0.3 Quantum energy levels in atoms  (Page 6/9)

The ionization energies for the first twenty elements are given in . We note that there is a single ionization energy for hydrogen and helium. This is consistent withthe shell model of these atoms since, in both of these atoms, the electron or electrons are in the innermost shell. The energies ofthese electrons correspond to the $n=1$ energy level of the hydrogen atom. In lithium and beryllium, there are two ionization energies.Again, this is consistent with the shell model, since now there are electrons in both of the first two shells. Note also that theionization energy of the inner shell electrons increases as we go from hydrogen to lithium to beryllium, because of the increase innuclear charge. The lower energy electrons correspond to the $n=1$ energy level of hydrogen and the higher energy electrons correspond to the $n=2$ energy level.

Surprisingly, though, boron has three ionization energies, which does not seem consistent with the shellmodel. From the hydrogen atom energy levels, we would have expected that all $n=2$ electrons would have the same energy. We can note that the two smaller ionization energies in boron are comparable inmagnitude and smaller by more than a factor of ten than the ionization energy of the electrons in the inner shell. Thus, theelectrons in the outer $n=2$ shell apparently have comparable energies, but they are not identical. The separation of the secondshell into two groups of electrons with two comparable but different energies is apparent for elements boron to neon.

As such, we conclude from the experimental data that the second shell of electrons should be described as two subshells with slightly different energies. For historical reasons, these subshells are referred to as the as the"2s" and "2p" subshells, with 2s electrons slightly lower in energy than 2p electrons. The energies of the 2sand 2p electrons decrease from boron to neon, consistent with the increase in the nuclear charge.

Beginning with sodium, we observe four distinct ionization energies, and beginning with aluminum there arefive. Note for these elements that the fourth and fifth ionization energies are again roughly a factor of ten smaller than the secondand third ionization energies, which are in turn at least a factor of ten less than the first ionization energy. Thus, it appears thatthere are three shells of electrons for these atoms, consistent with our previous shell model. As with $n=2$ , the $n=3$ shell is again divided into two subshells, now called the 3s and 3psubshells.

These data also reveal how many electrons can reside in each subshell. In each n level, there are two elementswhich have only the ionization energy for the s subshell. Hence, s subshells can hold two electrons. By contrast, there are 6 elementswhich have both the s and p subshell ionization energies, so the p subshell can hold 6 electrons.