At what temperature, hydrogen molecules will escape from the earth's surface ? (Take, radius of earth `R_(e)=6.4xx10^(6)m`, mass of hydrogen molecule `m=0.34 xx 10^(-26)`kg, Boltzmann constant `k=1.38xx10^(-23)JK^(-1)` and acceleration due to gravity `= 9.8 xx ms^(-2)`) also take rms speed of gas as `v_(rms) = sqrt((3kT)/(m))`.

Explanation

To find the temperature at which hydrogen molecules will escape from the Earth's surface, we need to equate the root mean square (rms) speed of hydrogen molecules to the escape velocity from the Earth's gravitational field.

### Step 1: Calculate the Escape Velocity (V_es)

The escape velocity from the Earth's surface can be calculated using the formula:
\[ V_{es} = \sqrt{2gR_e} \]
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