Questions
At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from
the earth's atmosphere?
(Take, mass of oxygen molecule,
and Boltzmann's constant,
)
detailed solution
Correct option is B
The minimum velocity with which the body must be projected vertically upwards, so that it could escape from theearth's atmosphere is its escape velocity (ve ).As, ve = 2gRSubstituting the value of g (9.8 ms-2) and radius of earth (R = 6.4 × 106m), we get νe=2×9.8×6.4×106 ≅11.2 km s-1=11.2×103 m s-1Let the temperature of molecule be T when it attains ve.According to the question, vrms =ve.where, vrms is the rms speed of the oxygen molecule⇒ 3kBTmO2=11.2×103or T=112×1032mO23kBSubstituting the given values, i.e. kB = 1.38 × 10-23 JK-1and mO2 = m = 2.76 × 10-26 kg,we get T=11.2×1032276×10-263×1.38×10-23≃8.326×104 KTalk to our academic expert!
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