course index

Recall from last lectures:

• Blackbody radiation: Ad hoc quantization of energy of "radiators" and electromagnetic radiation gives predictions that agree with observed radiation spectrum, l_maxT = 0.2898×10^-2m.°K.
• Introduced Planck's constant h = 6.63×10^-34Js.
• Photoelectric effect: Electromagnetic radiation quantized in packets, photons, of energy E = hf.
• KE_max = hf - f.
• X-rays: radiation created by stopping energetic electrons with heavy atoms, l_min = hc / eDV.
• X-ray diffraction: X-ray photons behave like waves!
• The Compton effect: X-ray photons behave like particles! (at least under certain circumstances).
• Dl = l - l₀ = (h/m_ec) (1 - cosq).

27.7 Pair Production and Annihilation

Thus far, we've discussed processes that show that

1. quantized energy is needed to explain the blackbody spectrum,
2. electromagnetic radiation is quantized in photons, and
3. photons behave like particles under certain conditions (scattering).

Pair production occurs when the energy of a very high energy photon is converted into mass, specifically an electron and its anti-particle, a positron (sketch a diagram, like Figure 27.18). The reason why an electron and a positron are produced is to conserve charge -- the photon is neutral, so the pair of particles must also be neutral. There are other conservation laws that force the positive particle to be a positron, rather than, say, a proton. (An anti-particle is identical to its particle except for the sign of the charge.) This process must also conserve energy and momentum. It turns out that a nearby nucleus is required to allow momentum to be conserved. Conservation of energy then requires that the energy of the photon be greater than the rest energy of the electron and positron:

Pair annihilation is the process where an electron and positron combine, converting their mass into energy (photons). We can generally assume that the electron and positron are at rest. Again, momentum and energy are conserved. The initial momentum is zero if the electron and positron are at rest, so after annihilation, two photons are created, moving in opposite directions. The photons have equal momentum and energy. The sum of the photon energies equals the sum of the electron and positron rest mass energy, or

27.8 Photons and Electromagnetic Waves

How can photons act like waves and particles?! You will probably believe me when I tell you that they can show properties of each, and wonder why physicists make such a big deal about it. For our purposes, I'd like to explore this point a little deeper.

Particles are rather familiar by now. Particles have a definite location in space, and may have a physical size, or be infinitismal, like geometric points. Usually the particles we deal with have mass, but let's relax this requirement for photons, since they have no mass. When they move, particles follow a definite path, a curve through space.

Waves have been less discussed in this course, but many of their properties may be familiar to you. A wave is a movement of energy without any net motion of matter. (Water waves do not actually cause molecules of water to move with the wave, only up and down.) Waves don't have a specific location in space, but are spread over some area. This lack of localization is most strikingly demonstrated in the ability of waves to interfere, producing interference or diffraction patterns.

Photons have properties of particles and waves simultaneously. This may seem contradictory, but the modern quantum theory handles the contradictions perfectly. The real problem is when, for a particular situation, we try to decide between treating photons approximately (without the full quantum theory) as waves or as particles. Usually the case is clear cut.

For instance, photons of FM radio radiation should be treated as waves, since the energy of a single photon, about 10^-8eV, is much too small to produce a signal. Only the collective effect of billions of photons can be detected. Such a large number of photons will not appear grainy, rather it will appear smooth, like a continuous, unquantized wave. Interference and diffraction of radio waves is quite common.

On the other hand, an x-ray photon can have an energy of several thousand electronvolts, large enough for a single photon to produce a substantial, detectable signal. X-ray photons should generally be treated individually, as particles.