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At what temperature the mean speed of th...

At what temperature the mean speed of the molecules of hydrogen gas equals the escape speed from the earth?

Text Solution

Verified by Experts

Mean speed of the molecule `=(sqrt(8RT)/(pi M))`
Escape velocity =(sqrt(2 gr))`
` (sqrt(8RT))/(sqrt(pi M))= (sqrt(2gr))`
` rArr (8RT)/(piM)= 2gr`
` rArr T = 2gr ((piM)/8R)`
` = (2 xx 98 xx 6400000 xx 3.14 xx 2 xx 10)/(8 xx 8.3)`
`=11863.9 =11800 m/s`
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