Question

The RMS speed of a molecule of a diatomic gas is $U$. When the temperature is doubled, the molecules dissociate into two atoms. The new RMS speed of the atom is:

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

Answer 1

The correct option is C $2U$

Initial RMS speed, $U=\sqrt{\frac{3RT}{M}}$

When temperature is doubled,

$U_f=\sqrt{\frac{3R\times \left(2T\right)}{M/2}}=2\sqrt{\frac{3RT}{M}}=2U$

Hence, the correct answer is option $\text{C}$.