Question

Initially, the root mean square (rms) velocity of $N_2$ molecules at certain temperature is $u$. If this temperature is doubled and all the nitrogen molecules dissociate into nitrogen atoms, then the new rms velocity will be :

• A. $2u$
• B. $14u$
• C. $4u$
• D. $u/2$

Answer 1

The correct option is A $2u$

$rm{s}_{(}{N}_2)=\sqrt{\frac{3RT}{M_{(}{N}_2)}}=\sqrt{\frac{3RT}{28}}=u$.

After dissociation,

$rm{s}_{(}N)=\sqrt{\frac{3R\left(2T\right)}{M_{(}N)}}=\sqrt{\frac{3R\left(2T\right)}{14}}=2u$.

Hence option A is correct.