14.4 The Old Quantum Theory 641
atomic number in 1913, showing that each element was characterized by the charge on
its nucleus.Ernest Rutherford, 1st Baron Rutherford
of Nelson, 1871–1937, was a British
physicist originally from New Zealand
who won the 1908 Nobel Prize in
chemistry for his discovery of the atomic
nucleus, and who coined the terms
alpha, beta, and gamma radiation.
Henry Gwyn-Jeffreys Moseley,
1887–1915, was a British physicist who
was also a lieutenant in the British Army
and was killed in action in Turkey in
1915.
Robert Andrews Millikan, 1868–1953,
was an American physicist who
received the 1923 Nobel Prize in
physics for determining the charge on
the electron.
The atomic nucleus can be regarded as being made up of protons and neutrons.
Protons and neutrons now appear to be made up of quarks, and the “superstring” theory
proposes that quarks, electrons, and other fundamental particles consist of vibrations of
tiny strings.^2 For most chemical purposes, it is sufficient to regard an atom as consisting
of a positive nucleus and a number of negative electrons.Planck’s Theory of Black-body Radiation
If an object has a temperature near 1000◦C, it glows visibly red, no matter what material
it is made of. At higher temperatures it glows orange, yellow, white, or even blue if
the temperature is high enough. It is found experimentally that at any temperature an
object with a lower reflectivity glows more intensely. Ablack body, a model system
that reflects no radiation at any wavelength, has the maximum emissivity at every
wavelength.
The best laboratory approximation to a black body is not an object, but a small hole
in the side of a hollow box. Any light falling on the hole from outside will be absorbed
as it is reflected around in the box. Measurements on the light emitted through the hole
when the box is heated show that the amount of light emitted and its spectral distribution
depend only on the temperature of the walls of the box. Figure 14.10 shows thespectral
radiant emittanceηof a black body as a function of wavelength for several absolute
temperatures. This quantity is defined such thatη(λ)dλis the energy per unit time per
unit area emitted in the wavelengths lying betweenλandλ+dλ. The visible part of
the electromagnetic spectrum, which ranges from about 400 nm to 700 nm, is labeled
in the figure.
The maximum in the curve shifts to shorter wavelengths as the temperature is raised.
At 5800 K the maximum in the curve is near 500 nm, in the green portion of the visible
region. Black-body radiation of this temperature appears to be “white” light, similar
to sunlight. Below 2000 K only the red part of the visible spectrum (around 600 to
700 nm) is significantly represented. Near room temperature almost all of the radiation
is in the infrared region. It is this infrared radiation from the surface of the earth that is
involved in the greenhouse effect in the earth’s atmosphere.
Thetotal radiant emittance(the spectral radiant emittance summed over all wave-
lengths) is equal to the area under the curve. TheStefan–Boltzmann lawis an empirical
law that relates the total radiant emittance to the absolute temperature of the black body:(total radiant emittance)σT^4 (14.4-1a)The Stefan–Boltzmann constantσhas the experimental valueσ 5. 67051 × 10 −^8 Jm−^2 s−^1 K−^4 5. 67051 × 10 −^8 Wm−^2 K−^4 (14.4-1b)where the joule (J) is the unit of energy and the watt (W, equal to joules per second) is
the unit of power.
Rayleigh and Jeans constructed a classical theory of black-body radiation. They
defined as their system the set of standing electromagnetic waves that could exist inside
a box made of electrically conductive material. An electric field cannot penetrate a per-
fect conductor (one with zero resistance), because a finite electric field would produce
an infinite current. Electromagnetic waves must have nodes at perfectly conducting(^2) See for example, B. Greene,The Elegant Universe, Vintage Books, New York, 2000.