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 would exist in the atmosphere under the given assumptions. We will use the concept of root mean square speed and the ideal gas law.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Temperature (T) = 300 K
- Gravitational acceleration (g) = 10 m/s²
- Molar mass of oxygen (M) = 32 g/mol = 32 x 10⁻³ kg/mol
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