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Astronomy 2 Overview of the Universe Winter 2006 5. Lectures on Spectroscopy and Atomic Physics. Joe Miller.
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Astronomy 2Overview of the UniverseWinter 20065. Lectures on Spectroscopy and Atomic Physics. Joe Miller
Spectroscopy: the study of the spectra of light.The spectrum of a light source is a presentation of the intensities of the various wavelengths of light that make up that light. The intensity of light is shown as a function of wavelength. A common spectrum is a rainbow.Carefully studied, a spectrum can give us direct information on how the light was produced. Spectroscopy is an absolutely fundamental and extremely powerful tool for our understanding of the universe.
Kirchoff”s Laws of Spectroscopy: empirical laws discovered in the 19th century with no understanding of the underlying physical principles (in some ways analogous to Kepler’s Laws).First Law:A glowing solid or glowing liquid or glowing very high density gas emits a continuous spectrum.Continuous spectrum: all wavelengths are emitted.Example: tungsten light bulb, hot toaster wire.
Second Law:A glowing gas emits radiation only at specific, discrete wavelengths.This is often called an “emission line spectrum,”because spectrographs used to record spectra typically have recorded these emissions as narrow lines.Where we are headed: the pattern of emission lines emitted by a glowing gas is determined by the chemical elements in the gas and their physical condition.
Third Law:A cool gas in front of a source of a continuous spectrum produces an absorption spectrum.The light of certain, specific wavelengths is removed from the continuous spectrum. These dark spectral regions are often referred to as “absorption lines.”Here is hydrogen gas in absorption:
Spectra can be very complicated! Example: the spectrum of the sun
To understand the physics of astronomical objects, how they work, we must understand the physical processes that result in these three different kinds of spectra: the production and absorption of light itself.Light is generally produced and absorbed by processes that take place in the realm of the atom or molecule and involve energy transfers with electrons. To understand these processes requires an understanding of how atoms work.
The structure of the atom:A simple atom has two parts: the nucleus and a cloud of electrons in orbit around it.The simplest atom is hydrogen:It has a single particle called a proton at its center and single particle called an electron in orbit around the proton. The proton has a positive charge (+), and the electron has a negative (-) charge.
The hydrogen atomLike charges repel, opposite charges attract according to a formula that looks a lot like the Law of Gravity:where F is the electrostatic force, C is a constant, q1 and q2 are the charges on the two particles, and d is their separation. The minus sign acknowledges that the force can be attractive (+) or repulsive. This is called Coulomb’s Law and is another example of an inverse square law.
Helium, the next most complex atom:Helium has a nucleus of two protons plus two more particles called neutrons. Neutrons have no charge, but help bind the nucleus together. Helium in its normal state has two electrons orbiting the nucleus.The atomic number of helium = the number of protons =2The atomic weight = no. of protons plus neutrons = 4.It is the number of protons and electrons that determines the chemical nature and behavior of an atom, and thus the atomic number determines what the element is. For example, iron has 26 protons, but normally 30 neutrons, so its atomic weight is 56.
IsotopesIsotopes are different versions of the same element with different atomic weights. That is, though the various isotopes of a give element must all have the same number of protons, and thus the same atomic number, they have different numbers of neutrons.Two examples:1. Deuterium is a form of hydrogen that has a nucleus of one proton (that’s why it’s still hydrogen) plus one neutron.2. Tritium is another form of hydrogen with one proton and two neutrons in the nucleus.
Isotopes (cont.)If a nucleus has too many or two few neutrons, it may be unstable and fall apart by radioactive decay.Many isotopes are naturally occurring, but many are also made only in nuclear reactors. Ions:When an atom has an equal number of electrons and protons, it is neutral; there is no net charge. However, if an electron is removed, the atom left behind is now said to be an ion and has a net positive charge. The process of removing an electron is called ionization. Atoms with many electrons can be singly ionized, doubly ionized, etc., gaining ever more charge as more electrons are removed.
How light is created inside the atomBohr’s Theory (the beginnings of quantum mechanics.)In Bohr’s picture, electrons can reside in only in certain orbits and nowhere else. These orbits are said to be “quantized.” The closer an orbit is to the nucleus, the more tightly bound is the electron there to the nucleus.
To move an electron from a low orbit to a higher one requires energy. Conversely, an electron moving from a higher orbit to a lower one gives up energy. Often the energy involved is a photon, either being absorbed or emitted.
Consider the hydrogen atom:There are many possible transitions (electron jumps) between level just in the lower levels.
An alternative way of looking at things: the energy level diagram: hydrogen (left) and sodium (right).
The immense variety of spectraEach atom has its own particular set of energy levels. Thus it has its own set of possible electron decay paths which lead to the creation of photons and therefore its own set of wavelengths for the pattern of spectral lines it can form. Furthermore, the same can be said of each stage of ionization of each atom. Neutral oxygen is capable of producing a different set of spectral lines than singly ionized oxygen, doubly ionized oxygen yet another unique set, and so on. Fortunately for the spectroscopist, not all elements and ions of all elements are equally abundant, or interpreting spectra would be an almost impossible job.
Even so, spectra can be very complicated! A portion of the spectrum of the sun:
Summary of electron transitions: • Excitation: electron goes from a lower orbit to a higher one: two ways to do this- • Radiative (photo-) excitation: a photon of exactly the right energy to go up from one level to another is absorbed. Part of a photon’s energy can’t be used. It’s all or nothing. The photon is destroyed. • Collisional excitation- an atom collides with another atom or electron. Some of the kinetic energy is lost, exciting the electron to a higher level. • Ionization: if the absorbed photon or the collision gives the electron enough energy, it can be removed entirely from the atom. This is called either photo-ionization or collisional ionization.
Electron transitions (cont.) • De-excitation: an electron goes from a higher orbit to a lower one. • Radiative de-excitation- the electron drops to a lower energy level and gives up a photon of energy equal to the difference in energies between the two levels. • Collisional de-excitation- the atom collides with another atom or electron, and the energy released as the electron drops from one level to another is put into kinetic energy of the collision. • Recombination- the opposite of ionization. An ion captures an electron and becomes one stage less ionized. A photo is given off with energy corresponding to the energy lost by the electron as it is captured.
The formation of a continuous spectrum: a great puzzle of the 19th century.The continuous spectrum is produced in part by electrons that are not necessarily confined to bound orbits, but are relatively free to wander around. Also, in the case in a solid or gas under high pressure, atoms and molecules bound together by electric fields and shared electrons store energy in this binding and can release it in the form of radiation. Together, these processes can give rise to photons of any amount of energy and thus give rise to photons of a continuous range of wavelengths. However theoretical attempts in the 19th century to predict the relative likelihood of various energy photons being produced, that is, to account for the shape of the spectrum emitted by a glowing solid, failed. It predicted that the spectrum would rise forever into the ultraviolet. This was called the ultraviolet catastrophe.
The solution to the spectrum of continuous radiation:Planck’s theory of black body radiation.Planck needed to use the new theory of quantum mechanics to do the problem correctly. He defined a new type of object- a black body- as an object capable of emitting or absorbing any wavelength without any hindrance: a perfect emitter or absorber. Using quantum theory, he derived the spectrum of a black body and showed that its shape only depended on temperature. He thus theoretically provided the basis for Wien’s and Stefan-Boltzmann’s Law, which we will now turn to.
Illustration of black body radiation at different temperatures:
Wien’s law: an empirical law.The wavelength of maximum light output from a black body depends inversely on the temperature.The hotter an object is, the bluer its maximum light output becomes.
Stefan-Boltzmann Law:The amount of radiation emitted per unit area of a black body goes up as the fourth power of the temperature. Doubling the temperature results in 16 times as much energy output per unit area.With these physical principles and ideas, we are now ready to investigate the nature of the stars!
