First slide

Rms speed

Question

The root mean square speed.of the rnolecules 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

Moderate

A

$\sqrt{2} v$
B

v
C

2v
D

4v

Solution

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

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