Question

The root mean square$\left(rms\right)$ of molecules of nitrogen gas is $v$ at a certain temperature. When the temperature is doubled, the molecules dissociate into individual atoms. The new $rms$ speed of the atom is:

• A. $\sqrt{2}v$
• B. $2v$
• C. $v$
• D. $4v$

Answer 1

The correct option is B $2v$

We know that $RMS$ velocity is given by: $v=\sqrt{\frac{3RT}{M}}$
According to the conditions given:
The final temperature $\left(T_2\right)$ and final molar mass $\left(M_2\right)$ is,
$T_2=2T,M_2=\frac{M}{2}$
$v_2=\sqrt{\frac{3R\times 2T}{\frac{M}{2}}}=2v$
Hence, the correct Option is (b).