Determine the wavelength of the radiation emitted by hydrogen during the transition from n = 10 to n = 9 .

Step-by-step solution

The wavelength of the emitted radiation is given by the Rydberg formula: 1 = R_H ( 1 n₁^2 - 1 n₂^2 ) Given n₁ = 9 , n₂ = 10 , and Rydberg constant R_H = 1.097 10^7 m ⁻¹ : 1 = 1.097 10^7 ( 1 9^2 - 1 10^2 ) 1 = 1.097 10^7 ( 1 81 - 1 100 ) 1 = 1.097 10^7 ( 19 8100 ) = 8100 19 1.097 10^7 m = 8100 20.843 10^7 m 388.62 10⁻⁷ m 38862 nm The closest value among the given options is 38860 nm .