# Photoelectron spectroscopy

Introduction to photoelectron spectroscopy (PES). How to analyze a photoelectron spectrum and relate it to the electron configuration of an element.

## Key points

• Photoelectron spectroscopy is an experimental method used to determine the electronic structure of atoms and molecules.
• Photoelectron spectrometers ionize samples by bombarding them with high-energy radiation, such as UV or x-rays, and detecting the number and kinetic energy of ejected electrons.
• The frequency and energy of incident photons can be used to calculate the binding energy of the ejected electron using the following equation: $\text{BE}=h\nu-\text{KE}_{\text{electron}}$
• The PES spectrum is a graph of electron count vs. electron binding energy.
• The peaks in PES spectra correspond to the electrons in different subshells of the atom. The peaks with the lowest binding energy correspond to the valence electrons, while the peaks at the highest binding energy correspond to the inner-shell or core electrons.

## Introduction: Ionization energy

If you look in the back of your chemistry textbook, you will most likely find a table in the appendix that lists the various ionization energies, or ionization potentials, for most of the elements on the periodic table. The ionization energy is how much energy is required to remove an electron from a neutral atom in the gaseous phase, and typically has units of kilojoules or electron volts per mole. The first ionization energy of an element $\text A$ can be written as the following reaction:
$1^{\text{st}}\,\text{Ionization energy}+\text{A}(g)\rightarrow\text{A}^+(g)+e^-$
where $\text{A}(g)$ represents a neutral atom in the gas phase, $e^-$ is the electron ejected from the atom, and $\text{A}^+(g)$ is the resulting cation formed. But how do chemists calculate the ionization energies? Magic! (Just kidding). Scientists can use photoelectron spectroscopy (PES) to experimentally determine the energy it takes to remove electrons from atoms and molecules.

## The basics of photoelectron spectroscopy

The physical phenomenon behind photoelectron spectroscopy is similar to the photoelectric effect. (For more details, check out this article on the photoelectric effect). From early experiments with the photoelectric effect, physicists learned that shining high-energy radiation on metals could eject electrons. By analyzing the kinetic energy of the ejected electrons, features about the electronic structure of the sample material could be determined.
Photoelectron spectroscopy applies the photoelectric effect to atoms and molecules in the solid, gas, and liquid phase. There are $2$ main types of photoelectron spectroscopy, depending on the energy of the radiation used to eject electrons:
$1$. Ultraviolet photoelectron spectroscopy (UPS)
Illuminating a sample with ultraviolet (UV) light will typically ionize the material by ejecting valence electrons. Valence electrons reside in the outermost shells of an atom. Due to shielding by the core electrons, the valence electrons feel a reduced attraction to the nucleus. Therefore, valence electrons require less energy to remove compared to core electrons.
$2$. X-ray photoelectron spectroscopy (XPS)
Because x-rays are higher in frequency and energy than UV rays, shining them on a sample can provide enough energy to eject core electrons. Core electrons are inner-shell electrons that are closer to the nucleus, and thus require more energy to remove compared to valence electrons.
Once electrons are ejected from the sample, a detector is able to calculate the kinetic energies of the electrons, as well as the relative number of electrons with that kinetic energy. We can use this information to calculate the minimum energy required to remove electrons from different subshells within an atom. This is called the binding energy of the electron, and the binding energies depend on the chemical structure and elemental composition of a sample.
Let's now examine the relationship between kinetic energy and binding energy in more detail.

## The relationship between binding energy and kinetic energy of photoelectrons

When an electron in the sample absorbs an incident photon, it gains that photon's energy. The energy required to eject a given electron from the atom is known as the binding energy. Core electrons have larger binding energies than valence electrons, because core electrons are closer to the nucleus and thus have a stronger attraction to the nucleus. Electrons will only be ejected from atoms if the energy of the incoming photons is greater than the binding energy of the electrons.
A photoelectron spectrometer.
A schematic of a photoelectron spectrometer. UV light or x-rays are used to ionize the sample, and the energy analyzer determines the kinetic energies and counts of the photoelectrons. Image from Wikimedia Commons, public domain.
Once ejected, the photoelectron is traveling with a certain velocity, and therefore has kinetic energy. By the law of conservation of energy, the energy of the ionizing photon must be equal to the binding energy $(\text{BE})$, plus the kinetic energy of the photoelectron $(\text{KE}_{\text{electron}})$. We can write this mathematically as follows:
$\text{E}_\text{photon}=\text{BE}+\text{KE}_{\text{electron}}$
Also, recall that the energy of a photon is given by the relationship:
$\text{E}_\text{photon}=h\nu$
where $h$ is Planck's constant $(6.626\times10^{-34}\text{ J}\cdot\text{s})$, and $\nu$ is the frequency of the photon in Hertz $\text{(Hz)}$. Substituting this relationship into the equation from the conservation of energy, we get:
$h\nu=\text{BE}+\text{KE}_{\text{electron}}$
Since we know the frequency of radiation used in the experiment and the kinetic energy of ejected photoelectrons, the binding energies can be calculated. We can solve the equation above for binding energy:
$\text{BE}=h\nu-\text{KE}_\text{electron}$
The detector in the spectrometer is also able to determine the relative number of photoelectrons with a particular kinetic energy. This number is known as the photoelectron count. From this information, the spectrometer generates a spectrum that plots photoelectron count vs. binding energy. Let's now examine some PES spectra for different elements.

## Analyzing PES spectra

### PES spectrum of lithium

PES spectra are plots of photoelectron count vs. binding energy, where binding energy usually has units of electron volts ($\text{eV}$), kilojoules ($\text{kJ}$), or megajoules ($\text{MJ}$) per mole. Keep in mind that higher binding energies correspond with electrons in lower-energy subshells$-$that is, electrons that are closer to the nucleus, and therefore require more energy to remove.
A typical spectrum will feature peaks at different binding energies. The area under each peak corresponds to the relative number of electrons that have a particular binding energy. We will often assume all the peaks have the same width, in which case the height of a peak is proportional to the number of electrons.
Because electrons in a particular subshell of an atom have approximately the same binding energy, each peak in a PES spectrum corresponds to a subshell. To illustrate, let's first look at a simulated PES spectrum for lithium, $\text{Li}$. As we look at the spectrum, it will be useful to keep in mind the ground-state electron configuration for lithium, which is $1\text{s}^22\text{s}^1$.
For a review of how to write an electron configuration, check out this video on orbitals and electron configuration.
We also have more videos in the tutorial on electronic structure of atoms that go through examples of writing the electron configuration for elements in the different parts of the periodic table!
PES spectrum of lithium, which has 1 electron with a binding energy of 0.52 MJ/mol and 2 electrons with a binding energy of 6.26 MJ/mol.
Simulated PES spectrum of lithium
Notice here that there are $2$ peaks representing electrons in $2$ different subshells. The first peak corresponds to $1$ electron with a binding energy of $0.52\text{ MJ}$. The second peak is a higher binding energy peak at $6.26\text{ MJ}$, and this peak corresponds to $2$ electrons. How do we determine which subshell of lithium corresponds to each peak?
To answer this question, we will be analyzing the highest binding energy peaks first to build up the electronic structure starting from the electrons closest to the nucleus. In this spectrum, the peak with the highest binding energy represents the $2$ core electrons that occupy the $\text{1s}$ subshell of lithium. The $1$ electron at the lower binding energy corresponds to the single valence electron that occupies the $\text{2s}$ subshell. This analysis corresponds nicely with the electron configuration of lithium, $1\text{s}^22\text{s}^1$.

### PES spectrum of oxygen

Let's look at an element with more electrons. This is a simulated PES spectrum for oxygen, $\text{O}$. As we analyze the spectrum, let's keep in mind oxygen's ground-state electron configuration: $\text{1s}^2\text{2s}^2\text{2p}^4$.
Simulated PES spectrum of oxygen
In this spectrum, we have $3$ different peaks representing electrons in $3$ different subshells. Starting with the highest binding energy peak, the peak at $52.6\text{ MJ}$ represents oxygen's $2$ core electrons in the $1\text{s}$ subshell. The next peak at $3.04\text{ MJ}$ corresponds to oxygen's electrons in the $\text{2s}$ subshell, which are valence electrons. The peak at the lowest binding energy, $1.31\text{ MJ}$, corresponds to oxygen's $4$ valence electrons that occupy the $\text{2p}$ subshell.
Once again, this spectrum matches with the ground-state electron configuration for neutral oxygen, which is $\text{1s}^2\text{2s}^2\text{2p}^4$. Notice that the sum of the electron counts for each peak in the spectrum is the total number of electrons in a neutral oxygen atom, which is equal to the atomic number of oxygen:
Concept check: How many peaks would you expect in the PES spectrum of neutral calcium?
To answer this question, we can first write out the ground-state electron configuration for calcium:
$\text{1s}^2\text{2s}^2\text{2p}^6\text{3s}^23\text{p}^64\text{s}^2$
The peaks in a PES spectrum correspond to the electrons in different subshells within an atom. That means if we know the number of subshells occupied in an atom, we will know how many peaks to expect in the PES spectrum.
In the electron configuration for calcium, we count that there are a total of $6$ different subshells: $1\text{s}$, $2\text{s}$, $2\text{p}$, $3\text{s}$, $3\text{p}$, and $4\text{s}$. Therefore, we would expect the spectrum to have $6$ unique peaks.

## Identifying an element based on its PES spectrum

A sample of an unknown element was analyzed using a photoelectron spectrometer to produce the following spectrum. What is the identity of our mystery element?
Simulated PES spectrum of a mystery element!
We can start by adding up the electron counts for all the peaks in the spectrum to find the total number of electrons in the neutral atom:
Therefore, our mystery element has a total of $13$ electrons. Since a neutral atom has the same number of electrons and protons, this suggests our mystery element is aluminum which has an atomic number of $13$. Let's make sure that the peaks in the spectrum are consistent with aluminum's electron configuration, which is: $\text{1s}^2\text{2s}^2\text{2p}^6\text{3s}^2\text{3p}^1$.
We can start by looking at the highest binding energy peak, which corresponds to the electrons ejected from the innermost subshell of the atom. We can see that the highest binding energy peak at $151\text{ MJ}$ has an electron count of $2$. The relative electron count and binding energy of this peak match with the $2$ core electrons in the $1\text{s}$ subshell.
The next peak occurs at a binding energy of $12.1\text{ MJ}$, and it has an electron count of $2$. This peak represents the $2$ electrons in the $2\text{s}$ subshell. Note that the binding energy of these $2$ electrons is more than $10$ times smaller than that of the $1\text{s}$ electrons. This is consistent with the electrons in the $2\text{s}$ subshell being further from the nucleus than the electrons in the $1\text{s}$ subshell, which means they require less energy to remove.
The next peak at $7.19\text{ MJ}$ has an electron count of $6$. This matches the next highest-energy subshell in aluminium, the $2\text{p}$ subshell, which can hold a maximum of $6$ electrons.
Lastly, the final two peaks which have the lowest binding energy represent the valence electrons. The peak with an electron count of $2$ at $1.09\text{ MJ}$ represents the $2$ $3\text{s}$ electrons, and the peak at $0.58\text{ MJ}$ represents the $1$ electron that occupies the $3\text{p}$ subshell. We can see that the binding energies and relative electron counts for all the peaks in the PES spectrum match the electron configuration for aluminum, hooray!

## Summary

• Photoelectron spectroscopy is a useful analytical tool used by chemists to determine the electronic structure of atoms and molecules.
• Photoelectron spectrometers ionize samples by bombarding them with high-energy radiation, such as UV or x-rays, and detecting the number and kinetic energy of ejected electrons.
• The frequency and energy of incident photons can be used to calculate the binding energy of the ejected electron using the following equation: $\text{BE}=h\nu-\text{KE}_{\text{electron}}$
• The PES spectrum is a graph of electron count vs. electron binding energy.
• The peaks in PES spectra correspond to the electrons in different subshells of the atom. The peaks with the lowest binding energy correspond to the valence electrons, while the peaks at the highest binding energy correspond to the inner-shell or core electrons.