Q. The temperature at which the $r.m.s.$ speed of hydrogen molecules is equal to escape velocity on earth surface, will be
A) $1060\ K$
B) $5030\ K$
C) $8270\ K$
D) $10063\ K$
Explanation
(d) Escape velocity from the earth’s surface is $11.2\ km/sec$
So, $v_{rms} = v_{escape} = \sqrt{\frac{3RT}{M}} \Rightarrow T = \frac{\left( v_{escape} \right)^{2} \times M}{3R}$
$= \frac{\left( 11.2 \times 10^{3} \right)^{2} \times (2 \times 10^{- 3})}{3 \times 8.31} = 10063K$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.