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## Homework Statement

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?

## Homework Equations

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?