Question

The root mean square velocity of molecules of a gas is 200 m/s. What will be the root mean square velocity of the molecules, if the molecular weight is doubled and the absolute temperature is halved?

Options

• 50 m/s

• 200 m/s

• 100 m/s

• `100/sqrt2` m/s

Answer 1

100 m/s

Explanation:

The root mean square velocity of gas molecule is

`"v"_"rms" = sqrt("3RT"/"M")`

`=> "v"_"rms" prop sqrt("T"/"M")`

∴ `("v"_"rms")_1/("v"_"rms")_2 = sqrt("T"_1/"M"_1) xx sqrt("M"_2/"T"_2)`

Here, `"T"_2 = "T"_1/2` and M₂ = 2M₁

`("v"_"rms")_1/("v"_"rms")_2 = sqrt("T"_1/"M"_1) xx sqrt((4"M"_1)/"T"_1)` = 2

or `("v"_"rms")_2 = ("v"_"rms")_1/2 = 200/2` = 100 m/s