Unit 4
Unit 4 Photon Interactions

Unit 4 Photon Interactions

A photon passing through matter interacts with the atoms and electrons. These can be summarized as four important types.

1. The photoelectric effect - This happens when a photon knocks an electron out of an atom resulting in the disappearance of the photon.

— Directing a beam of light of certain short wavelength onto a clean metal surface causes electrons to be ejected from the surface.
— This photoelectric effect is used in many devices, including TV cameras, camcorders, and night vision viewers.
— This effect cannot be understood without quantum physics and Einstein used it to supported his photon concept.
— The energy of the photons is given by the equation E = hf, where h = Planck's constant and f the frequency of the radiation.

Experimental Evidence

— The maximum kinetic energy (of the most energetic ejected electrons) does not depend on the intensity of the light source. In classical physics the energy of the ejected electron should vary with the energy of the light wave (amplitude of the wave). Explanation: The energy of the photons is given by the equation E = hf (quantum mechanics), so the maximum energy given to an electron depends on the frequency and not the intensity (in classical physics)
—There is a cut-off frequency under which electrons are not ejected no matter how intense the radiation. In classical physics electrons should be ejected for all frequencies if the intensity is great enough. Explanation: The energy of the photons is given by the equation E = hf (quantum mechanics), so the maximum energy given to an electron depends on the frequency and not the intensity (in classical physics). To escape from the atom the electron must acquire a certain minimum energy called the work function (Φ). Electrons can only escape if hf > Φ.



Photoelectric Equation

— Einstein's statement on the conservation of energy for a single photon is the equation hf = EKMax + Φ.
— To escape an e3lectron must pick up energy at least equal to Φ (hence the cut-off frequency) and the addition energy of the photon appears as EK (hence there is a EKMax which is the difference between the energy of the photon and Φ. Thus higher frequencies of the radiation produce more energetic photo-electrons.
— The slope of the graph on the left is [h/e]. From this graph (experimental results) the value of is the expected value as measured by other methods.

2. Excitation - The photon may knock an atomic electron to a higher energy state in the atom if its energy is not sufficient to knock the electron out altogether. In this process the photon also disappears, and all its energy is given to the atom. Such an atom is then said to be in an excited state, and we shall discuss it more later.


— Heated solids, liquids and dense gases emit light with a continuous spectrum of wavelengths. This radiation is assumed to be due to oscillations of atoms and molecules, which are largely governed by the interaction of each atom or molecule with its neighbors. Rarified gases on the other hand when excited to emit light do so at only certain wavelengths giving rise to line spectra rather than continuous spectra which are specific top the material. the opposite or absorption spectra are observed when continuous spectra are passed through the same materials.

In rarified gases (low density) the light emitted or absorbed are by individual atoms rather than interacting atoms.

— The Balmer series of spectral lines for hydrogen is shown on the left. These fit the formula:

1     1   1
= R -
λ      22   n2

where R is called the Rydberg constant. and n = 3.4, ....

The Lyman series (in the UV region) and Pashen series (in the IR region) show the same patterns.


— These can only be explained with quantum physics as the classical physics of the Rutherford model cannot explain them, quite apart from the obvious difficulties of a charged particle (electron) rotating in an electric field without emitting light and spiraling into the nucleus.


3. Compton Effect- Sometimes the photon is scattered from an electron or nucleus lose some energy in the process. However, the photon is not slowed down as its speed is still c. As it has lost some energy its frequency must be lowered (recall E = hf).

X-Ray photon moving towards an electron.
X-Ray photon bypasses electron and no scatter (scattering angle = 0).
X-Ray photon scattered at angle φ with longer wavelength λ''and energy transferred to electron at angle θ.
X-Ray photon backscattered with longer wavelength λ' and maximum energy transferred to electron.

— Compton directed a beam of X-rays of a particular wavelength to a carbon target. The scattered X-rays contained a range of wavelengths with two prominent peaks for every angles observed.

— However, classical physics could not explain the scattering of x-rays as the scattered rays should have the same wavelength and frequency as the incident rays.

— This has extended the concept of photons to also possess linear momentum. When a photon interacts with matter, it behaves as a collision in the classical sense with the conservation of Energy and Momentum.

4. Pair production: A photon can actually create matter, such as the production of an electron and a positron. (Recall: A positron has the same mass as an electron, but the opposite charge,)


— In pair production, the photon disappears in the process of creating the electron–positron pair. This is an example of
— Mass is being created from pure energy in accord with Einstein’s equation E = mc2 (the photon cannot create an electron only as electric charge would not then be conserved.)
— if a positron comes close to an electron, the two quickly annihilate each other and their energy, including their mass, appears as electromagnetic energy of photons (the inverse of pair production)
— Positrons are rarer than electrons nature so they do not last long.
— since the electron and positron move in the same direction along one of the axes, pair production must have a massive object like a nucleus to carry momentum in the opposite direction (Law of conservation of Momentum)


Some applications of the above effects are:

— Electron–positron annihilation is the basis for the type of medical imaging known as PET.

— Nuclear medicine

— Burglar alarms and automatic doors often make use of the photocell circuit

— Photocells are used in many devices, such as absorption spectrophotometers, to measure light intensity.

— Semiconductors

Concept by Kishore Lal. Programmed by Kishore Lal... Copyright © 2015 Kishore Lal. All rights reserved.