The rms speed of oxygen molecules in a gas is `v`. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become

Options

A. v
B. `sqrt2v`
C. 2v
D. 4v

Answer

C

Explanation

As the rms speed is given by
`v_(rms)=sqrt((3RT)/(M))rArrv_(rms)propsqrt((T)/(M))`
When temperature is double and molecules dissociates into atoms, then
`(v_(rms1))/(v_(rms2))=(sqrt((T)/(M)))/(sqrt((2T)/(M//2)))=(sqrt((T)/(M)))/(sqrt((4T)/(M)))=(sqrtT)/(sqrt4T)=1/2`
If `v_(rms1) is v, then v_(rms2)` will be 2v.