Photons and the Electromagnetic field

©Fernando Caracena

The electromagnetic spectrum

In the late 19th Century scientists were exploring the nature of two types of electromagnetic spectra: black body radiation and light from gases that were made to emit radiation by stimulating them with electric currents (emission spectra). A black body is an object that absorbs all radiation falling on it. Heated to incandescences, a black body also gives off a maximum of radiation. A good approximation of a black body is an oven that has a small hole to the inside. When it is cool, it looks black in there; but heat the oven to incandescence, and blinding light comes out of the peep hole. Emission spectra are the line spectra emitted by various elements and chemical compounds that are made to glow by either heating them or passing an electric current through the. Each element emits light that when decomposed into its spectral components shows characteristic lines of various frequencies, to the point that different substances can be identified by their emission spectra.

Even before the beginning of quantum physics, scientists found the spectral properties of light emitted by matter to be very useful. Each element excited electrically emitted light that could be resolved into spectral components (emission spectrum) that were characteristic of that element. When light produced from various elementary gases stimulated electrically was resolved into a spectra the results were sharp lines of various colors

such as in Fig. 3, which shows a portion of the hydrogen emission spectrum. When light having a continuous spectrum, such as from a hot glowing object, passes through a gas, such as hydrogen, the atoms of that gas absorb light that would correspond to that element's own emission spectrum, so that the light that passes trough, when resolved into spectral components had dark lines where the emission spectral lines would be. For example, put a continuous spectrum in the place of the black background in Fig. 3, and make the colored lines black—that is how the absorption spectrum would look like.

The emission and absorption spectra were a very important tool in astronomy. Using such spectra and the model of an expanding universe, astronomers have been able to determine that the universe originated in a "Big Bang" 13.7 billion years ago; that it is expanding; and that rate of expansion is increasing with time. Further, astronomers have found that the early universe consisted almost entirely of hydrogen, the other elements having been cooked in stars and blown out into space by stellar explosions, called nova and supernova.

Photons

While Planck was having his doubts about quanta, Einstein was busy showing that there are optical phenomena that can be explained in terms of photons, or particles of light. He was able to explain the photoelectric effect, in which light incident on a metal plate causes electrons to be emitted if the incident light is above a frequency threshold that is characteristic of the type of metal.

When an electron is pushed out of the surface of an electrically neutral metal plate, it sees a positive image of itself until at some distance away, that image disappears. Until the image charge disappears, the electron experiences a loss of energy through an electrostatic attraction to its positively charged image. This attraction is manifested as a separation energy that does not allow electrons to leave the metal unless they have acquired more than this energy. Einstein called this separation energy the work function, w_f, which is characteristic of each type of metal. That energy is related to the threshold frequency of incident light that begins to eject photoelectrons from the metal in question, that is obtained by equating the work function to the energy of the incident photon

w_f  =h ν_m .                                                     (2a)

Now we have enough information to specify how much energy an electron ejected from a metal (w_f ) by a photon has in terms of the frequency (ν_i) of the incident light

ε_e= h ν_i – w_f

ε_e= h ν_i – h ν_m .                                            (2b)

Einstein was awarded the Nobel Prize partially for his explanation of the photoelectric effect, which was a confirmation of the Planck quantum hypothesis. The question that remained was about reconciling the was and particle nature of light. Because waves fill a space continuously, they produce the phenomenon of interference, a well know wave phenomenon that is captured in the famous double slit experiment, or Young's experiment. this experiment and the connection with quanta is discussed in detailed in a Wikipedia article. Richard Feyman also discussed this topic in on of a set of of great lectures on physics.These two links should serve a a good background for any further discussions on quantum mechanics, which any serious reader of these blogs would do well to check out.