Photoelectric Effect

The phenomenon, that a surface (typically alkali metals) when exposed to electromagnetic radiation (visible light) emits electrons, was discovered by Hertz and Hallwachs in 1887 during experiments with a spark-gap generator. Hertz found that the sensitivity of his spark-gap device can be increased by exposition to visible or ultraviolet light and that light obviously had some electrical effect. He did not further pursue investigation of this effect.Shortly after Hertz’s discovery in 1899, English physicist J.J.Thomson showed that UV light, which fall onto metal surface, trigger the emission of electrons from the surface. In 1902, Hungarian physicist Philipp Lenard made the first quantitative measurements of the photoelectric effect. He observed that the energy of individual emitted electrons increased with the frequency of the light (which is related to the color).

the luminiferous aether

The luminiferous aether. It was hypothesised that the Earth moves through a “medium” of aether that carries light. It has been replaced in modern physics by the theory of relativity and quantum theory.
Source: wikipedia.org

While this is interesting, it is hardly explainable by classical theory of electromagnetic radiation which assumed the existence of a stationary medium (the luminiferous aether) through which light propagated. Subsequent investigations into the photoelectric effect results in the fact that these explorations did not fit with the classical theory of electromagnetic radiation.In 1905, Albert Einstein published four groundbreaking papers on the photoelectric effect, Brownian motion, special relativity, and the equivalence of mass and energy. These papers were published in the Annalen der Physik journal and contributed significantly to the foundation of modern physics. In the paper on the photoelectric effect (“On a Heuristic Viewpoint Concerning the Production and Transformation of Light”) he solved the paradox by describing light as composed of discrete quanta (German: das Lichtquant), rather than continuous waves.This theory was builded on Max Planck’s blackbody radiation theory, which assumes that luminous energy can be absorbed or emitted only in discrete amounts, called quanta. The photon’s energy in each quantum of light is equal to its frequency (ν) multiplied by a constant known as Planck’s constant (h), or alternately, using the wavelength (λ) and the speed of light (c):

E=hc/λ=hν

Photoelectric effect with photons from visible spectrum on potassium plate - threshold energy - 2eV

Photoelectric effect with photons from visible spectrum on potassium plate – threshold energy – 2eV

Each photon above a threshold frequency (specific for each material) has the needed energy to eject a single electron, creating the observed effect. Einstein’s theory predicts that the maximum kinetic energy of 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. Experimentation in the photoelectric effect was carried out extensively by Robert Millikan in 1915, Robert Millikan showed that Einstein’s prediction was correct. This discovery contributed to the quantum revolution in physics and earned Einstein the Nobel Prize in Physics in 1921.

  • 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 .
  • Electrons are only emitted by the photoelectric effect if photon reaches or exceeds a threshold energy.
  • A free electron (e.g. from atomic cloud) cannot absorb 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.

Definition of Photoelectric effect

In the photoelectric effect, a photon undergoes an interaction with an electron which is bound in an atom. In this interaction the incident photon completely disappears and an energetic photoelectron is ejected by the atom from one of its bound shells. The kinetic energy of the ejected photoelectron (Ee) is equal to the incident photon energy (hν) minus the binding energy of the photoelectron in its original shell (Eb).

Ee=hν-Eb

Therefore photoelectrons are only emitted by the photoelectric effect if photon reaches or exceeds a threshold energy – the binding energy of the electron – the work function of the material. 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. This vacancy is will be quickly filled by an electron from a shell with a lower binding energy (other shells) or through capture of 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 be also 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.

Photoelectric effect with photons from visible spectrum on potassium plate - threshold energy - 2eVPhotoelectric effect with photons from visible spectrum on potassium plate – threshold energy – 2eV
Gamma absorption by an atom. Source: laradioactivite.com/

Cross-Sections of Photoelectric Effect

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

τ(photoelectric) = constant x ZN/E3.5

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 of 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 “absoption edges” and they correspond to the binding energies of electrons from atom’s bound shells. For photons with the energy just above the edge, the photon energy is just sufficient to undergo the photoelectric interaction with electron from  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 electron from K-shell in energetically impossible and therefore the probability drops abruptly. These edges occur also at binding energies of electrons from other shells (L, M, N …..).

Cross section of photoelectric effect.Cross section of photoelectric effect.