Other Atoms

After its early success attempts were made to extend Bohr's model to atoms other than hydrogen. The most successful models of this type were those atoms with a single electron but with Z protons in the nucleus; examples of these are singly ionized helium, doubly ionized Lithium, and so on. In these atoms one simply replaces the charge e of the proton in the hydrogen atom by the charge Ze of the nucleus. Then, for example, the formula for the emission spectra (28.14) gets modified to

$${\textstyle\frac{1}{\lambda}} {\frac{m k^2 Z^2 e^4}{4\pi c\hbar^3}} \left( \frac{1}{n_f^2}-\frac{1}{n_i^2}\right),$$ (16)

which again agrees well with experiments for these atoms. However, the success of this approach when applied to other atoms containing two or more electrons is limited, mainly due to the complicated nature of the multiple Coulomb interactions between electrons and protons, and generally approximations or numerical techniques must be used.