For any given series of spectral lines of atomic hydrogen,

For any given series of spectral lines of atomic hydrogen, let $\Delta \bar{v}=\bar{v}_{\max }-\bar{v}_{\min }$ be the difference in maximum and minimum frequencies in $\mathrm{cm}^{-1}$. The ratio $\Delta \bar{v}_{\text {Lyman }} / \Delta \bar{v}_{\text {Balmer }}$ is :