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The ratio of the root mean square speed, average speed and maximum possible speed for a gas will be -
1. \(\sqrt 3 \sim 2\sqrt 2 \sim 3\sqrt 3 \)
2. \(\sqrt 2 \sim 2\sqrt 2 \sim 3\sqrt 3 \)
3. \(\sqrt 3 \sim \sqrt 2 \sim 2\sqrt 2 \)
4. \(\sqrt 3 \sim 2\sqrt 2 \sim \sqrt 2 \)

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Correct Answer - Option 4 : \(\sqrt 3 \sim 2\sqrt 2 \sim \sqrt 2 \)

Concept:

  • The gaseous particles are in continuous motion with each other.
  • There are three measure parameters to measure speed of the gas. 

Root - mean - square velocity of Gaseous particles:

Root mean square velocity (RMS value) is the square root of the mean of squares of the velocity of individual gas molecules. It is given by

\(\Rightarrow {V_{rms}} = \sqrt{ {\frac{{3RT}}{M}} }\)

Average velocity:

It is the arithmetic mean of the velocities of different molecules of a gas at a given temperature. It is given by

\({V_{av}} = √ {\frac{{8RT}}{{\pi M}}}\)

Most probable velocity:

It is the velocity possessed by maximum fraction of molecules at the same temperature. It is given by

\({V_p} = √ {\frac{{2RT}}{M}} \)

Explanation:

The required ratio between these parameters are 

\(√ {\frac{{3RT}}{M}} \;\;:√ {\frac{{8RT}}{{\pi M}}\;} \;:√ {\frac{{2RT}}{M}} \)

By Canceling all constant terms from the above expression we have

√3 : √8 ; √2

Or

√3 : 2√2 ; √2

So, the correct option is √3 : 2√2 ; √2

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