

$μ = {(\frac{2 E}{m})}^{\frac{1}{2}}$

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B

$μ = {(\frac{3 E}{2 m})}^{\frac{1}{2}}$

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C

$μ = {(\frac{E}{2 m})}^{\frac{1}{2}}$

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D

$μ = {(\frac{E}{3 m})}^{\frac{1}{2}}$

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Solution

The correct option is D i.e $μ = {(\frac{2 E}{m})}^{\frac{1}{2}}$
$E = \frac{3}{2} K T$ ..........(i)

RMS speed $(μ) = \sqrt{\frac{3 K T}{m}}$ .........(ii)
Put the value of 3KT from eq. (i) to equation (ii), we get

$\Rightarrow μ = {(\frac{2 E}{m})}^{\frac{1}{2}}$

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