At which temperature the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at \(47^{\circ} \mat…

\(\begin{matrix}{v}_{rms}=\sqrt{\frac{3RT}{M}} \\ \Rightarrow {v}_{rms}\propto \sqrt{\frac{T}{M}}\end{matrix}\)

\[
\frac{T_1}{M_1} = \frac{T_2}{M_2}
\]

\[
T_1 = T_2 \times \frac{M_1}{M_2}
\]

Substituting the values:

\[
T_1 = 320 \times \frac{2}{32}
\]

\[
T_1 = 320 \times \frac{1}{16}
\]

\[
T_1 = 20\ \text{K}
\]