Kinetic Theory Of Gases Question 36
Question: A nitrogen molecule has some rms speed at $ 0{}^\circ C $ on the surface of the earth. With this speed, it goes straight up. If there is no collisions with other molecules, the molecule will rise up to a height of
Options:
A) 82 km
B) 12.4 km
C) 10.6 km
D) 152 km
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ v _{rms}=\sqrt{\frac{3RT}{M}}=\sqrt{\frac{3\times 8.31\times 273}{28\times {{10}^{-3}}}}=493m/s $ Thus $ \frac{1}{2}mv _{rms}^{2}=\frac{mgh}{1+\frac{h}{R}}. $ After substituting the values and simplifying, we get h= 12.4 km
BETA
