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=5 to the level 𝑛=1.

Question

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 = 5to the level n = 1 

Answer 1

1/λ = R (1/(n_f)² - 1/(n_i)²) where n_f is the final energy level and n_i is the initial energy level

R = 1.097x10⁷ m^-1

λ = wavelength in m

1/λ = 1.097x10⁷ m^-1 (1/1)2 - 1/(5)² = 1.097x10⁷ m^-1 (0.96) = 1.05x10⁷ m^-1

λ = 9.52x10^-8 m