The ratio of longest wavelength lines in the Balmer and Paschen series of hydrogen spectrum is

Question

The ratio of longest wavelength lines in the Balmer and Paschen series of hydrogen spectrum is (A) (5/36) (B) (7/20) (C) (7/144) (D) (5/27)

Tardigrade Admin · Accepted Answer

The wavelength of Balmer series is given by

\frac{1}{λ _{B}} = R [\frac{1}{2 ^{2}} - \frac{1}{3 ^{2}}] = \frac{5}{36} R

.......(i)
The wavelength for paschen series is given by

\frac{1}{λ _{p}} = R [\frac{1}{3 ^{2}} - \frac{1}{4 ^{2}}] = \frac{7}{144} R

......(ii)
On dividing Eq. (ii) by Eq (i), we get

\frac{λ _{B}}{λ _{p}} = \frac{7}{20}

Q. The ratio of longest wavelength lines in the Balmer and Paschen series of hydrogen spectrum is