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  4. 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

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Q. 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

Kinetic Theory

Solution:

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