1. At what temperature the mean speed of the molecules of hydrogen gas equals the escape speed from the earth

2. Estimate the number of collisions per second suffered by a molecule in a sample of hydrogen gas at STP. The mean free path (average distance covered by a molecule between two successive collisions )=1.38×10^-5_.

Dear Vinayak Pawar,

Solution of Question no 1:

Let at temp T K it happens hence the equation is

√(8RT/∏M)=√(2GMe/Re)

where Re=radious of the earth.

        Me=mass of the earth.

M=molar mass of H2.

solving we get T=11810.1 degree

=12083.1 K

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Regards,

Askiitians Experts
Soumyajit Das IIT Kharagpur

Dear Mr. Vinayak Pawar,

Solution of Question no 1:
Let at temp T K it happens hence the equation is

√(8RT/∏M)=√(2GMe/Re)

where Re=radious of the earth; Me=mass of the earth; M=molar mass of H₂.
solving we get T=11810.1 degree

=12083.1 K

Please feel free to post as many doubts on our discussion forum as you can.
If you find any question Difficult to understand - post it here and we will get you the answer and detailed
solution very  quickly.
We are all IITians and here to help you in your IIT JEE  & AIEEE preparation.

All the best.
Regards,
Askiitians Experts
Pramod Kumar
IITR Alumni