If the longest wavelength of spectral line of Paschen series of Li ²⁺ ion spectrum is x Å , then the longest wavelength (in Å ) of Lyman series of hydrogen spectrum is

Step-by-step solution

v =R_H Z^2 ( 1 n₁^2 - 1 n ₂^2 ) For paschen series longest wavelength aligned & n ₁=3 & n ₂=4 & v = R _ H (3)^2 ( 1 (3)^2 - 1 (4)^2 ) & v =R_H 9 7 9 16 & v =R_H 7 16 aligned 1 = R _ H 7 16 or, = 16 7 R _ H = x ...(i) for Lyman series of hydrogen spectrum aligned & v =R_ H Z ^2 [ 1 ~N ₁^2 - 1 ~N ₂^2 ] & v = R _ H (1)^2 [ 1 1^2 - 1 2^2 ] & v = R _ H 3 4 & = 4 3 R _ H ...(ii) aligned By equation (i) and (ii) we get = 7 x 12