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Question

The temperature, at which the root mean square velocity of hydrogen molecules equals their escape velocity from the earth is closest to
(Take g=10 m/s2)

A
104 K
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B
650 K
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C
3×105 K
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D
800 K
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Solution

The correct option is A 104 K
We know that,
Escape velocity, Ve=2gR[Rradius of earth]Ve=2×10×6400×103 [R=6400 km=6400×103 m]Ve11314 m/s
Also, Vrms=3RTM11314=3×8.3×T2×103
[Given Ve=Vrms, Molar mass of hydrogen, M=2 g]
T=113142×2×1033×8.3T=10281 K104 K

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