Question

What will be the ratio of the wavelength of the first time to that of the second time of Paschen series of H atom ?

Answer 1

wavelength of the first transition of paschen series = ${\lambda }_1$

wavelength of the second transition of paschen series = ${\lambda }_2$

$\frac{1/{\lambda }_1}{1/{\lambda }_2}=\frac{v_1^{-}}{v_2^{-}}=\frac{R[1/n_1^2-1/n_2^2]}{R[1/n_1^2-1/n_2^2]}$

$=\frac{R[1/3^2-1/4^2]}{R[1/3^2-1/5^2]}$

$=\frac{7/144}{16/225}=683/100$

$\frac{{\lambda }_1}{{\lambda }_2}=100/683$