Photoelectron spectroscopy Knowledge-Based Study

Study notes

1. Photoelectron spectroscopy (PES) is an experimental technique used to measure the binding energies of electrons in atoms and molecules, providing direct experimental evidence for quantized energy levels and subshell electron configurations.

   The method is based on the photoelectric effect. A sample of gaseous atoms is irradiated with high-energy photons, typically from ultraviolet light or X-rays. When a photon strikes an electron with energy greater than the electron's binding energy, the electron is ejected as a photoelectron.

   By conservation of energy, the energy of the incident photon is partitioned between the binding energy (ionization energy) required to remove the electron from its subshell and the kinetic energy of the ejected electron:

   $E_{\text{photon}} = \text{IE} + \text{KE}$

   Rearranging this relationship allows the binding energy to be determined directly:

   $\text{IE} = h\nu - \text{KE}$

   Because the frequency ($\nu$) of the incident light is known and the kinetic energy ($\text{KE}$) of the ejected electrons is measured by a detector, the binding energy of electrons in each atomic subshell can be calculated precisely.

   A photoelectron spectrum displays data with binding energy on the horizontal axis and the relative number of ejected electrons (signal intensity) on the vertical axis.

   • Horizontal Axis (Binding Energy): Conventionally plotted with binding energy decreasing from left to right (highest energy at the origin). Positions farther to the left represent electrons held more tightly by the nucleus, corresponding to lower principal energy levels closer to the nucleus.
   • Vertical Axis (Peak Intensity): The height or integrated area of each peak is directly proportional to the number of electrons occupying that particular subshell.

   Each distinct peak in the spectrum corresponds to a distinct occupied subshell. For example, a neutral neon atom ($1s^2 2s^2 2p^6$) produces three distinct peaks:

   • A peak at the highest binding energy (farthest left) representing the 2 electrons in the $1s$ subshell.
   • An intermediate peak representing the 2 electrons in the $2s$ subshell, having the same height as the $1s$ peak.
   • A peak at the lowest binding energy (farthest right) representing the 6 electrons in the $2p$ subshell, which is three times as tall as the $2s$ peak.

   PES spectra reflect fundamental periodic trends and Coulombic attractions described by Coulomb's law:

   $F \propto \frac{q_1 q_2}{r^2}$

   Two primary factors dictate the position of peaks along the energy axis:

   • Shell Distance ($n$): Electrons in shells with smaller principal quantum numbers are closer to the nucleus, experiencing significantly stronger attraction and requiring vastly higher energies to eject. Thus, $1s$ peaks appear at much higher binding energies than valence subshell peaks.
   • Effective Nuclear Charge ($Z_{\text{eff}}$): When comparing the same subshell across different elements, increasing the number of protons in the nucleus increases $Z_{\text{eff}}$. This pulls the electron cloud closer and increases electrostatic attraction.

   For instance, comparing the $1s$ peak of lithium ($Z = 3$) to that of beryllium ($Z = 4$), beryllium's higher nuclear charge holds its core electrons more tightly. Consequently, the $1s$ peak of beryllium appears at a higher binding energy than that of lithium.