Question

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

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

Answer 1

The correct option is A $2v$

We know that : $v_{rms}=\sqrt{\frac{3RT}{M_0}}$

Given: $T^{\prime }=2T,M_o^{\prime }=\frac{M_o}{2}$

$v_{rms}=v=\sqrt{\frac{3RT}{M_0}}$

$v_{rms}=\sqrt{\frac{3R\times 2T}{M_0/2}}=2\sqrt{\frac{3RT}{M_0}}=2v$

FINAL ANSWER : (c)