In Balmer series, wavelength of the 2^ nd line is ' ₁ ' and for Paschen series, wavelength of the 1^ st line is ' ₂ ', then the ratio ' ₁ ' to ' ₂ ' is

Step-by-step solution

For spectral series, 1 =R Z^2 ( 1 n ₁^2 - 1 n ₂^2 ) For the Balmer series, n ₁=2 The wavelength for 2^ nd line of the Balmer series is aligned & 1 ₁ = RZ ^2 ( 1 2^2 - 1 4^2 ) & 1 ₁ = RZ ^2 ( 1 4 - 1 16 ) & 1 ₁ = RZ ^2 ( 3 16 ) ₁= [ 16 3 ] aligned For the Paschen series, n ₁=3 The wavelength for 1^ st line of the Paschen series is aligned 1 ₂ & = RZ ^2 ( 1 3^2 - 1 4^2 ) 1 ₂ & = RZ ^2 ( 1 9 - 1 16 ) ₂ & = 144 7 1 ₂ & = RZ ^2 ( 7 144 ) ₁ ₂ & = 16 3 7 144 = 7 27 aligned