Chapter 27 Learning ObjectivesConcepts and Skills to Review
Heat transfer by radiation (Section 14.8)
The spectroscope (Section 25.6)
Relativistic momentum and kinetic energy (Sections 26.6 and 26.8)
Rest energy (Section 26.7)
Summary
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:
h = 6.626 × 10-34 J·s
(27-3)
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
E = hf
(27-4)
The maximum kinetic energy of an electron is the difference between the photon energy and the work function φ, which is the amount of energy that must be supplied to break the bond between an electron and the metal.
Kmax = hf - φ
(27-7)
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.
1 eV = 1.60 × 10-19 J
(27-5)
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:
hfmax = K
(27-9)
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 θ:
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 by individual atoms form line spectra. Each element has its own characteristic spectrum. Spectroscopy provided clues to the structure of the atom.
Assumptions of the Bohr model of the hydrogen atom:
The electron can exist without radiating only in certain circular orbits.
The laws of Newtonian mechanics apply to the motion of the electron in any of the stationary states.
The electron can make a transition between stationary states through the emission or absorption of a single photon.
The stationary states are those circular orbits in which the electron's angular momentum is quantized in integral multiples of h/(2π).
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 are annihilated and two photons are created.
