Atomic Structure and Spectra-quantization of Energy

If we accept that light exists as photons, then the presence of specific and sharp frequencies in the emission spectra of atoms must be interpreted as restricting the internal energy of atoms to specific values. For single-electron atoms the frequencies of the observed photons satisfy the simple relationship 

When m gets very large, 1 / m2 approaches zero. So if we pick the zero of energy to correspond to the limit of very large m, we find  

The energy required to take a hydrogen atom from n = 1 (the lowest state) to n = oo is 2.1799 x 10 18 Joules, which is called the ionization energy. 

The different values of n in Equation 5.25 then correspond to orbits with different radii, angular momenta, and rotation rates. For example, for hydrogen (Z = 1), we would get 

Substituting Equation 5.27 into the expression for the angular momentum (Equation 5.20) gives  

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Section 5.5 Atomic Structure and Spectra-quantization of Energy... 

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