First slide

Rms speed

Question

Four molecules of a gas are having speeds of l, 4, 8 and 16 ${ms}^{- 1}$ . The root mean square velocity of the gas molecules is

Easy

A

$7.25 {ms}^{- 1}$
B

$52.56 {ms}^{- 1}$
C

$84.25 {ms}^{- 1}$
D

$9.2 {ms}^{- 1}$

Solution

$C = \sqrt{\frac{1^{2} + 4^{2} + 8^{2} + 16^{2}}{4}} {ms}^{- 1}$
= $\sqrt{\frac{1 + 16 + 64 + 256}{4}} {ms}^{- 1}$
= $\sqrt{84.25} {ms}^{- 1} = 9.2 {ms}^{- 1}$

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