The rms speed of oxygen molecule at a certain temperature is `600ms^(-1)`. If the temperature is doubled and oxygen molecule dissociates into atomic oxygen atoms, the new rms speed is

Options

A. `120ms^(-1)`
B. `150ms^(-1)`
C. `1200ms^(-1)`
D. `600ms^(-1)`

Answer

C

Explanation

`v_("rms")=sqrt((3RT)/M)`
Given, at temperature `T_(1)`,
`v_("rms")=600=sqrt((3RT_(1))/M)" "...(i)`
At temperature, `T_(2)=2piT_(1)`,
due to dissociation
`v_("rms")=v=sqrt((3R(2T_(1)))/((M//2)))" "...(ii)`
Dividing Eq. (i) by Eq. (ii), we get
`rArrv/600=2" "rArrv=1200ms^(-1)`