physics intro ppt for lecture notes.....

Editor's Notes

• #1: At least 95% of the celestial information we receive is in the form of light. Because of this fact, astronomers have devised many techniques to decode as much as possible the messages that are encoded in the often extremely faint rays of light. These messages include information about the object's temperature, motion, chemical composition, gas density, surface gravity, shape, structure, and more! Roughly 85% of the information in light is uncovered by using spectroscopy---spreading the light out into its different constituent colors or wavelengths and analyzing the spectrum.
• #2: In order to understand light, you first need to have an understanding of electric fields and magnetic fields. Electrical charges and magnets alter the region of space around them so that they can exert forces on distant objects. This altered space is called a force field (or just a field). Rather than describing the action of forces by having a distant object somehow reach out across space and push or pull on a body, the body simply responds to its local environment. An electric charge or a magnet responds to the field immediately surrounding it. That field is produced by a distant object. In the same way, a massive object can produce a gravity field that distant objects will respond to. Scientists have known since the early part of the 19th century that electrical fields and magnetic fields are intimately related to each other and applications of this connection are found all around you. Moving electric charge (electric current) creates a magnetic field. Coils of wire can be used to make the large electromagnets used in car junk yards or the tiny electromagnetics in your telephone receiver. Electric motors used to start your car or spin a computer's harddisk around are other applications of this phenomenon. In fact, ordinary magnets are produced from tiny currents at the atomic level. A changing magnetic field creates electrical current---an electric field. This concept is used by power generators---large coils of wire are made to turn in a magnetic field (by falling water, wind, or by steam from the heating of water by burning coal or oil or the heat from nuclear reactions). The coils of wire experience a changing magnetic field and electricity is produced. Computer disks and audio and video tapes encode information in magnetic patterns of alternating magnetic directions and magnetic strengths. When the magnetic disk or tape material passes by small coils of wire, electrical currents (electric fields) are produced. James Clerk Maxwell (lived 1831--1879) put these ideas together and proposed that if a changing magnetic field can make an electric field, then a changing electric field (from an oscillating electric charge, for example) should make a magnetic field. A consequence of this is that changing electric and magnetic fields should trigger each other and these changing fields should move at a speed equal to the speed of light. To conclude this line of reasoning, Maxwell said that light is an electromagnetic wave. Later experiments confirmed Maxwells's theory.
• #3: Light, electricity, and magnetism are manifestations of the same thing called electromagnetic radiation. The energy you see coming out of the computer screen you are using to read this page is made of fluctuating electric and magnetic energy fields. The electric and magnetic fields oscillate at right angles to each other and the combined wave moves in a direction perpendicular to both of the electric and magnetic field oscillations. This energy also comes in many forms that are not detectable with our eyes such as infrared (IR), radio, X-rays, ultraviolet (UV), and gamma rays. We feel infrared light as heat and our radios pick up the messages encoded in radio waves emitted by radio stations. Ultraviolet light has high enough energy to damage our skin cells, so our bodies will produce a darker pigment in our skin to prevent exposure of the deeper skin cells to the UV (we tan as a defense mechanism). The special bulbs called “black lights” produce a lot of UV and were used by hospitals to kill bacteria, amoebas, and other micro-organisms. X-rays are produced by very hot things in space. X-rays have more energy than UV, so they can pass through skin, muscles, and organs. They are blocked by bones, so when the doctor takes your X-ray, the picture that results is the shadow image of the X-rays that passed through your body. Because X-rays have such high energy, they can damage or kill cells. A few brief exposures to low-intensity X-rays is okay. The X-ray technician would be exposed to thousands of X-ray exposures if s/he did not use some sort of shielding. Gamma rays are the most energetic form of electromagnetic radiation and are produced in nuclear reactions.
• #4: There are some general properties shared by all forms of electromagnetic radiation: 1.It can travel through empty space. Other types of waves need some sort of medium to move through: water waves need liquid water and sound waves need some gas, liquid, or solid material to be heard. 2.The speed of light is constant in space. All forms of light have the same speed of 299,800 kilometers/second in space (often abbreviated as c). From highest energy to lowest energy the forms of light are Gamma rays, X-rays, Ultraviolet, Visible, Infrared, Radio. (Microwaves are high-energy radio waves.) 3.A wavelength of light is defined similarly to that of water waves---distance between crests or between troughs. Visible light (what your eye detects) has wavelengths 4000-8000 Ångstroms. 1 Ångstrom = 10-10 meter. Visible light is sometimes also measured in nanometers (“nm” in the figure above): 1 nanometer = 10-9 meter = 10 Ångstroms, so in nanometers, the visible band is from 400 to 800 nanometers. Radio wavelengths are often measured in centimeters: 1 centimeter = 10-2 meter = 0.01 meter. The abbreviation used for wavelength is the greek letter lambda: . White light is made of different colors (wavelengths). When white light is passed through a prism or diffraction grating, it is spread out into all of its different colors. You see this happen every time you see a rainbow. Not all wavelengths of light from space make it to the surface. Only long-wave UV, Visible, parts of the IR and radio bands make it to surface. More IR reaches elevations above 9,000 feet (2765 meters) elevation. That is one reason why modern observatories are built on top of very high mountains. Fortunately, as far as life is concerned, our atmosphere shields us from the gamma rays, X-rays, and most of the UV. It also blocks most of the IR and parts of the radio. Astronomers were not able to detect these forms of energy from celestial objects until the space age, when they could put satellite observatories in orbit. Besides using wavelength to describe the form of light, you can also use the frequency--the number of crests of the wave that pass by a point every second. Frequency is measured in units of hertz (Hz): 1 hertz = 1 wave crest/second. For light there is a simple relation between the speed of light (c), wavelength (), and frequency (f): f = c/lambda Since the wavelength is in the bottom of the fraction, the frequency is inversely proportional to the wavelength. This means that light with a smaller wavelength has a higher (larger) frequency. Light with a longer wavelength has a lower (smaller) frequency.
• #5: The term intensity has a particular meaning here: it is the number of waves or photons of light reaching your detector; a brighter object is more intense but not necessarily more energetic. Remember that a photon's energy depends on the wavelength (or frequency) only, not the intensity. The photons in a dim beam of X-ray light are much more energetic than the photons in an intense beam of infrared light. The type of light produced by an object will depend on its temperature, so let's digress slightly to investigate what “temperature” is. Temperature is a measure of the random motion (or energy) of a group of particles. Higher temperature (T) means more random motion (or energy). A natural scale would have zero motion at zero degrees (absolute zero). This scale is the Kelvin scale. It scales exactly like the Celsius system, but it is offset by 273 degrees.
• #6: The direction of light propagation can be changed at the boundary of two media having different densities. This property is called refraction, and is illustrated in the following figure for the boundary between air and water. The apparent and actual positions of the fish differ because the direction of light propagation has been changed as light passes from the more dense water into the less dense air. If we adopt the convention that the light passes from medium 1 into medium 2, the general rule is that the refraction is Away from the perpendicular if medium 2 is less dense than medium 1 Toward the perpendicular if medium 2 is more dense than medium 1 Thus, in the above example the refraction is away from the perpendicular because air is less dense than water. Such effects form the basis of the refracting telescope, and of optical devices using lenses in general. The amount of refraction of light at a boundary between two media depends on three things: 1.The nature of the media (embodied in a characteristic quantity called the index of refraction for a medium). 2.The angle of indidence for the light ray on the boundary. 3.The wavelength of light. The dependence of refraction on the wavelength of light is called dispersion. This dependence has both positive and negative implications for astronomy. On the positive side, it is the basis for the prism and its ability to separate light according to wavelength; on the negative side, it is the source of chromatic aberration in optical devices (the failure of different wavelengths to focus at the same point). Dispersion is the basis for the prism and its ability to spatially separate light according to wavelength. Light separated into its frequency (and therefore energy or wavelength) components is called a spectrum of light. A spectrograph is a refined instrument that produces a spectrum. Although a prism can disperse light according to color, in modern spectrographs it is more common to accomplish the same task by using a diffraction grating. The diffraction grating works on a completely different principle (diffraction rather than refraction) but it also can separate light spatially according to wavelength. We will see in subsequent sections that the spectrograph is a central tool of modern astronomy.
• #7: When light is passed through a prism or a diffraction grating to produce a spectrum, the type of spectrum you will see depends on what kind of object is producing the light: is it a thick or thin gas, is it hot or cool, is it a gas or a solid? There are two basic types of spectra: continuous spectrum (energy at all wavelengths) and discrete spectrum (energy at only certain wavelengths). Astronomers usually refer to the two types of discrete spectra: emission lines (bright lines) and absorption lines (dark lines in an otherwise continuous spectrum) as different types of spectra. A rainbow is an example of a continuous spectrum. Most continuous spectra are from hot, dense objects like stars, planets, or moons. The continuous spectrum from these kinds of objects is also called a thermal spectrum, because hot, dense objects will emit electromagnetic radiation at all wavelengths or colors. Any solid, liquid and dense (thick) gas at a temperature above absolute zero will produce a thermal spectrum. A thermal spectrum is the simplest type of spectrum because its shape depends on only the temperature. A discrete spectrum is more complex because it depends on temperature and other things like the chemical composition of the object, the gas density, surface gravity, speed, etc. Exotic objects like neutron stars and black holes can produce another type of continuous spectrum called “synchrotron spectrum” from charged particles swirling around magnetic fields, but I will discuss them in another chapter later on. For now, let's look at a thermal spectrum. Sometimes astronomers use the term “blackbody” spectrum for a thermal spectrum. A “blackbody” is an object that absorbs all the light falling on it, reflecting none of it, hence, it appears black. When the “blackbody” object is heated, it emits light very efficiently without any gaps or breaks in the brightness. Though no object is a perfect ``blackbody'', most stars, planets, moons and asteroids are near enough to being ``blackbodies'', that they will produce spectra very similar to a perfect thermal spectrum.
• #8: Some key features of a thermal (continuous) spectrum are as follows: 1.There is light from a dense object at all possible IF the object is above 0 K (absolute zero). Since everything in the universe is above 0 K, all dense objects (solids, liquids, thick gases) will produce a thermal spectrum. 2.The shape of a continuous spectrum depends on only the temperature of the object NOT its chemical composition. This allows you to determine the temperature of an object from a great distance away. 3.As the temperature of an object increases, more light is produced at all wavelengths than when it was cooler. You can see this effect with a light bulb wired to a dimmer switch. As you raise the current going to the bulb, the bulb's filament gets hotter and brighter. 4.As the temperature of an object increases, the peak of thermal spectrum curve shifts to smaller wavelengths (higher frequencies)---cool things appear red or orange, hotter things appear yellow or white, and very hot things blue or purple. This is opposite to what artists use for “cool” colors (blues) or “hot” colors (reds)! You can also see this effect with the light bulb wired to a dimmer switch. The dim bulb will have an orange color and as you make it brighter, the bulb will turn yellow and even white. Wilhelm Wien (lived 1864--1928) discovered that the peak of the thermal spectrum curve, peak in nanometers, is related to the temperature by peak = 2.9 × 106 / temperature (in K). This simple relation is now known as Wien's Law. Using this you will find that cool objects like cars, plants, and people radiate most of their energy in the infrared. Very cold objects radiate mostly in the radio band. 5.A small change in the temperature produces a HUGE change in the amount of energy emitted by every unit area of the object. If you add up all of the energy emitted every second by an area of one square meter on the object's surface, you find it equals ×temperature4, where is another universal constant of nature [= 5.67×10-8 J/(m2 K4 s)]. This relation is called the Stefan-Boltzmann law. Because the temperature is raised to the fourth power, a small rise in the temperature of an object will produce a HUGE increase in the amount of energy it emits. When you add up all of the energy of all of the square meters on the object's surface, you get the luminosity---the total amount of energy emitted every second by the object. The luminosity = (total surface area) × (×temperature4). If our Sun were just twice as hot as it is now, it would produce 24 = 16 times more energy than it does now!
• #9: Close examination of the spectra from the Sun and other stars reveals that the rainbow of colors has many dark lines in it, called absorption lines. They are produced by the cooler thin gas in the upper layers of the stars absorbing certain colors of light produced by the hotter dense lower layers. You can also see them in the reflected light spectrum from planets. Some of the colors in the sunlight reflecting off the planets are absorbed by the molecules on the planet's surface or in its atmosphere. The spectra of hot, thin (low density) gas clouds are a series of bright lines called emission lines. In both of these types of spectra you see spectral features at certain, discrete wavelengths (or colors) and no where else. The type of spectrum you see depends on the temperature of the thin gas. If the thin gas is cooler than the thermal source in the background, you see absorption lines. Since the spectra of stars show absorption lines, it tells you that the density and temperature of the upper layers of a star is lower than the deeper layers. In a few cases you can see emission lines on top of the thermal spectrum. This is produced by thin gas that is hotter than the thermal source in the background. Unlike the case for absorption lines, though, the production of emission lines does NOT require a thermal source be in the background. The spectrum of a hydrogen-emission nebula (“nebula” = gas or dust cloud) is just a series of emission lines without any thermal spectrum because there are no stars visible behind the hot nebula. Some objects produce spectra that is a combination of a thermal spectrum, emission lines, and absorption lines simultaneously! What is very useful about discrete spectra is that the pattern of lines you see depends on the chemical composition of the thin gas. Each element or molecule produces a distinct pattern of lines---each element or molecule has a “fingerprint” you can use to identify it. This allows you to remotely determine what stars, planets, nebulae, etc. are made of! The composition canNOT be found from just one line because one element may have one spectral line at the same wavelength as another element's spectral line. However, an element's pattern of lines is unique. Using a single line to identify a gas would be like identifying the name of someone using just one letter of their name---many people will have that same letter in their name, but the pattern of letters (which letters and how they are arranged) is unique to that one person. Of course, stars, planets, nebulae, etc. are made of more than one type of material, so you see the discrete spectra of many elements and molecules superimposed on each other---all of the spectral lines add together. An experienced astronomer can disentangle all the different patterns and sort out the elements and molecules (but it does take time!).
• #10: Niels Bohr (lived 1885--1962) provided the explanation in the early 20th century. He said that the electron can be only found in energy orbits of a certain size and as long as the electron is in one of those special orbits, it would radiate no energy. If the electron changed orbits, it would radiate or absorb energy. This model sounds outlandish, but numerous experiments have shown it to be true. In Bohr's model of the atom, the massive but small positively-charged protons and massive but small neutral neutrons are found in the tiny nucleus. The small, light negatively-charged electrons move around the nucleus in certain specific orbits (energies). In a neutral atom the number of electrons = the number of protons. The arrangement of an atom's energy orbits depends on the number of protons and neutrons in the nucleus and the number of electrons orbiting the nucleus. Because every type of atoms has a unique arrangement of the energy orbits, they produce a unique pattern of absorption or emission lines. All atoms with the same number of protons in the nucleus are grouped together into something called an element. Because the atoms of an element have the same number of protons, they also have the same number of electrons and, therefore, the same chemical properties. For example, all atoms with one proton in the nucleus have the same chemical properties and are called Hydrogen. All atoms with two protons in the nucleus will not chemically react with any other atoms and are known as Helium. The atoms called Carbon form the basis of life and have six protons in the nucleus. Elements are sub-divided into sub-groups called isotopes based on the number of protons AND neutrons in the nucleus. All atoms of an element with the same number of neutrons in the nucleus are of the same type of isotope. An element's isotopes will have very nearly the same chemical properties but they can behave very differently in nuclear reactions. For example, all of the isotopes of the element Hydrogen have one electron orbiting the nucleus and behave the same way in chemistry reactions. The ordinary Hydrogen isotope has 0 neutrons + 1 proton while another Hydrogen isotope called Deuterium has 1 neutron + 1 proton and another Hydrogen isotope called Tritium has 2 neutrons + 1 proton in the nucleus. Tritium is radioactive---its nucleus spontaneously changes into another type of nucleus. Most atoms in nature are neutral, the negative charges exactly cancel the positive charges. But sometimes an atom has a hard collision with another atom or absorbs an energetic photon so that one or more electrons are knocked out of the atom. In some rare cases, an atom may temporarily hold onto an extra electron. In either case, the atom has an extra positive or negative charge and is called an ion. For example, the carbon ion C+ has 6 protons and 5 electrons and the iron ion Fe2+ has 26 protons and 24 electrons. Because the number of electrons are different, an ion of an element will behave differently in chemical reactions than its neutral cousins.
• #11: Electrons have only certain energies corresponding to particular distances from nucleus. As long as the electron is in one of those energy orbits, it will not lose or absorb any energy. The energy orbits are analogous to rungs on a ladder: electrons can be only on rungs of the ladder and not in between rungs. The orbits closer to the nucleus have lower energy. Atoms want to be in the lowest possible energy state called the ground state (all electrons as close to the nucleus as possible).
• #12: Let's see how Bohr's model of the atom explains the three types of spectra. An emission line is produced by an atom in a “excited” energy state---the electron is not in as low an energy orbit as possible. Remember rule #3! In order to go to a lower energy orbit, the electron must lose energy of a certain specific amount. The atom releases the energy is the form of a photon with that particular energy. The energy of photon = the difference in energy of the energy orbits (energy ladder rungs). Example: An atom with an electron at the E2 orbit and wants to get to the lower E1 energy orbit. It gives off a photon with energy E = h × f = E2 - E1. The electron may reach the ground state in one jump or it may temporarily stop at one or more energy levels on the way, but it canNOT stop somewhere between the energy levels. Different jumps produce photons of different energies. A larger jump to a lower energy level, will produce a photon with greater energy (smaller wavelength). The atom produces light of certain wavelengths. (Remember that light is both a photon and a wave!) The more atoms undergoing a particular transition, the more intense the emission line will be. The intensity depends on the density and temperature of the gas.
• #13: An absorption line is produced when a photon of just the right energy is absorbed by an atom, kicking an electron to a higher energy orbit. The photon had energy = the difference in energy of the energy orbits. Because the energy levels in an element's atoms are fixed, the size of the outward jumps made by the electrons are the same as the inward jumps. Therefore, the pattern of absorption lines is the same as the pattern of emission lines. Other photons moving through the gas with the wrong energy will pass right on by the atoms in the thin gas. They make up the rest of the continuous spectrum you see. Example: An atom with electron in the E1 orbit sees a photon with energy Ephoton = E2 - E1. The photon is absorbed and electron moves to E2. The photon is later re-emitted but in a random direction---not necessarily in the same direction as the original photon! An observer will see less photons from the direction of the continuous source at that specific frequency (color) than other frequencies (colors). Photons of other energies pass right on by without being absorbed. The atom can absorb photons of just the right energy to move an electron from one energy level to another level. The more atoms undergoing a particular absorption transition, the darker (or “stronger”) the absorption line. The strength of the absorption line depends on the density and temperature.
• #14: One important practical consequence of the interaction of electromagnetic radiation with matter and of the detailed composition of our atmosphere is that only light in certain wavelength regions can penetrate the atmosphere well. These regions are called atmospheric windows. The following figure shows the amount of absorption at different wavelengths in the atmosphere. It is presented in terms of the half-absorption altitude, which is defined to be the altitude in the atmosphere (measured from the Earth's surface) where 1/2 of the radiation of a given wavelength incident on the upper atmosphere has been absorbed. Windows correspond to those regions where the half-absorption altitude is very small. The dominant windows in the atmosphere are seen to be in the visible and radio frequency regions, while X-Rays and UV are seen to be very strongly absorbed and Gamma Rays and IR are somewhat less strongly absorbed. We see clearly the argument for getting above the atmosphere with detectors on space-borne platforms in order to observe at wavelengths other than the visible and RF regions. We shall discuss the importance of such observations in a later section.