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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

`V_(escape) = 11200 ms^(-1)`
Say at temperature T it attains `V_(escape)`
`V_(escape) = sqrt( (3k_B T)/(m_(O_2) ) ) `
` T = ( (V_(escape))^2 xx m_(O_2) )/(3k_B) = ( (11200)^2 xx 2.76 xx 10^(-26) )/(3 xx 1.38 xx 10^(-23) )`
` = (3.46 xx 10^8 xx 10^(-26) )/(4.14 xx 10^(-23) ) = 0.8357 xx 10^5`
` T = 8.357 xx 10^4 K`
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