Question

If nitrogen gas molecules goes straight up with its rms speed at $0^{\circ }$ from the surface of the earth and there are no collisions with other molecules, then it will rise to an approximate height of

• A. 8 km
• B. 12 km
• C. 12 m
• D. 8 m

Answer 1

The correct option is B 12 km

Given : Temperature of the gas $T=0^{o}C=273K$

Molecular mass of $N_2$ gas $M=28g=28\times {10}^{-3}kg$

Using $v_{rms}=\sqrt{\frac{3RT}{M}}=\sqrt{\frac{3\times 8.314\times 273}{28\times {10}^{-3}}}=\sqrt{243184.5}$ ..........(1)

Let the height upto which the gas molecule reaches be $h$.

$\therefore v_{rms}=\sqrt{2gh}$

$⟹$ $v_{rms}^2=2gh$

$243184.5=2\times 10\times h$ $⟹h=12159.2m\approx 12$ km