Question

The binding energy per nucleon for most nuclides doesn’t vary much (see Fig. 43.2). Is there similar consistency in the atomic energy of atoms, on an “energy per electron” basis? If so, why? If not, why not?

Short answer

No, there is no similar consistency in the atomic energy of atoms on an energy per electron basis because the binding energy of electrons is electromagnetic. In contrast, the nucleons are bounded by the strong nuclear force, which does saturate.

Step-by-step solution

Define the energy

The energy $E$of a photon is related to the wavelength $\lambda$of the photon and the frequency $f$of the wave as:

$$\begin{gathered} E=hf \\ E=\frac{hc}{\lambda } \end{gathered}$$

Where the value of Planck’s constant$h=6.626\times {10}^{-34}J·s$.

Explanation

The hydrogen atom has binding energy $13.6eV$for $13.6eV$each electron. Lead is bounded by about $82keV$for each $K-$shell electron, for the contribution of $164keV$already.

Divide $164keV$by localid="1663878606887" $82keV$to get per electron. Because of the binding energy of the other $80$electrons, the actual value will be higher.

No, there is no similar consistency in the atomic energy of atoms on an energy per electron basis because the binding energy of electrons is electromagnetic, whereas the nucleons are bounded by the strong nuclear force, which does saturate.