A vessel is partitioned in two halves by a fixed diathermic separator. Two different gases are filled in left (L) and right (R) halves. The rms speed of the molecules in L part is equal to the mean speed of molecules in the R part. Then the ratio of the mass of a molecule in L part to that of a molecule in R part is : 

\(\frac{3}{8}\pi\)

rms velocity of molecule in left part : v_rms

v_rms = \(\sqrt{\frac{3KT}{m_L}}\)

Average speed of molecule is right part : v_avg

v_avg = \(\sqrt{\frac{8KT}{\pi m_R}}\)

According to question : \(\sqrt{\frac{3KT}{m_L}}\) = \(\sqrt{\frac{8KT}{\pi m_R}}\)

\(\frac{3}{m_L} = \frac{8}{\pi m_R}\)

\(\Rightarrow \frac{m_L}{m_R} = \frac{3\pi}{8}\)