# A question on oxygen electron binding energies

• hiyok
In summary, the electron binding energies of oxygen atom can be explained by the Octet Rule, which states that a filled shell has lower energy. This is due to the cancellation of orbital angular momentum and spin in atoms with filled shells. Additionally, the charge of the atom also plays a role in its reactivity, with elements closer to a closed-shell configuration being easier to oxidize or reduce. The exact quantities of these energies may vary, but the spin pairing energy is generally smaller than the orbital angular momentum energy.
hiyok
Hello, I'd like to ask a question about the electron binding energies of oxygen atom. As is known, when an oxygen atom gains one additional electron to form an anion with charge -1 it gives some 1.4ev, while it gives nearly 7.8ev if two additional electrons are bound to it. Considering that the second electron should feel a strong repulsion as it gets closer to the negatively charged anion, this seems remarkable. The only possibility to resolve this seems to take into account additonal energies. But what are they? And what are their magnitudes?

Well, that's the Octet Rule from high-school chemistry. O2- has eight electrons and is more stable than O- because it has a filled shell. Searching, this has come up before, but I don't seem to find a satisfactory answer.

Classically, your observation would be correct. However, it was the complete failure of classical physics in explaining atomic phenomena which lead to the development of quantum physics in the first place. Bound electrons can't have just any value for their energy, and this has some pretty big consequences.

The states (orbitals) that they're 'allowed' to occupy are characterized by four 'quantum numbers',
n, l, m and s. Which are the principal, azimuthal, magnetic and spin quantum numbers.
The following rules apply: n is an integer, l is an integer <= n, m is an integer from -l to +l. and spin is -1/2 or +1/2. Each n corresponds to an old-fashioned electron 'shell', n=0 is the K shell, n=1 is the L shell and so on.

If n=0, then l=0 and m = 0 and we have only the two possible spin states. The K shell can contain two electrons. (where l=0 these are known as 's' orbitals) This is the valence shell for hydrogen and helium.

When n=1, you have another pair of s obitals for l=0, m=0, and you also have n=1, l=1, m=-1,0,+1 - which (together with spin) holds six electrons (l=1, 'p orbitals').
So the L shell (the second row of the periodic table) holds 8 electrons in total and O2- has a filled L shell.

Okay, now to answer your question: Why does a filled shell have low energy?
The answer to this is in what the quantum numbers represent. The magnetic ('m') quantum number represents the orientation of the electrons angular momentum. In an oxygen atom with 7 electrons, m=0 is occupied, together with either m=1 or -1 (it doesn't matter). In other words the electrons of the atom have what's called orbital angular momentum.

But if the orbital is filled, the +m and -m electrons angular momentum will cancel out. So an atom with a filled shell has no (total) orbital angular momentum. And that's the main contributing factor to the lower energy.

There's a second factor though - spin. (which is also a kind of angular momentum, sort of). An atom with an odd number of electrons (a radical in chemistry terminology) also has electronic spin. Whereas if it has an even number of electrons, the electrons can form a pair with -1/2 and +1/2 and cancel out their spin as well. Which also lowers the energy. (In chemistry that's the 'spin-pairing energy') This is also why radicals tend to be chemically reactive.

I can't give any exact quantities offhand, but the spin pairing energy is generally the smaller of the two. (they're not entirely independent quantities) Note though, that your observation also plays a role: Charge matters, which is why elements on the edges of the periodic table (closer to a closed-shell configuration) are easier to oxidize or reduce, and why oxygen naturally 'prefers' to gain two electrons rather than lose six of them.

Thank you for your question about the electron binding energies of oxygen atoms. The phenomenon you described is known as the electron affinity of an atom, which is the energy released when an atom gains an electron to form a negatively charged ion. This energy is dependent on the electronic structure and configuration of the atom.

In the case of oxygen, the first electron affinity is lower than the second electron affinity because the first electron is added to a partially filled orbital, while the second electron is added to a fully filled orbital. This results in a stronger repulsion between the negatively charged anion and the incoming electron, leading to a higher energy requirement for the second electron to be added.

Additionally, there are other factors that can influence the electron binding energies of oxygen, such as the nuclear charge and the shielding effect of inner electrons. These factors can affect the overall energy levels of the atom and contribute to the observed differences in electron affinities.

Further research and experimentation are needed to fully understand the exact magnitudes of these additional energies and their role in determining the electron binding energies of oxygen. I hope this helps to answer your question. Thank you.

## 1. What is the electron binding energy of oxygen?

The electron binding energy of oxygen is approximately 1312 kJ/mol. This is the amount of energy required to remove one electron from a neutral oxygen atom.

## 2. How is the electron binding energy of oxygen determined?

The electron binding energy of oxygen is determined through spectroscopic techniques, such as photoelectron spectroscopy. This involves bombarding oxygen atoms with high-energy photons and measuring the energy of the ejected electrons.

## 3. Why is the electron binding energy of oxygen important?

The electron binding energy of oxygen is important because it affects the reactivity and chemical properties of oxygen. It also plays a role in the formation of chemical bonds and the stability of molecules.

## 4. How does the electron binding energy of oxygen vary in different environments?

The electron binding energy of oxygen can vary depending on the chemical environment it is in. For example, it may be higher or lower in a molecule compared to a single oxygen atom due to the influence of other atoms and their electron sharing.

## 5. What factors can affect the electron binding energy of oxygen?

The electron binding energy of oxygen can be affected by factors such as the atomic number (number of protons) of the oxygen atom, the presence of neighboring atoms, and the electronic configuration of the atom (i.e. whether it has a full or partially filled outer electron shell).

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