Consider an ideal gas model with an addition assumption. Instead of Maxwellian distribution of speed, all gas molecules at a certain level (say sea level) move with same speed equal to root mean square speed at a given temperature. If the temperature at sea level is 300 K, upto what height the oxygen gas would exist in atmosphere. take `g=10m//s^(2)` as constant.

Explanation

To solve the problem, we need to determine the height up to which oxygen gas can exist in the atmosphere, given that all gas molecules move with the same speed equal to the root mean square (RMS) speed at a certain temperature.

### Step-by-Step Solution:

1. **Calculate the RMS Speed of Oxygen at 300 K**:
The formula for the root mean square speed (v_rms) of gas molecules is given by:
\[
v_{rms} = \sqrt{\frac{3RT}{M}}
...