Note 14 — Chapter II · Exploring the Atom

The mathematician will readily see the reason for this rule, which is, in brief, as follows: the energy needed to separate two electric charges + e and - e, at a distance r apart, is e²/r, and the energy needed to re-arrange or break up a structure of electrons and protons of linear dimensions r will generally be comparable with this. If λ is the wave-length of the requisite radiation, the energy made available by the absorption of this radiation is the quantum hC/λ. Combining this with the circumstance that the value of h is very approximately

860 e² ,

C

we find that the requisite wave-length of radiation is about 860 times the dimensions of the structure to be broken up.