• # question_answer 31) The root mean square speed of the gas molecules is 300 m/s. What will be the root mean square speed of the molecules if the atomic weight is doubled and absolute temperature is halved? A)  300 m/s          B)  150 m/sC)  600 m/s                      D)  75 m/s

${{v}_{rms}}=\sqrt{\frac{3RT}{2M}}$or $300=\sqrt{\frac{3RT}{2M}}$ and $v_{rms}^{'}=\sqrt{\frac{3R(T/2)}{2M}}=\frac{1}{2}\times 300=150\,m/s.$ Hence, the correction option is [b].