As noted in Section 3, the hydrogen nucleus has a charge of Z = +1. With an electron added, the combined system is neutral, with a net charge of zero. The hydrogen atom is neutral. If we add one electron to the He nucleus, where Z = +2, the net charge will be +1. We indicate this with the notation He⁺. (For neutral entities, we omit the charge, using H rather than H⁰. For species with a +1 or –1 charge, we use just + or –.) Charged species are called ions. Positively charged ions are cations, while negatively charged ions are anions.

He⁺ is smaller than H. There is greater attraction between the single electron and a nucleus with charge Z = +2 than when the nuclear charge is Z = +1.

We can add one electron to any bare nucleus. We call this the series of hydrogen-like or hydrogenic ions, and we find that their size decreases steadily, in a well-defined manner:

5.1

Every other ion beyond C⁺⁵ will be smaller than the one before it and larger than the one after it.

We mentioned earlier in the discussion that solving the Schrödinger equation gives us the wavefunction and the energy of an atom or molecule. The images above are the wavefunctions for the ground states of H atom and the He⁺, Li⁺², Be⁺³, B⁺⁴, and C⁺⁵ cations. This graph plots the energy of each of the hydrogen-like ions through Ar⁺¹⁷:

5.2

Unlike many things in chemistry, the energies of the hydrogen-like ion series are very well behaved because there is an exact solution to the Schrödinger equation for a single electron bound to any nucleus,

E = -13.606 Z² eV.

Note that these energies do not change for different isotopes of the same element. It also does not matter if the electron is spin up (↑) or spin down (↓).

In this section we've seen that every nucleus can attract and capture at least one electron to form a stable atom (for H) or cation (for He and heavier nuclei). However, we will see below that it is also true that every nucleus can bind a second electron to form a system that is even more stable than their one electron systems. Each nucleus can, in fact, hold onto at least Z electrons. It is now time to examine the role of electron spin, because the behavior of systems with more than one electron is quite different for different combinations of spin up and spin down electrons.