Question

"If a hydrogen atom emits a photon of light with a wavelength of 102.6 nm when an electron returns to n = 1 , what n-value was the atom in originally?"

Answer 1

According to Rydberg equation 1/lambda = R[1/n^2_2 - 1/n^2_1] where R = Rydberg constant = 1.097 times 10^7 m^-1 lambda = wavelength = 102.6 nm = 102.6 times 10^-9 m n_2 = final quantum state = ? n_1 = initial quantum state = 1 1/lambda = R[1/n^2_2 - 1/n^2_1] 1/102.6 times 10^-9 m = 1.097 times 10^7 m^-1 [1/n^2_2 - 1/1^2] [1/n^2_2 - 1/1^2] = 1/102.6 times 10^-9 m times 1.097 times 10^7 m^-1 [1/n^2_2 - 1] = 1/112.52 times 10^-2 = 1/1.125 = 0.888 n^2_2 = 1.888 n^2 = 0.529 n_2 = 0.72