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# Photoelectron Spectroscopy

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In your science career, you will find that Albert Einstein laid the foundation for many technologies. Here we will discuss Einstein's theory of the Photoelectric Effect which led to the formulation of the Theory of Quantum Mechanics. This article will discuss the Photoelectron Spectroscopy method, emphasizing theory and applications.

• First, we will talk about the basics of photoelectron spectroscopy (PES).
• Then, we will look at X-ray photoelectron spectroscopy.
• After, we will analyze the features of photoelectron spectroscopy graphs.
• Subsequently, we will explore angle-resolved ultraviolet photoelectron spectroscopy.
• Finally, we will go over the main fields of application of PES and suggest areas for further study.

## Background: Photoelectron Spectroscopy

Before we dive straight into photoelectron spectroscopy, let's cover the important background information.

Quantum: a packet of energy, or energy of a quantum state. The plural of quantum is quanta.

Quantum State (Energy state) refers to the energy of an electron in orbit about the nucleus of a molecule.

Excited State: when an electron in a substance absorbs a quantum and is promoted to a higher energy state.

Electromagnetic (EM) radiation: any type of light (e.g., UV, IR, Visible, etc.) or particle rays (like X-rays).

Have a look at the article on the Electromagnetic Spectrum for more information on this.

### The Photoelectric Effect

Photoelectron Spectroscopy (PES) is based on the theory of the photoelectric effect:

• The photoelectric effect is the emission of electrons from a metal surface when electromagnetic (EM) radiation hits it.

The photoelectric effect is observed when electromagnetic (EM) radiation, such as UV light or X-rays, reflects off of the surface of a solid. In other words, the photoelectric effect occurs when a quantum of EM radiation ionizes an electron from a molecule in a solid.

Figure 1: Schematic of photoelectric effect experiment. Study Smarter Original

The photoelectric effect occurs when light, used to probe the surface of a solid, possesses a quantum () that has an energy that exceeds the binding energy of an electron bound to a surface molecule.

$$BE_{electron}=h\nu_0$$

The interaction of a quantum of EM radiation with a molecule on the surface of a probed solid will excite a molecularly bound electron from the ground state to an excited, "positive ion state" (please see figure 2).

Figure 2: Energy Diagram - Excitation of a ground state electron, bound to a molecule, -M-, within a solid, by a quantum of EM radiation.

We note that any excess energy () past the energy needed to excite an electron from a molecular ground state to a positive ion state ( BEelectron = 0 ) will be converted to the kinetic energy of the outgoing electron. This kinetic energy (KEelectron ) moves the ionized electron past the surface of the solid into the vacuum (please see figure 3).

Figure 3: Energy Diagram - Excitation of a ground state electron into the vacuum by a quantum of EM radiation.

For a detailed explanation of the terms, formulas, and processes involved in the above figure, please refer to the next section, "Photoelectron Spectroscopy Theory".

### Photoelectron Spectroscopy Theory

The energy of a quantum of EM radiation from the light source is :

$$E_{quantum}=h\nu$$

Where:

• h: is Planck's constant equal to 6.626·10-34 J*s

• ν: is the frequency of the radiation.

According to Einstein's theory of the photoelectric effect, the kinetic energy, (KEelectron ), of an electron that is knocked off of a molecule on the surface of a solid is:

$$KE_{electron}=h\nu-h\nu_0$$

Where:

• is the energy of the incoming quantum.

• 0 is the energy required to promote an electron from a bound state to a positive ion state (please see figure 2).

In terms of the electron binding energy, (BEelectron = hν0), the kinetic energy of the electron emitted from the surface of the solid is:

$$KE_{electron}=h\nu-BE_{electron}$$

Then, moving (BEelectron ) to the left-hand side, we get:

$$KE_{electron}+BE_{electron}=h\nu=E_{quantum}$$

Where:

• = Equantum is the energy of the incoming EM radiation.

• KEelectron is the kinetic energy of the electron emitted from the surface of the solid.

• BEelectron is the binding energy of an electron in a molecule on the surface of a solid.

Lastly, we note that the binding energy of an electron in a molecule on the surface of a solid material is:

$$BE_{electron}=E_{quantum}-KE_{electron}$$

## X-ray Photoelectron Spectroscopy

Now let's look at some examples using x-ray photoelectron spectroscopy.

An X-ray source illuminates the surface of a small silver plate located within a vacuum tube that is transparent to X-rays. Typical X-ray sources emit quanta at energies ranging from 124 eV to 145 eV (eV is short for electron-volts). If a quantum of 135 eV is emitted from the source, what would the frequency of this radiation be? What would the energy per mole of the X-ray packets be?

1. Calculation of the frequency of the X-ray packet:

Given that the X-ray quantum has an energy of 135 eV, we first convert electron-volts, eV, to kilo Joules, kJ, by the following conversion factor:

$$1eV=1.6022X10^{-22}kJ$$

Notice that, conversion factors are another form of the number one, which can be seen in the present case by the following rearrangement:

$$1=\frac{1.6022X10^{-22}kJ}{1\,eV}$$

Then, multiplying the energy of the X-ray quantum by the conversion factor, in order to cancel the dimension of electron-volts, eV, we get an energy, in kilo Joules, kJ:

$$E_{X-ray}=135\,eV*\frac{1.6022X10^{-22}kJ}{1eV}=2.16X10^{-20}kJ$$

Now, we can calculate the frequency associated with this energy by using the relation:

$$E_{X-ray}=h\nu_{X-ray}=2.16X10^{-20}kJ$$

Using Planck's constant in the dimensions of Joules-seconds:

$$h=6.626X10^{-34}J*s$$

And isolating for the frequency, ν X-ray, we get:

$$\nu_{X-ray}=\frac{E_{X-ray}}{h}=\frac{2.16X10^{-20}kJ}{6.626X10^{-34}J*s}*\frac{1000\,J}{kJ}=3.26X10^{12}*s^{-1}$$

2. Calculation of energy of X-ray quanta per mole:

Again using the conversion for one electronvolt, eV, to kilo Joules, kJ:

$$1\,eV=1.6022X10^{-22}kJ$$

Then as before, for the X-ray quantum at 135 eV, we would get:

$$E_{X-ray}=135\,eV*\frac{1.6022X10^{-22}kJ}{1eV}=2.16X10^{-20}kJ$$

Now to convert this energy to mega Joules per mole, MJ/mol, we use another conversion factor involving Avogadro's number:

$$1\,mol=6.022X10^{23}$$

Then:

$$1=\frac{6.022X10^{23}}{1\,mol}$$

And multiplying this conversion factor, we get:

$$E_{X-ray}=2.16X10^{-20}kJ*\frac{6.022X10^{23}}{mol}*\frac{1\,MJ}{1000\,kJ}=13\,MJ*mol^{-1}$$

This then is the energy per mole of the X-ray quanta.

## Photoelectron Spectroscopy

Now, let's talk about what photoelectron spectroscopy is in more detail.

• PES is used to measure the ground's relative energies and electrons' excited states within a molecule.

• The relative energy of an electron ground state versus an excited, positive ion state is measured in PES.

Photoelectron spectroscopy (PES) - the application of Einstein's photoelectric effect theory to obtain an electronic spectrum. PES utilizes EM radiation (UV-light or X-rays) to obtain electronic spectra.

Electronic spectrum - electronic signals detected as a result of the irradiation of a sample with EM radiation.

• Irradiation: to shine EM radiation (e.g., UV light or X-rays) on a material.

## Photoelectron Spectroscopy Graph

Here we consider the PES graph of a hypothetical material. Notice the graph is in terms of the binding energy versus the relative number of electrons detected after irradiation of the sample.

Figure 4: Hypothetical Photoelectron Spectroscopy (PES) experiment. (Inset: Energy Diagram)

We note that the abscissa, or vertical axis, for the Photoelectron spectrum is in terms of the "Relative number of electrons." For example, the spectrum for Lithium metal, which is made up of two 2s (inner core) electrons and one 2p (valence) electron, would have a PES graph that looks something like this:

Figure 5: Approximate PES graph of Lithium.

Thus, the vertical axis of the PES graph maps the relative numbers of electrons within an electron shell. This information and the binding energy associated with peaks can be used to identify the atoms that make up a material.

Please refer to the article on "Valence Electrons" and "Orbitals" if you need a refresher on these topics!

Let's continue with this example and calculate the binding energy for Lithium's valence (2s1 ) electron. Using the X-ray quantum for which we calculated the energy, we would have:

$$E_{X-ray}=13\,MJ\cdot mol^{-1}=KE_{electron}+BE_{electron}$$

If we are further given the information that the measured kinetic energy of the emitted electron was, $$KE_{electron}=12.49\,MJ\cdot mol^{-1}$$, we would then have a binding energy for the valence electron of Lithium:

$$BE_{electron}=E_{X-ray}-KE_{electron}=0.51\,MJ\cdot mol^{-1}$$

## Practical Surface Analysis by Auger and X-ray Photoelectron Spectroscopy

The surface analysis by Auger and X-ray spectroscopy is used to:

• Probe the surface of a solid material in greater detail, yielding information about molecular geometry and the electronic structure of molecules.

• Probe quantum states of molecules at the surface of a solid material.

• Produce images in electron microscopes.

## Angle-Resolved Ultraviolet Photoelectron Spectroscopy

The angle-resolved ultraviolet photoelectron spectroscopy (ARPES) technique is used to:

• Probe the surface of a solid material to obtain information about the allowed energies and momentum of conduction electrons in a metal.

• Map the material band structure, or conduction band energies, on a metal surface.

• Probe the quantum mechanical structure of conduction electrons in a metal or semiconductor like Silicon.

## Application of Photoelectron Spectroscopy (PES)

The applications of PES are mainly in condensed matter physics, electron microscopy, electronic mapping conduction in metals, and characterizing quantum effects in metals and semiconductors.

Although this is a brief survey of the PES technique, the ability to probe the quantum mechanical nature of molecules at the surface of solids might appeal to some of you. I would suggest that students interested in PES study quantum mechanics, chemical physics, and condensed matter physics at the college level would lead research work utilizing PES in the lab. Best of luck in your future studies.

## Photoelectron Spectroscopy - Key takeaways

• The photoelectric effect occurs when a quantum of EM radiation ionizes an electron from a molecule in a solid.
• Quantum - a packet of energy, or energy of a quantum state.
• The binding energy of an electron in a molecule on the surface of a solid material is given by the formula: $$BE_{electron}=E_{quantum}-KE_{electron}$$
• The relative energy of an electron ground state versus an excited, positive ion state is measured in PES.
• The vertical axis of the PES graph yields the number of electrons within an electron shell.

The application of Einstein's theory of the photoelectric effect in order to obtain an electronic spectrum. PES utilizes EM radiation (UV-light or X-rays) to obtain electronic spectra.

PES uses Einstein's theory of the photoelectric effect to get an electronic spectrum.

X-ray PES uses X-rays and the photoelectric effect to obtain an electronic spectrum.

Yes, PES can give the percentages of the atoms contained in the alloy.

## Photoelectron Spectroscopy Quiz - Teste dein Wissen

Question

what is photoelectron spectroscopy

The application of Einstein's theory of the photoelectric effect in order to obtain an electronic spectrum. PES utilizes EM radiation (UV-light or X-rays) to obtain electronic spectra.

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Question

How are photoelectron spectroscopy and the photoelectric effect related?

PES uses Einstein's theory of the photoelectric effect to get an electronic spectrum.

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Question

What is x ray photoelectron spectroscopy?

X-ray PES uses X-rays and the photoelectric effect to obtain an electronic spectrum.

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Question

Can photoelectron spectroscopy graphs determine the amount of atoms?

Yes, PES can give the percentages of the atoms contained in the alloy.

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Question

What is a quantum?

A packet of quantum energy. The plural of quantum is quanta.

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Question

What is an excited state?

Occurs when an electron in a substance absorbs a quantum and is promoted to a higher energy state.

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Question

What is an energy state?

Refers to the energy of an electron in orbit about the nucleus of a molecule.

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Question

Any type of light (e.g. UV, IR, Visible, etc.) or particle rays (like X-rays).

Show question

Question

Is PES based on the photoelectric effect?

Yes.

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Question

When does the photoelectric effect occur?

The photoelectric effect occurs when a quantum of EM radiation ionizes an electron from a molecule in a solid.

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What is PES used to measure?

PES is used to measure the relative energies of the ground and excited states of electrons within a molecule.

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What is XPS used for?

• Probe the surface of a solid material.
• Identify elements that exist within surface of the solid or that are covering the material.
• Generate the empirical formula of metal alloys.

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What is ARPES used for?

• Probe the surface of a solid material in order to obtain information about the allowed energies and momentum of conduction electrons in a metal.
• Map the material band structure, or conduction band energies, on a metal surface.
• Probe the quantum mechanical structure of conduction electrons in a metal or semiconductor like Silicon.

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Question

When does the photoelectric effect occur?

The photoelectric effect occurs when a quantum of EM radiation ionizes an electron from a molecule in a solid.

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What are the three components of PES?

A high-energy EM radiation source, an electron detector, and a vacuum environment.

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What principle is PES based on?

The photoelectric effect

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What units are used in a PES spectrum?

Ionization energy vs # of electrons detected

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What does each peak represent?

An electron subshell

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What is each peak's height based off of?

Relative electron abundance (think the subscript in electron configurations)

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How are peaks grouped?

Based on orbitals (think the coefficients of electron configurations)

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What are the two types of PES?

UV and X-ray

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Which type of PES uses higher energy EM radiation?

X-ray PES

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What does X-ray PES look at in an atom?

The electron shells that are closer to the nucleus.

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What does UV PES look at in an atom?

The valence electron shell.

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How can PES be applied?

To analyze radicals, deduce structure, and facilitate reactions sensitive to valence electron count.

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Molecules that contain one free electron.

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What energy range do UV photons usually have?

1eV to 100eV

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What energy range do X-ray photons usually have?

100 eV to 100,000 eV

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Which type of PES uses lower energy EM radiation?

UV PES

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Question

An object is considered a _____ if it is capable of absorbing all the radiation that strikes it.

blackbody

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Max Planck's quantum energy theory states that heated objects emit radiation (such as light) in small, discrete amounts of energy called ______ .

quanta

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Which scientist aimed to explain the photoelectric effect?

Max Planck

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According to the photoelectric effect, the brighter the light, the _____ electrons can be ejected from a metal surface.

more

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In the photoelectric effect, electrons emitted from a metal's surface are called ______

photoelectrons

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By using Planck's theory, Einstein proposed the dual nature of light, which was that light had wave-like characteristics, but was made of streams of tiny energy bundles or particles of EM radiation called ____

photons

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A photon is referred to as a particle of ______ radiation with no mass that carries a quantum of energy.

electromagnetic

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What are the characteristics of a photon?

• They are neutral, stable and have no mass.

• Photons are able to interact with electrons.

• The energy and speed of photons depend on their frequency.

• Photons can travel at the speed of light, but only in a vacuum, such as space.

• All light and EM energy are made of photons.

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_______ is the distance between a wave's two adjacent peaks or troughs.

Wavelength

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____ is the number of complete wavelengths that pass at a specific point per second.

Frequency

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_____ is a kind of energy that behaves like a wave as it travels through space.

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Frequency and wavelength are  ______ proportional to one another.

inversely

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A quantum is the _____ quantity of electromagnetic (EM) energy that can be emitted or absorbed by an atom.

smallest

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When an electron in a substance is promoted from a lower shell to a higher shell, it undergoes the process of the ____ of a photon.

absorption

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When an electron in a substance moves from a higher shell to a lower shell, it undergoes the process of the ____ of a photon

emission

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