Question

The root mean square speed of the molecules of a diatomic gas is v. When the temperature is doubled, the molecules dissociate into two atoms. The new root mean square speed of the atom is

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

Answer 1

Answer: (C)

2v

Answer 2

$v_{rms} = \sqrt{\frac{3RT}{M}}$. According to problem T will becomes T/2 and M will becomes M/2 so the value of $v_{rms}$ will increase by $\sqrt{4} = 2$times i.e. new root mean square velocity will be 2v.