1900, The quantum view.

In 1905, Einstein proposed that light came in quantized packets of energy. This hypothesis explained the photoelectric effect. In the photoelectric effect, no matter how intense a red light was shone on a metal, electrons were never knocked free of the metal. No matter how dim a blue light, the electrons were always instantly knocked free of the metal. It takes energy to knock electrons out of a metal. Einstein's quantized packets of energy came to be called photons.

Photons interact with charges with their entire energy or with no energy at all.

The energy of a photon is proportional to its frequency.

So, low frequency red light had low energy per photon
while high frequency blue light had high energy per photon.
Only the blue photons had enough energy to eject electrons from metal.

( mathematically,

E = hf

where E is the energy of a photon
h is Planck's constant = 6.6x10
and f is the frequency)

A single high frequency photon carries more energy than a single low frequency photon. The intensity of a light beam however depends not only on the energy per photon but also on the total number of photons. Thus a beam of low energy infrared photons can carry more energy than a beam of high energy x-rays if there are a huge number of infrared photons and few x-rays. (Just as the price of hamburger depends on both the price per pound and the weight of the hamburger you select.)

Photons also carry momentum. When the control rockets on the Mariner Mercury spacecraft failed, NASA engineers used the force from sunlight bouncing off the solar panels to change the orbit of the spacecraft. They achieved their three planned rendezvous with Mercury.

The momentum of a photon is p = hf/c or h/l where l is the wavelength.

A photon also possesses angular momentum.

While photons are said to have zero "rest mass" they always travel at the speed of light and so are never at rest. So that photons always have mass.
Since E = mc
then m = E/c
or m = hf/c

Quantum mechanics blends the wave and particle aspects of light. A wave equation is used to calculate the probability of an interaction while the interaction involves a particle-like creation or destruction of an entire quantum. In colloquial language,

Light travels like a wave and interacts like a particle.

The color of the photon is determined by its energy (which is proportional to the frequency of the probability waves which make up the photon.)
The intensity of light is determined by the energy per photon and the number of photon per second.
And finally, the purity of the color of the photon is determined by both the breadth of the mix of different frequency photons and by the length of the individual photons.

An average photon from excited mercury in a fluorescent light has a length of 3 meters, (It has a length in time of 10-8 s which at the speed of light 3 x 108 m/s means 3 m) It has a frequency near 1015 Hz and so the wave packet contains 1015 x 10-8 s = 107 oscillations. The wave packet covers all of space but it is mostly contained within a region which has a width of about one wavelength.

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Scientific Explorations
© 1999

22 May 2000