Answer
$-246^{\circ}C$
Work Step by Step
$v_{rms}=\sqrt {\frac{3k_{B}T}{m}}$
Given that $v_{rms}$ for $H_{2}$ and $N_{2}$ are equal.
$\implies (\frac{3k_{B}T_{H_{2}}}{m_{H_{2}}})^{1/2}= (\frac{3k_{B}T_{N_{2}}}{m_{N_{2}}})^{1/2}$
$\implies T_{H_{2}}=\frac{m_{H_{2}}}{m_{N_{2}}}\times T_{N_{2}}$
$T_{N_{2}}=100^{\circ} C=(100+273)K=373\,K$
$T_{H_{2}}=\frac{2u}{28u}(373\,K)=27\,K$
$=(27-273)^{\circ}C=-246^{\circ}C$
