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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? [Given:mass of oxygen(m)= `2.76 times 10^-26 kg` Boltzmann constant `k_B=1.38 times 10^-23 J.K^-1`]

A

`5.016 times 10^4 K`

B

`8.360 times 10^4 K`

C

`2.508 times 10^4 K`

D

`1.254 times 10^4 K`

Text Solution

Verified by Experts

The correct Answer is:
B
Escape velocity of a body for earth
`v_e=sqrt(2gr)=sqrt(2times9.8times6400times10^3)`
`=11200m//s`
Let us consider, at temperature TK escape velocity of the oxygen molecules will be `(v_e)` then
`sqrt((3k_BT)/m)=v_e`
or,`(3times1.38times10^-23)/(2.76times10^-26).T=(11200)^2`
or,`T=8.363times10^4 K`
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