The formula to calculate the wavelength of Hα-line in Balmer series is given by
λαhc=13.6[41−91]...(1)
The formula to calculate the wavelength of Hβ-line in Balmer series is given by
λβhc=13.6[41−161]...(2)
Divide equation (2) by equation (1)
⇒λβλα=41−9141−161
=6436×512
=2027