Patterns and Relationships in Electron Energies

The electronic structure of an atom can be determined based on data, such as photoelectron spectroscopy (PES) and ionization energy values. In particular, the relative energies of the electrons in a multi-electron atom can be analyzed and compared. This data provides information regarding which electrons are furthest from the nucleus (they have the lowest ionization energies, meaning they are easiest to remove).

Example 1.

Consider the following species: \(\require{mhchem}\ce{S}\), \(\require{mhchem}\ce{S^{2-}}\), and \(\require{mhchem}\ce{Ar}\). Which species would have a highest ionization energy?

A. \(\require{mhchem}\ce{S}\)

B. \(\require{mhchem}\ce{S^{2-}}\)

C. \(\require{mhchem}\ce{Ar}\)



C. \(\require{mhchem}\ce{Ar}\)

The species with the highest ionization energy is the one with the greatest net (effective) nuclear charge. Argon has \(18\) protons and \(18\) electrons. Each of its electrons experiences a greater attraction to the protons in the nucleus. \(\require{mhchem}\ce{S^{2-}}\), with \(16\) protons and \(18\) electrons, would require the lowest amount of energy to remove an electron.

Example 2. 

Why does the photoelectron spectrum of the He atom only show one peak?

A. There is only one electron in a helium atom.

B. The electrons are identical, since they are the same distance from the nucleus.

C. The electrons are not attracted to the nucleus.



B. The electrons are identical, since they are the same distance from the nucleus.

The electrons in a helium atom are in the same shell and subshell. As such, they are the same distance from the nucleus and have the same energy. This means they would require the same amount of energy to ionize, resulting in only one peak in the photoelectron spectrum.

Example 3.

An electron in a hydrogen atom falls from the fifth energy level (n = 5) to the second energy level (n=2). What is true about this process?

A. A photon is emitted.

B. A photon is absorbed.

C. A photon is neither emitted nor absorbed.



A. A photon is emitted.

An electron changine between energy levels (also called stationary states) must change its energy by either absorbing or emitting a photon of energy. The atom emits a photon of energy when transitioning from a higher energy shell down to a lower energy shell. The atom absorbs a photon of energy to transition from a lower energy shell up to a higher energy shell.