Rms speed

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Question

At what temperature is $V_{r m s}$ of hydrogen molecules equal to the escape speed from the Earth's surface?

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Solution

${V_{rms}}\, = \,{V_{escape}}\, \Rightarrow \,\sqrt {\frac{{3RT}}{M}} \, = \,11.2\,km/s$
$T = \frac{{(11.2 \times 10^{3})}^{2} \times 2 \times 10^{- 3}}{8.3 \times 3} = 10076 K$

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