Can earth reatin Hydrogen in its atmosphere, assuming that the average atmospheric temperature is 0C(273k)?

Question

Why or why not. Take the mass of H to be the mass of a proton (a good approximation) explain yourself with calculations

Answer 1

Calculate the thermal velocity of hydrogen using the old KE=Thermal energy equation

1/2mv^2 = 3/2kT

where k is boltzmann's constant, the 3/2 is the factor for a monoatomic ideal gas (three degrees of freedom of motion) and m is the mass of a proton.

Now compare this to the escape velocity of the Earth which you can look up or calculate by setting kinetic energy equal to gravitational potential. Solve for v in

1/2mv^2=2GMm/r

where m is the mass of the atom which cancels out, M is the mass of the Earth, G is the universal gravitational constant and r is the starting radius; the radius of the Earth will do for pretty much the entire atmosphere.

Also remember the Boltzmann distribution of kinetic energies in a gas! You might need to plot this out for hydrogen and stick a mark where escape velocity is. I don't recall if this is important for hydrogen or not, but it might be.

P.S. You can look up "G" and "k" in many places on the web. I bet even the google calculator has it.

Answer 2

Hydrogen oxidizes very rapidly in the presence of oxygen.
It could not be sustained in earths atmosphere. 1 plus 1=2.