Question

At what temperature hydrogen molecules will escape from the earth's surface?
(Take mass of hydrogen molecule $=0.34\times {10}^{-26}$ kg, Boltzman constant $=1.38\times {10}^{-23}$ J/K, radius of the earth $=6.4\times {10}^6$ and acceleration due to gravity $=9.8m/s^2$

• A. 10 K
• B. ${10}^{2}K$
• C. ${10}^{3}K$
• D. ${10}^{4}K$

Answer 1

Answer: (D)

${10}^{4}K$

The root mean square velocity of gas

$v_{mns}=\sqrt{\frac{3KT}{m}}..\left(i\right)$

Escape velocity of gas molecules

$v_{es}=\sqrt{2g{R}_e}...\left(ii\right)$

At the root mean square velocity of gas, molecule must be equal to the escape velocity.

From Eqs. (i) and (ii), we get

$\sqrt{\frac{3KT}{m}}=\sqrt{2g{R}_e}$

$T=\frac{2g{R}_{e}m}{3K}$

$\approx {10}^{4}K$