From what height must an oxygen molecule fall in a vacuum so that its kinetic energy at the bottom equals the average energy of an oxygen molecule at 300 K?
E_avg=3/2*kb*T (kb is the boltzmann's constant)
PE = mgh = KE_final = 1/2*m*v_rms^2
The Attempt at a Solution
I know that E_avg is equal to 6.21*10^-21. This is then equal to mgh.
I must be having difficulties calculating the mass of O2. There are 32g/mol = .032kg/mol. Dividing by Avogadro's number, this gives 5.3135*10^-26 kg per O2 molecule. Then plugging this into the equation h = E_avg/(mg) returns the height as 1.19*10^4 m... This is wrong. Can anyone help me figure out where I made an error?