Question

At what temperature will hydrogen molecules escape from earth surface?

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

Answer 1

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

According to the question, RMS velocity = escape velocity

$\sqrt{\frac{3RT}{M}}=\sqrt{2g{R}_e}$

Solving for T,

$T=\frac{2g{R}_{e}M}{3R}=\frac{2\times 9.8\times 6.4\times {10}^6\times 2\times {10}^{-3}}{3\times 8.3}=10000K$

Hence, Option D is correct.