Question

At what temperature will the hydrogen molecules escape from Earth's surface?

• A. 10${}^4$ K
• B. 10${}^3$ K
• C. 10${}^2$ K
• D. 10${}^1$ K

Answer 1

The correct option is A 10${}^4$ K

We have the escape velocity as $v_e=11.2km/s$, boltzmann constant as $1.38\times {10}^{-23}{m}^{2}kg{s}^{-2}{K}^{-1}$and molecular mass of hydrogen as $2\times 1.66\times {10}^{-27}amu$
We have the formula as
$\frac{3}{2}kT=\frac{1}{2}m{v}_e^2$
or
$T=\frac{m{v}_e^2}{3k}=\frac{2\times 1.66\times {10}^{-27}\times {11.2}^2\times {10}^6}{3\times 1.38\times {10}^{-23}}={10}^{4}K$