The Rutherford–Bohr model is a model of the atom which assumes electrons can orbit in quantized levels, know as shells. For hydrogen, the binding energy of the nth shell is given by

$ E = - \frac{13.6}{n^2} \, eV $

As such, the energy of a photon being absorbed or emitted by an atom which causes an electron to jump from nj to ni is

$ E = \frac{hc}{\lambda} = 13.6 (\tfrac{1}{n_j} - \tfrac{1}{n_i}) $

where h is Planck's constant, c is the speed of light and λ is the wavelength of the photon. The ionization energy is the energy needed to completely remove an electron, or when ni = ∞. Assuming the atom is in its ground state (nj = 1), this is simply 13.6 eV.

The above equation can be written as

$ \frac{1}{\lambda} = \frac{13.6}{hc} (\tfrac{1}{n_j} - \tfrac{1}{n_i}) $

$ \tfrac{13.6}{hc} $ is known as the Rydberg constant.

For atoms with more than one electron, these equations no longer apply since the shielding effect comes into play. Such cases require the use of Slater's rules.

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