The ratio of the frequencies of the long wavelength limits of Lyman and Balmer series of hydrogen spectrum is

27 : 5

For Lyman series

$v_{\text {Lymen }}=\frac{c}{\lambda_{\max }}=R c\left[\frac{1}{(1)^2}-\frac{1}{(2)^2}\right]=\frac{3 R C}{4}$

For Balmer series

$v_{\text {Balmer }}=\frac{c}{\lambda_{\text {max }}}=R c\left[\frac{1}{(2)^2}-\frac{1}{(3)^2}\right]=\frac{5 R C}{36}$

∴  $\frac{v_{\text {Lymen }}}{v_{\text {Balmer }}}=\frac{27}{5}$