Gas molecules are in a constant state of motion, thus colliding with each other and with the wall of container. Maxwell and Boltzmann proposed due to such collisions, the velocities of gas molecules are always variable. A fraction of molecules can be considered to have a particular molecular velocity at a time. Maxwell calculated the distribution of velocity among fraction of total number of molecules based on probability. The average, most probable and root mean square velocities of the fraction of gas molecules are expressed as
\[
u_{\text {avg }}=\sqrt{\frac{8 R T}{\pi M}} u_{\mathrm{mp}}=\sqrt{\frac{2 R T}{M}} u_{\mathrm{rms}}=\sqrt{\frac{3 R T}{M}}
\]
The ratio \( u_{\mathrm{rmm}}: u_{\mathrm{avg}}: u_{\mathrm{mp}} \) is
(A) \( 1: 0.921: 0.816 \)
(B) \( 2: 0.0921: 1 \)
(C) \( 3: 0.0921: 8 \)
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