At what temperature will the rms speed of O2 molecules (molar mass 32) equal the rms speed of H2 molecules (molar mass 2) at 50 K?

JEE Main levelSingle correct optionDifficulty 2 of 3ig020

At what temperature will the rms speed of $O X_{2}$ molecules (molar mass 32) equal the rms speed of $H X_{2}$ molecules (molar mass 2) at $50 K$ ?

u_{rms} = 3 RT / M

. Equal speeds require

T / M

equal:

\frac{T _{O X_{2}}}{32} = \frac{50}{2}

, so

T_{O X_{2}} = 25 \times 32 = 800 K