Question

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 ?

Answer 1

Answer:

The  value is  $h = 11930 \ m$

Explanation:

From the question we are told that

    The  temperature is  $T = 300 \ K$

     

Generally the root mean square speed of the  oxygen molecules is mathematically represented as

        $v = \sqrt{\frac{3 * R * T }{M} } = \sqrt{ 2 * g * h }$

Here  R is the gas constant with a value  $R = 8.314 \ J\cdot K^{-1} \cdot \ mol^{-1}$

    M  is the molar mass of oxygen molecule with value $M = 0.032 \ kg /mol$

So  

     $\frac{3 * 8.314 * 300 }{0.032} = 2 * 9.8 * h$

=>    $h = 11930 \ m$