If Rydberg's constant is R , the longest wavelength of radiation in Paschen series will be α 7 R , where α = ______.

Step-by-step solution

In the Paschen radiation series, the longest wavelength corresponds to the transition between n = 3 and n = 4 . The formula for the wavelength in the given transition can be written as, 1 λ = R Z 2 1 n 1 2 - 1 n 2 2 . . . 1 From equation (1), it follows that 1 λ = R Z 2 1 3 2 - 1 4 2 = R Z 2 1 9 - 1 16 = 7 R Z 2 9 × 16 ⇒ λ = 144 7 R Hence, α = 144 .