relativistic momentum and kinetic energy (Sections 26.6 and 26.8)
rest energy (Section 26.7)
Mastering the Concepts
A quantity is quantized when its possible values are limited to a discrete set.
Max Planck found an equation to match experimental results for blackbody radiation. The equation led him to postulate that the energy of an oscillator must be quantized in integral multiples of hf, where f is the frequency of the oscillator. Planck's constant is now recognized as one of the fundamental constants in physics:
In the photoelectric effect, EM radiation incident on a metal surface causes electrons to be ejected from the metal. To explain the photoelectric effect, Einstein said that EM radiation itself is quantized. The quantum of EM radiation—that is, the smallest indivisible unit—is now called the photon. The energy of a photon with frequency f is
<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663835/27_02.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (3.0K)</a>
The maximum kinetic energy of an electron is the difference between the photon energy and the work function f, which is the amount of energy that must be supplied to break the bond between an electron and the metal.
One electron-volt is equal to the kinetic energy that a particle with charge ±e (such as an electron or a proton) gains when it is accelerated through a potential difference of magnitude 1 V.
In an x-ray tube, electrons are accelerated to kinetic energy K and then strike a target. The maximum frequency of the x-ray radiation emitted occurs when all of the electron's kinetic energy is carried away by a single photon:
In Compton scattering, x-rays scattered from a target have longer wavelengths than the incident x-rays; the wavelength shift depends on the scattering angle q
<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663835/27_06.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (5.0K)</a>
Compton scattering can be viewed as a collision between a photon and a free electron at rest. The momentum and kinetic energy of the incident photon must equal the total momentum and kinetic energy of the scattered photon and recoiling electron.
Emission and absorption of EM radiation by individual atoms form line spectra at discrete wavelengths. Each element has its own characteristic spectrum determined by its discrete (quantized) set of energy levels. The energy of the photon emitted or absorbed when an atom makes a transition between energy levels is equal to the difference between the atomic energy levels:
<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663835/27_08.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (4.0K)</a>
where the ground state energy (lowest energy level) is
The Bohr model of the hydrogen atom assumed that the electron moves in a circular orbit around the nucleus. The radii and energies of these orbits are quantized. Although calculations using the Bohr model give the correct energy levels [Eqs. (27-22) and (27-23)], it has serious deficiencies and has been replaced by the quantum mechanical description of the hydrogen atom (Chapter 28).
Fluorescent materials absorb ultraviolet radiation and decay in a series of steps; one or more of the steps involve the emission of a photon of visible light.
In pair production, an energetic photon passing by a massive particle creates an electron-positron pair. In pair annihilation, an electron-positron pair is annihilated and two photons are created.
