Blackbody Radiation

Blackbody = something that absorbs all electromagnetic radiation incident on it. A blackbody does not necessarily look black. Its color depends on its temperature. The Sun and other stars behave approximately like blackbodies. The amount of electromagnetic radiation, with a given wavelength, emitted by a square meter of a blackbody’s surface in one second is given by the Planck blackbody radiation law. It is displayed as a graph on the following slide. The temperature scale used by physicists and astronomers is the absolute Kelvin scale. The temperature at which a body can emit no energy is absolute zero. One Kelvin = 1 Celsius degree = 1.8 Fahrenheit degree. The freezing point of water is about 273 K = 32 o F.

Comparison of the Solar (T = 5800 K) Continuous Spectrum with that of a 3500 K Star The 3500 K star is brightest at a wavelength around 828 nm. This is infrared radiation, so we don’t see it. Since the visible part of this star’s spectrum is strongest at red and orange wavelengths, it has a faint red - orange color. wavelength in nanometers flux in watts per square meter

Planck’s Law for Blackbody Radiation wavelength in nanometers flux in watts per square meter For a star with T = 7500 K For a star with T = 5800 K The peak of the graph for the star with a surface temperature of 7500 K is at a wavelength of 386 nm (violet). In the visible light from this star, there would be a bit more blue and violet than the other colors. The star would have a faint blue color. Our sun has a surface temperature of 5800 K. The wavelength at which it is brightest is 500 nm (green). It has a faint yellow color. The visible spectrum (about 400 to 700 nm) is superimposed on the graph).

Wien’s Law and the Stefan-Boltzman Law 7000 K 5800 K 3500 K F Notice that (a) the higher the temperature, the shorter the wavelength at which the star is brightest and (b) the higher the temperature the greater the area under the graph. ( a) is Wien’s law. Stated more precisely, it says that the wavelength max at which the blackbody is brightest is inversely proportional to its absolute temperature T. If T is in Kelvins and is in nm, then (b) is the Stefan-Boltzman Law: The energy radiated in one second by one square meter of the blackbody’s surface (E) is directly proportional to the fourth power of its temperature. If E is in watts per square meter and T is in Kelvins, or  is a constant whose value we won’t need because we’ll always use the second form of the Stefan-Boltzman law.

Example 1: The surface temperature of the Sun is about 5800 K, and the surface temperature of Sirius is about 11,000 K. Compare the surface flux (the electromagnetic energy emitted by 1 m 2 of surface in 1 second) of the star Sirius with the surface flux of the Sun. T A = 11,000 K T B = 5800 KA = Sirius and B = Sun Sirius is about 13 times brighter than the sun. Example 2: At what wavelength does Sirius emit the most electromagnetic energy? T = 11,000 K This is a bit shorter than violet, so Sirius is brightest at ultraviolet wavelengths. The visible wavelengths at which it is brightest are violet and blue, so Sirius has a pale blue color.

Atoms A neutral atom consists of a nucleus, made of protons and neutrons, and enough electrons to neutralize the positive charge of the protons. The diameter of the nucleus is about 1 femtometer (1 fm = m). The “cloud” of electrons, on the other hand, occupies a volume with a diameter of about 0.1 nm (1 nm = m). Since m p = 1836 m e and m n = 1839 m e, most of the mass of an atom is concentrated in its nucleus. An ion is an atom that has either a deficit or a surplus of electrons. The process of removing an electron from an atom is called “ionization”. The number of protons in the nucleus determines the chemical identity of the atom.

The Bohr Model of the Hydrogen Atom n = 1 n = 2 n = 3 The electron in a hydrogen atom moves in a circular orbit. The radius can only have one of a set of discrete values, r n (n = 1, 2, 3, …). n = 1, the lowest possible orbit, is called the ground state of the atom. The states above the ground state are called excited states. The electron can transfer to a higher orbit if it absorbs a photon of energy equal to the energy difference between the two orbits. When an electron transfers to a lower orbit, it emits a photon with energy equal to the energy difference between the two orbits. A transfer from one orbit to another is called a transition.

An energy level diagram is a graphical representation of the energies that are available to the electron in the atom. The following is an energy level diagram for the hydrogen atom. Lyman Series - ultraviolet Balmer Series - visible Paschen Series - infrared The higher energy levels are increasingly close together and blend into the continuum at an energy of 13.6 eV above the ground state. When a hydrogen atom absorbs a photon with energy greater than or equal to 13.6 eV, the electron is removed from the atom eV is the ionization potential of the hydrogen atom. Any atom can be described in terms of its energy levels. He, for example, has twice as many protons as H. Its energy levels are closer together, and the ionization potential for removing one electron from a neutral He atom in its ground state is 24.5 eV. n = 1 n = 2 n = 3 n = 4 n = 5  

Kirchoff’s Rules I. A solid, liquid, or dense gas has a continuous spectrum. II. A hot, low-density gas has an emission (bright line) spectrum. III. When light with a continuous spectrum passes through a cool gas, the result is an absorption spectrum.

The dominant component of a star’s spectrum is a set of absorption lines. The visible lines in the absorption spectrum of the Sun are shown below.

Dependence of Stellar Spectra on Temperature (Spectral Classification) 40,000 K20,000 K10,000 K 7500 K5500 K4500 K3000 K

Spectral Classes Type Hydrogen Balmer Line Strength Approximate Surface Temperature Main CharacteristicsExamples O Weak> 25,000 K Singly ionized helium lines either in emission or absorption. Strong ultraviolet continuum. 10 Lacertra B Medium11, ,000Neutral helium lines in absorption. Rigel Spica A Strong7, ,000 Hydrogen lines at maximum strength for A0 stars, decreasing thereafter. Sirius Vega F Medium6, ,500Metallic lines become noticeable. Canopus Procyon G Weak5, ,000 Solar-type spectra. Absorption lines of neutral metallic atoms and ions (e.g. once-ionized calcium) grow in strength. Sun Capella K Very Weak 3, ,000 Metallic lines dominate. Weak blue continuum. Arcturus Aldebaran M Very Weak < 3,500 Molecular bands of titanium oxide noticeable. Betelgeuse

The Luminosity Effect In a dense stellar atmosphere, the atoms collide more frequently than in a low density stellar atmosphere. The collisions broaden the absorption lines in the star’s spectrum. Giant stars are larger and less dense than main sequence stars, so their absorption lines are narrower than those of main sequence stars. The spectra shown above illustrate this effect. Notice that the absorption lines in the spectra of the giant (13 Mono ) and supergiant (HR 1040) stars are narrower than the absorption lines in the main sequence star  Lyrae. This enables us to use the star’s spectrum to determine its luminosity as well as its temperature. From “An Atlas of Stellar Spectra” by Morgan, Keenan, and Kellman

T = 50,000 K

T = 27,000 K

T = 11,000 K

T = 7200 K

T = 6000 K

T = 5100 K

T = 3700 K

Composition of the Sun Element% by Number of Atoms % by Mass Hydrogen Helium Carbon Nitrogen Oxygen Neon Magnesium Silicon Sulfur Iron