Kirchoff's Laws
1. 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.
2. 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.
3. 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.
4. 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?
• 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?