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=3 to the level 𝑛=1.

Answer 1

1/λ = R (1/n_f² - 1/n_i²)

λ = wavelength in meters

R = 1.0973x10⁷ m^-1

n_f = final energy level = 1

n_i = initial energy level = 3

1/λ = 1.0973x10⁷ m^-1 (1 - 1/9)

1/λ = 1.0973x10⁷ m^-1 (0.8889)

1/λ = 9.75x10⁶ m^-1

λ = 103 nm