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At what temperature will the rms speed o...

At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth's atmosphere? (Mass of oxygen molecules `(m)=2.76xx10^(-26)` kg Boltzmann's constant `(k_(B))=1.38xx10^(-23)JK^(-1))`

Text Solution

Verified by Experts

`nu_("escape")=11200ms^(-1)`
Say at temperature T it attains `nu_("escape")`
`nu_("escape")=sqrt((3k_(B)T)/m_(O_(2)))`
`T=((nu_("escape"))^(2)xxm_(0_(2)))/(3k_(B))=((11200)^(2)xx2.76xx10^(-26))/(3xx1.38xx10^(-23))`
`(3.46xx10^(8)xx10^(-26))/(4.14xx10^(-23))=0.8357xx10^(5)`
`T=8.357xx10^(4)K`
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