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The temperature, at which the root mean ...

The temperature, at which the root mean square velocity of hydrogen molecules equals their escape velocity from the earth, is closest to:
[Boltzmann constant ` k _ B = 1.38 xx 10 ^( -23) J//K ` Avogadro Number ` N _ A = 6.02 xx 10 ^( 26) // Kg ` Radius of Earth :
` 6.4 xx 10 ^( 6 ) ` m Gravitational acceleration on Earth ` = 10 ms ^( -2) ` ]

Text Solution

Verified by Experts

`v_(rms)=v_(e)`
`sqrt((3RT)/M)=11.2xx10^(3)`
or `sqrt((3kT)/m)=11.2xx10^(3)`
or `sqrt((3xx1.38xx10^(-23)T)/(2xx10^(-3)))=11.2xx10^(3):.v=10^(4)K`
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