Determine the wavelength of the radiation emitted by hydrogen during the transition from n = 5 to n = 4 .

Step-by-step solution

Using Rydberg's formula for the wavelength of emitted radiation: 1 = R_H ( 1 n₁^2 - 1 n₂^2 ) For the transition from n = 5 to n = 4 , we have n₁ = 4 and n₂ = 5 . 1 = R_H ( 1 4^2 - 1 5^2 ) 1 = R_H ( 1 16 - 1 25 ) 1 = R_H ( 25 - 16 400 ) = 9 R_H 400 = 400 9 R_H Substituting the value of the Rydberg constant R_H = 1.097 10^7 m ⁻¹ : = 400 9 1.097 10^7 m = 400 9.873 10^7 m 40.51 10⁻⁷ m 4051 nm The closest value among the given options is 4050 nm .