Photoelectron Spectroscopy (PES)

Photoelectron spectroscopy (PES) is a powerful experimental technique that provides direct evidence for the shell structure of atoms and the arrangement of electrons in orbitals. By firing high-energy photons — typically ultraviolet (UV) or X-ray radiation — at a gaseous sample of atoms, scientists can eject electrons from different energy levels and measure the energy required to remove each one. The resulting spectrum reveals distinct peaks that correspond to electrons in different subshells, offering a 'fingerprint' of an atom's electronic configuration. The physical principle underpinning PES is the photoelectric effect: when a photon of sufficient energy strikes an electron, it transfers its energy to that electron. If the photon energy exceeds the electron's binding energy (the energy holding it to the nucleus), the electron is ejected with a measurable kinetic energy. By conservation of energy, the binding energy equals the photon energy minus the kinetic energy of the emitted electron. Electrons in inner shells (closer to the nucleus) have higher binding energies and therefore appear at higher energy values on the PES spectrum, while valence electrons appear at lower binding energies. PES data correlates strikingly well with the theoretical subshell model of electronic configuration. For example, the PES spectrum of sodium (Na, Z = 11) shows three distinct groups of peaks corresponding to the 1s, 2s/2p, and 3s subshells — exactly matching the configuration 1s²2s²2p⁶3s¹. The relative heights (intensities) of the peaks are proportional to the number of electrons in each subshell, further validating the quantum mechanical model. Understanding PES is therefore essential for interpreting atomic structure and connecting experimental evidence to theoretical models.

Key takeaways
  • The Photoelectric Effect and Photon Energy
  • The Core Energy Equation
  • Reading a PES Spectrum
  • Evidence for Subshell Structure: The 2s/2p Distinction
  • Connecting PES to Electronic Configuration

The Photoelectric Effect and Photon Energy

PES is based on Einstein's explanation of the photoelectric effect (1905). A monochromatic beam of photons with a precisely known energy (E = hν, where h is Planck's constant and ν is frequency) is directed at gaseous atoms. If the photon energy exceeds the binding energy of an electron, the electron is ejected. The kinetic energy of the emitted electron is measured by a detector. Because every subshell has a characteristic binding energy, each group of electrons produces a distinct signal.

The Core Energy Equation

The relationship between photon energy, binding energy, and kinetic energy is: Binding Energy (BE) = hν − KE. Electrons in the 1s subshell experience the greatest nuclear attraction (highest BE ≈ hundreds to thousands of MJ/mol for heavier atoms), while valence electrons in the outermost shell have the smallest BE. In a PES spectrum, the x-axis is usually plotted as binding energy (increasing to the left by convention), and each peak's position directly reports the ionization energy of electrons in that subshell.

Reading a PES Spectrum

Each peak in a PES spectrum represents one subshell. Key features to interpret: (1) Position on the x-axis → binding energy → identifies which subshell; (2) Height/area of the peak → relative number of electrons in that subshell; (3) Number of peaks → number of occupied subshells. For example, oxygen (1s²2s²2p⁴) produces three peaks. The 1s peak is at highest binding energy (≈ 4170 kJ/mol in first-ionization terms), 2s is intermediate (≈ 1313 kJ/mol), and 2p is at lowest binding energy (≈ 870 kJ/mol). The 1s and 2s peaks have equal height (2 electrons each), while the 2p peak is twice as tall (4 electrons).

Evidence for Subshell Structure: The 2s/2p Distinction

A key piece of evidence from PES is that the second shell is NOT one uniform energy level — it splits into two peaks (2s and 2p), confirming that subshells exist within shells. This would not appear if electrons in n=2 all had identical energies. Similarly, for elements in period 3, three separate groups of peaks are observed: n=1, n=2 (itself split into 2s and 2p), and n=3 (split into 3s and 3p). This multi-peak structure is direct experimental proof of the quantum mechanical subshell model.

Connecting PES to Electronic Configuration

To deduce an electronic configuration from PES data: (1) Count the number of peaks — this equals the number of occupied subshells. (2) Rank peaks by binding energy: highest BE = innermost subshell (1s); lowest BE = outermost subshell (valence). (3) Use peak heights to determine electron counts in each subshell (ratios matter: a peak twice as tall as another means twice as many electrons). (4) Assign subshell labels using the known order of filling: 1s, 2s, 2p, 3s, 3p, 4s, 3d, etc. For instance, a spectrum with four peaks of relative heights 2:2:6:1 matches 1s²2s²2p⁶3s¹ → sodium.

The Key Equation

Ebinding=hν−EkineticE_{\text{binding}} = h\nu - E_{\text{kinetic}}
  • E_{\text{binding}} — Binding Energy (J or eV): The energy required to completely remove an electron from its subshell; equivalent to the ionization energy for that electron.
  • h\nu — Photon Energy (J): Energy of the incident photon, where h = 6.626 × 10⁻³⁴ J·s (Planck's constant) and ν is the photon frequency in Hz.
  • E_{\text{kinetic}} — Kinetic Energy of Ejected Electron (J or eV): The measured kinetic energy of the electron after it has been ejected from the atom; detected by the spectrometer.

Worked Example

Problem. A PES spectrum of an unknown element shows four peaks. From highest to lowest binding energy, the relative peak heights are in the ratio 2 : 2 : 6 : 2. The two lowest binding energy peaks are both small (relative height 2). Identify the element and write its full electronic configuration.

Mg:1s2 2s2 2p6 3s2\text{Mg}: 1s^2\,2s^2\,2p^6\,3s^2

Answer. The element is Magnesium (Mg, Z = 12) with electronic configuration 1s²2s²2p⁶3s².

Figure
Diagram
PES Spectrum of Sodium (Na): 1s²2s²2p⁶3s¹Binding Energy → (high to low, right to left)Relative Signal IntensityLow BEHigh BE1s~104,000kJ/mol2s~6,840kJ/mol2p~3,930kJ/mol3s~496kJ/mol2e⁻2e⁻6e⁻1e⁻Peak height ∝ number of electrons in subshell
Origins · 1 minKai Siegbahn and how this was discovered
KS
Kai Siegbahn
1918–2007 · Swedish

Kai Siegbahn developed X-ray photoelectron spectroscopy (XPS), also called ESCA (Electron Spectroscopy for Chemical Analysis), in the 1950s–1960s. His precise measurements of electron binding energies in atoms and molecules demonstrated that chemical environment shifts core electron binding energies, enabling identification of elements and their bonding states. He was awarded the Nobel Prize in Physics in 1981 for this foundational work. Kai's father, Manne Siegbahn, also won the Nobel Prize in Physics (1924) for X-ray spectroscopy, making them one of the very few father-son Nobel laureate pairs in history.

  • Ionization Energy — PES directly measures the ionization energies of electrons in each subshell; understanding IE trends is essential for interpreting peak positions in a PES spectrum.
  • Electron Configuration and the Aufbau Principle — PES spectra are interpreted by mapping peaks onto subshell labels (1s, 2s, 2p, etc.) according to the Aufbau filling order and Pauli exclusion principle.
  • Quantum Numbers and Orbitals — The existence of distinct s, p, d subshells — proven by separate PES peaks — arises from the principal, azimuthal, and magnetic quantum numbers describing electron states.
  • The Photoelectric Effect — PES is a direct application of the photoelectric effect; the equation BE = hν − KE links photon energy to electron ejection, the same physics Einstein explained in 1905.