Answer
$\frac{T_{2}}{T_{1}}=\frac{3}{2}$
Work Step by Step
We know, $v_{mp}=\sqrt (2RT_{2}/M)$ at tempterature $T_{2}$
and $v_{rms}=\sqrt (3RT_{1}/M)$ at temperature $T_{1}$
Now, $\frac{v_{mp}}{v_{rms}}=\frac{\sqrt (2RT_{2}/M)}{\sqrt (3RT_{1}/M)}=\sqrt \frac{2T_{2}}{3T_{1}}$
Since, $v_{mp}=v_{rms}$, So, $2T_{2}=3T_{1}$ that gives, $\frac{T_{2}}{T_{1}}=\frac{3}{2}$
