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Light rays coming out of a flashlight. The photons are depicted as small ellipses enclosing a wave each and moving in the direction of the rays. Energies of photons are labeled as E and E prime, where E is equal to h f and E prime is equal to h f prime.
An EM wave of frequency f size 12{f} {} is composed of photons, or individual quanta of EM radiation. The energy of each photon is E = hf size 12{E = ital "hf"} {} , where h size 12{h} {} is Planck’s constant and f size 12{f} {} is the frequency of the EM radiation. Higher intensity means more photons per unit area. The flashlight emits large numbers of photons of many different frequencies, hence others have energy E = hf size 12{E' = ital "hf"'} {} , and so on.

The photoelectric effect has the properties discussed below. All these properties are consistent with the idea that individual photons of EM radiation are absorbed by individual electrons in a material, with the electron gaining the photon’s energy. Some of these properties are inconsistent with the idea that EM radiation is a simple wave. For simplicity, let us consider what happens with monochromatic EM radiation in which all photons have the same energy hf size 12{ ital "hf"} {} .

  1. If we vary the frequency of the EM radiation falling on a material, we find the following: For a given material, there is a threshold frequency f 0 size 12{f rSub { size 8{0} } } {} for the EM radiation below which no electrons are ejected, regardless of intensity. Individual photons interact with individual electrons. Thus if the photon energy is too small to break an electron away, no electrons will be ejected. If EM radiation was a simple wave, sufficient energy could be obtained by increasing the intensity.
  2. Once EM radiation falls on a material, electrons are ejected without delay . As soon as an individual photon of a sufficiently high frequency is absorbed by an individual electron, the electron is ejected. If the EM radiation were a simple wave, several minutes would be required for sufficient energy to be deposited to the metal surface to eject an electron.
  3. The number of electrons ejected per unit time is proportional to the intensity of the EM radiation and to no other characteristic. High-intensity EM radiation consists of large numbers of photons per unit area, with all photons having the same characteristic energy hf size 12{ ital "hf"} {} .
  4. If we vary the intensity of the EM radiation and measure the energy of ejected electrons, we find the following: The maximum kinetic energy of ejected electrons is independent of the intensity of the EM radiation . Since there are so many electrons in a material, it is extremely unlikely that two photons will interact with the same electron at the same time, thereby increasing the energy given it. Instead (as noted in 3 above), increased intensity results in more electrons of the same energy being ejected. If EM radiation were a simple wave, a higher intensity could give more energy, and higher-energy electrons would be ejected.
  5. The kinetic energy of an ejected electron equals the photon energy minus the binding energy of the electron in the specific material. An individual photon can give all of its energy to an electron. The photon’s energy is partly used to break the electron away from the material. The remainder goes into the ejected electron’s kinetic energy. In equation form, this is given by
    KE e = hf BE , size 12{"KE"= ital "hf" - "BE"} {}
    where KE e size 12{"KE" rSub { size 8{e} } } {} is the maximum kinetic energy of the ejected electron, hf size 12{ ital "hf"} {} is the photon’s energy, and BE is the binding energy    of the electron to the particular material. (BE is sometimes called the work function of the material.) This equation, due to Einstein in 1905, explains the properties of the photoelectric effect quantitatively. An individual photon of EM radiation (it does not come any other way) interacts with an individual electron, supplying enough energy, BE, to break it away, with the remainder going to kinetic energy. The binding energy is BE = hf 0 size 12{"BE "= ital "hf" rSub { size 8{0} } } {} , where f 0 size 12{f rSub { size 8{0} } } {} is the threshold frequency for the particular material. [link] shows a graph of maximum KE e size 12{"KE" rSub { size 8{e} } } {} versus the frequency of incident EM radiation falling on a particular material.

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Source:  OpenStax, Basic physics for medical imaging. OpenStax CNX. Feb 17, 2014 Download for free at http://legacy.cnx.org/content/col11630/1.1
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