The absolute temperature at which the rms speed of a hydrogen molecule is equal to its escape speed from the Moon’s surface is (radius of Moon is R, g is acceleration duet to gravity on Moon’s surface, m is mass of hydrogen molecule and k is Boltzmann constant)

# The absolute temperature at which the rms speed of a hydrogen molecule is equal to its escape speed from the Moon’s surface is (radius of Moon is R, g is acceleration duet to gravity on Moon’s surface, m is mass of hydrogen molecule and k is Boltzmann constant)

1. A

$\frac{mgR}{2k}$

2. B

$\frac{2mgR}{k}$

3. C

$\frac{3mgR}{2k}$

4. D

$\frac{2mgR}{3k}$

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### Solution:

${\mathrm{V}}_{\mathrm{rms}}\ge {\mathrm{V}}_{\mathrm{esc}}\text{\hspace{0.17em}}⇒\sqrt{\frac{3\mathrm{RT}}{\mathrm{M}}}\ge \sqrt{2\mathrm{gR}}$

$\mathrm{T}\ge \frac{2\mathrm{MgR}}{3\mathrm{K}}$

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