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

The value is
`h = 11930 \ m`

Step-by-step 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{(3 * R * T )/(M) } = √( 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

`(3 * 8.314 * 300 )/(0.032) = 2 * 9.8 * h`

=>
`h = 11930 \ m`