Explain the relationship between different types of molecular speeds.

(N/A) The expressions for different types of molecular speeds are as follows:
Most probable speed $(u_{mp}) = \sqrt{\frac{2RT}{M}}$
Average speed $(u_{av}) = \sqrt{\frac{8RT}{\pi M}}$
Root mean square speed $(u_{rms}) = \sqrt{\frac{3RT}{M}}$
The relationship between these three speeds is:
$u_{rms} > u_{av} > u_{mp}$
The ratio between these three speeds is:

$u_{mp} : u_{av} : u_{rms}$	$1 : 1.128 : 1.224$
Ratio	$0.82 : 0.92 : 1.00$

Additionally,$u_{rms}$ can be expressed in terms of pressure $(p)$ and density $(d)$ as:
$u_{rms} = \sqrt{\frac{3RT}{M}} = \sqrt{\frac{3pV}{M}} = \sqrt{\frac{3p}{d}}$
Also,the speeds are related as:
$u_{av} = 0.9213 \times u_{rms}$
$u_{mp} = 0.8165 \times u_{rms}$