Question

If the r.m.s velocity of hydrogen becomes equal to the escape velocity from the earth surface, then the temperature of hydrogen gas would be:

• A. $1.6\times {10}^5$ $K$
• B. $50300$ $K$
• C. $82700$ $K$
• D. ${10}^4$ $K$

Answer 1

The correct option is A $1.6\times {10}^5$ $K$

$\sqrt{\frac{3kT}{m}}=11.186$ $km/sec$

Escape Velocity $V=11.186$ $km/sec$

$\Rightarrow \sqrt{\frac{3\times 1.38\times {10}^{-23}\times T}{32\times 1.66\times {10}^{-27}}}=11.186\times {10}^3$

$\Rightarrow T=160548.9$ $K=1.60\times {10}^5$ $K$