**the emission of photoelectrons**from a material matter when electromagnetic radiation (photons) hits its surface. The photoelectric effect only emits electrons if the photon reaches or exceeds

**threshold energy**. This discovery contributed to the quantum revolution in physics and earned Einstein the Nobel Prize in Physics in 1921.

**Einstein’s theory predicts that the maximum kinetic energy of the emitted electron is dependent only on the frequency of the incident light and not on its intensity**. Shining twice as much light (high-intensity) results in twice as many photons and more electrons releasing, but the maximum kinetic energy of those individual electrons remains the same.

In the photoelectric effect, a photon undergoes an interaction with an electron that is bound in an atom. The incident photon completely disappears in this interaction, and the atom ejects an energetic photoelectron from one **of its bound shells**. The kinetic energy of the ejected photoelectron (E_{e}) is equal to the incident photon energy (hν) minus the binding energy of the photoelectron in its original shell (E_{b}).

**E _{e}=hν-E_{b}**

Therefore, photoelectrons are only emitted by the photoelectric effect if the photon reaches or exceeds **threshold energy** – the electron’s binding energy – **the material’s work function**. For gamma rays with energies of more than hundreds keV, the photoelectron carries off the majority of the incident photon energy – hν. Following a photoelectric interaction, an ionized absorber atom is created with **a vacancy in one of its bound shells**.

An electron from a shell will quickly fill this vacancy with lower binding energy (other shells) or capture a free electron from the material. The rearrangement of electrons from other shells creates another vacancy, which, in turn, is filled by an electron from an even lower binding energy shell. Therefore a cascade of more **characteristic X-rays** can also be generated. The probability of characteristic x-ray emission decreases as the atomic number of the absorber decreases. Sometimes, the emission of an Auger electron occurs.

## Key Facts

- The photoelectric effect dominates
**at low-energies of gamma rays**. - The photoelectric effect leads to
**the emission of photoelectrons**from matter when light (photons) shines upon them. - The maximum energy an electron can receive in any one interaction is
*hν*. - The photoelectric effect only emits electrons if the photon reaches or exceeds
**threshold energy**. - A free-electron (e.g.,, from an atomic cloud) cannot absorb the entire energy of the incident photon. This is a result of the need to conserve both momentum and energy.
- The cross-section for the emission of n=1 (K-shell) photoelectrons is higher than that of n=2 (L-shell) photoelectrons. This is a result of the need to conserve momentum and energy.

## Cross-Sections of Photoelectric Effect

**At small values of gamma-ray energy, the photoelectric effect dominates**. The mechanism is also enhanced for materials of high atomic number Z. It is not simple to derive an analytic expression for the probability of photoelectric absorption of gamma-ray per atom comprehensive ranges of gamma-ray energies. The probability of photoelectric absorption per unit mass is approximately proportional to:

**τ _{(photoelectric)} = constant x Z^{N}/E^{3.5}**

where **Z** is the atomic number, the exponent **n** varies between 4 and 5. **E** is the energy of the incident photon. The proportionality to higher powers of the atomic number Z is the main reason for using high Z materials, such as lead or depleted uranium in gamma-ray shields. Although the probability of the photoelectric absorption of gamma photon decreases, in general, with increasing photon energy, there are **sharp discontinuities** in the cross-section curve. These are called **“absorption edges”** and correspond to electrons’ binding energies from an atom’s bound shells. For photons with the energy just above the edge, the photon energy is sufficient to undergo the photoelectric interaction with an electron from a bound shell, let say K-shell. The probability of such interaction is just above this edge, much greater than that of photons of energy slightly below this edge. For gamma photons below this edge, the interaction with electrons from K-shell is energetically impossible, and therefore the probability drops abruptly. These edges also occur at binding energies of electrons from other shells (L, M, N …).