Radiation Laws
Kirchoff's Laws
- First Law: A hot solid, liquid, or dense gas emits radiation at all
wavelengths ("a continuous spectrum of radiation"). For example,
a perfect blackbody does this.
If the light were passed through a prism, you would see the whole
rainbow of colors in a continuous band.
- Second Law: A thin hot gas in front of a cooler background emits radiation
at a discrete set of isolated wavelengths. These discrete, isolated
wavelengths are called the "emission lines" of the spectrum, because
if you were to pass the radiation through a prism, you would see isolated
lines of different colors. The whole spectrum is called an
"emission-line" spectrum. The wavelengths of the emission lines are unique to
the type of neutral atom or ionized atom that is producing the emission lines.
- Third Law: A thin cool gas in front of a hotter solid, liquid, or dense-gas
background removes the radiation from the background source at special
wave lengths. If the resulting radiation were passed through a prism,
there would be dark lines superimposed on the continuous band of colors
due to the background. These dark lines are called "absorption lines."
The wavelengths of the absorption lines are unique to
the type of neutral atom or ionized atom that is producing the emission lines.
- If a certain type of gas produces absorption lines at certain
wavelengths when it is in front of a hot background, then when that
same type of gas is seen in front of a cooler background, it produces
emission lines at the exact same wavelengths.
Explanation of Kirchoff's First Law
- Kirchoff's First Law boils down to blackbody radiation, since
solid objects and dense gases emit radiation like blackbodies.
Explanation of Kirchoff's Second and Third Laws
- Thin gases don't emit or absorb radiation like blackbodies. To understand
their emission and absorption, we must consider the structure of atoms, as
described by Quantum Mechanics.
- The Bohr model of the hydrogen atom: a dense nucleus containing the
hydrogen atom's single proton (and possibly one or more neutrons), surrounded
by an electron that can be on one of several different orbits.
- the n=1 level is called the "ground state" of the atom.
- if an electron in one of the energy levels is hit by light, it can
absorb a photon IF that photon has an energy precisely
equal to the energy difference between the electron's initial energy level
and some higher energy level, or if the photon has an energy greater
than the energy difference between the electron's initial level
and the n=infinity
energy level. In this last case, if the photon is absorbed, the electron
is knocked out of the atom---that is, the atom is "ionized".
- IMPORTANT POINT: since the different energy levels are discretely
spaced, some photons will not have precisely the right amount of energy
to cause the electron to jump to another level. Those photons are not
absorbed by the atom.
- An electron in an energy level above the ground state (i.e., with n > 1)
can spontaneously emit a photon and jump to a lower energy level. The energy
of the emitted photon is precisely the energy difference between the electron's
initial level and final level.
- So, atoms emit and absorb photons only at special energies. Remember, each
different photon energy corresponds to a different wavelength and frequency
(you should review the discussion of wavelength, frequency, and energy in
chapter 6).
Question: An astronomer studying a particular object in space finds that
the object emits light only in specific, narrow emission lines. The correct
conclusion is that this object
- is made up of a hot dense gas surrounded by a rarefied gas?
- is made up of a hot, low-density gas?
- cannot consist of gases but must be a solid object?
- is made up of a hot dense gas?
Interesting points about Kirchoff's Laws
- The same cloud of gas can produce absorption lines when viewed
from one angle (at which the cloud appears in front of a hot
background) and emission lines when viewed from another angle
(at which the cloud appears in front of a cold background).
- each type of gas has a unique and intrinsic set of absorption and
emission lines.
When astronomers look at astronomical objects, they can often tell
what elements are present in the object based upon the emission or
absorption lines that they see.
- Why do the spectra of stars include absorption lines? The reason is
that stars are very hot in their cores, but get colder towards their
surface.
The radiation that we see from a star passes through the outer
cooler gas at the star's surface. Since this outer layer is relatively
thin, and cooler than the layers underneath, it produces an absorption line
spectrum.
- Why do the spectra of stars include emission lines? Many stars are surrounded
by a very hot, thin gas (plasma) that is significantly hotter than the star's
surface. Kirchoff's second law in the list above then implies that this
hot tenuous gas can give off emission lines.
Role of temperature.
- electrons in an atom can jump from one energy level to a higher energy level
by absorbing a photon, or through collisions with other atoms. Why? Both collisions
and electromagnetic radiation involve electric fields.
- The hotter a gas, the faster the gas molecules are moving, and the greater
the energy of collisions between atoms. When collisions become more energetic,
they can knock electrons into higher and higher energy levels. When the gas gets
sufficiently hot (above 10,000 degrees Kelvin), the collisions are so energetic
that a good fraction of them can knock electrons right out of atoms, ionizing
the atoms.
- Normally, in the absence of energetic collisions, all the electrons in a gas
will emit photons until they drop down to the ground state. It is only when
collisions are present, or when photons from some source such
as a star pass through a gas, that
the electrons jump up to higher energy levels.
- What conditions are necessary for a star to produce Balmer absorption lines?
Remember, the absorption lines are produced when photons pass through the
outer coolest layer of the star. Within this layer,
there must be electrons in the n=2 level of the hydrogen atom, or there
will be no Balmer absorption line. If the star is
too cool, then collisions will be unable to knock electrons up into the
n=2 energy level. If the star is too hot, then collisions will be so
effective that all of the hydrogen at the star's surface will get ionized,
and again there will be no Balmer absorption line.
- For each element and molecule (a molecule is just a group of atoms),
different absorption and emission lines will be possible at different temperatures.
The surface temperature thus plays a crucial role in determining the spectrum of
radiation that a star emits.
- In addition, the continuous "black-body-like" radiation that a star emits
also depends critically on a star's surface temperature.
Question: The star P Cygni (in the constellation Cygnus, the Swan)
is surrounded by an extensive low-density atmosphere. Its spectrum consists
of a bright, continuous spectrum with many dark narrow absorption lines and
a few bright emission lines. The bright continuous part of the spectrum
is produced by
- the low-density atmosphere of the star emitting light in all directions?
- all parts of the star, the stellar surface and the atmosphere, equally?
- the hot, dense, opaque gas of the star's surface?
- only the part of the low-density atmosphere that is between us and the
surface of the star?