The rms speed of `N_2` molecules in a gas is u. If the temperature is doubled and the nitrogen molecules dissociate into nitrogen atoms, the rms speed becomes

Options

A. 2u
B. 4u
C. 14u
D. `sqrt(2)` u

Answer

A

Explanation

`u_(1)/u_(2) = sqr((n_(1)T_(1))/(n_(2)T_(2))) = sqrt((n xx T)/(2n xx 2T)) = sqrt(1/4) = 1/2`
`therefore u_(2) = 2u_(1)`
Therefore, if the temperature is doubled and the nitrogen molecules dissociate into nitrogen atoms, the rms speed becomes double.