Ratio of K_α and K_ß wavelength of X-rays spectrum is

For K_α wavelength, electron transits from L (n = 2) to K(n=1) state
$\therefore {\mathrm{\lambda }}_{\mathrm{k\alpha }}=\frac{\mathrm{hc}}{{\mathrm{E}}_{2\to 1}}$
For K_ß wavelength, electron transits from M(n=3) to K(n = 1) 
$\therefore {\mathrm{\lambda }}_{\mathrm{k\beta }}=\frac{\mathrm{hc}}{{\mathrm{E}}_{3\to 1}}$
So, $\frac{{\mathrm{\lambda }}_{\mathrm{k\alpha }}}{{\mathrm{\lambda }}_{\mathrm{k\beta }}}=\frac{{\mathrm{E}}_{3\to 1}}{{\mathrm{E}}_{2\to 1}}$= a constant for a given material
Different materials have different value of this ratio.