First slide

Rms speed

Question

The root mean square velocity of the gas molecules is 300 m/s. What will be the root mean square speed of the molecules if the atomic weight is double and absolute temperature is halved?

Easy

A

300 m/s
B

150 m/s
C

600 m/s
D

75 m/s

Solution

$v_{r m s} = \sqrt{\frac{3 R T}{M}}$

Or
$300 = \sqrt{\frac{3 R T}{M}}$
And
$v_{r m s}^{'} = \sqrt{\frac{3 R (T / 2)}{2 M}} = \frac{1}{2} \times 300 = 150 m / s$

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