Calculate the wavelength, in nanometers, of the spectral line produced when an electron in a hydrogen atom undergoes the transition from the energy level 𝑛=4 to the level 𝑛=1.

Answer 1

1 / λ = -1.097x10⁷ m^-1 (1/n_f² - 1/n_i²)

λ = wavelength in m

nf = final energy level = 1

ni = initial energy level = 4

1 / λ = -1.097x10⁷ m^-1 (1/16 - 1) = 1.097x10⁷ m^-1 (-0.9375)

1 / λ = 1.028x10⁷ m^-1

λ = 9.73x10^-8 m = 97.3 nm