2.1 Electromagnetic Radiation
2.2 Spectra
2.3 Optical Telescopes
2.4 Special Theory of Relativity
Reading: Zeilik, chapter 5
At the beginning of Zeilik's chapter 5 is a quotation by the nineteenth-century French philosopher, August Comte (pronounced something like kohmpt, except that, in French, the vowel is nasalized and the m and p aren't really heard). Comte was trying to come up with an example of something that people would never be able to figure out, no matter how clever or technologically advanced they were. He decided that one thing we would never know is the chemical composition of the stars. After all, the stars are so far away that we could never travel to a star and sample it!
Just four years after Comte died, scientists did figure out how to determine the chemical composition of the stars—without having to travel to outer space. The way astronomers learn not only the chemical makeup of the stars but also many of their other properties is by analyzing the light, or electromagnetic radiation, we receive from the stars.
Electromagnetic radiation includes all types of light, both visible light that you can detect with your eyes and various types of radiation that can be detected with certain types of equipment, but are invisible to your eyes. Light has some interesting properties. One is that it can be thought of as being made up either of waves or particles. (The particles are called photons—not to be confused with protons, which we'll discuss later). Experiments can be done to show that light definitely has wave-like properties. Other experiments demonstrate the particle-like properties of light. However, no experiment will show light as being both a particle and a wave at the same time. The details of the "wave-particle duality" of light are beyond the scope of this course. For now, this fact can be taken as truth. For further information, you may want to take a graduate physics course in quantum mechanics. :)
If we think of light as a wave, then, like any wave, it will have a particular wavelength, usually symbolized by the Greek letter lambda, l. See figure 1-16.
Figure 1-16
Note: To view this graphic, the Shockwave plug-in must be installed on your computer. Test to see if the plug-in is installed.
The wavelength is the distance between two successive crests of the wave. As the wave moves, the number of wave crests or wavelengths that pass by a given point each second is the frequency, f, of the wave. The wavelength times the frequency is equal to the speed of the waves, which we can conveniently abbreviate:
f ´ l = speed of waves
Wavelength is measured in units of distance, for example, meters per wavelength. Frequency is measured in wavelengths per second. When you multiply these two, the result will be in meters per second, which, as expected, are units of speed. In empty space (a vacuum), the speed of all electromagnetic radiation, including visible light, is the same. It's symbolized by c, and has the value:
c = 3 ´ 108 m/s.
So, for light, f ´ l = c. Remember, c is a constant. So, the higher the frequency, the shorter the wavelength, and the lower the frequency, the longer the wavelength. That is, frequency and wavelength are inversely proportional.
Here is a list of different kinds of electromagnetic radiation, in order from lowest frequency to highest frequency:
This sequence of types of electromagnetic radiation is sometimes called the electromagnetic spectrum. These various types of radiation are really all the same kind of waves; they just have different wavelengths (and frequencies). Therefore, from now on, the generic term light will be used to refer to electromagnetic radiation in general, not necessarily just visible light that you can detect with your eyes.
Unless you're colorblind, you can distinguish different wavelengths of visible light by their color. The rainbow of colors is also in order from longest wavelength to shortest.
It takes some energy to create a light wave, and as the light wave travels, it carries energy with it. The higher the frequency, the more energy is in the light wave. For example, x-rays carry more energy than visible light. To be precise, the energy in a light wave, E, is equal to a number, symbolized by h, multiplied by the frequency, f. We can conveniently abbreviate this:
E = h ´ f
The value of E must be expressed in units of energy (of which there are several). One unit of energy is the erg. This is a rather small amount of energy. If a fly lands on the wall, it imparts about 1 erg of energy to the wall. Another unit of energy is the joule (pronounced jool). A joule is a more substantial amount of energy: 1 joule = 10,000,000 ergs. You're probably familiar with a unit of power called a watt. A watt is a unit of power (rate of energy use) equal to 1 joule per second. So, a 100-watt light bulb uses 100 joules of energy each second.
The quantity h is a constant (the value of which you aren't required to know for this course). The value of h is such that, when it is substituted into the equation E = h ´ f, E will come out in the correct units.
If you combine all wavelengths (or colors) of visible light, to your eyes it will appear white. That's just the way our brain interprets the simultaneous activation of the different color light receptors in our eyes. You can separate out the various wavelengths (or colors) in white light by sending the light through a prism, as was first shown by Isaac Newton. See figure 1-18.
It works best to first have the light go through a narrow slit, then through a prism, and to have the light coming out of the prism land on a white screen. The shorter wavelengths refract (or bend) in the prism more than longer wavelengths. The result is that the different colors are spread out on the screen, creating a rainbow of colors. When a prism spreads white light out, the resulting sequence of colors visible on the screen is called a spectrum (plural spectra). If all the wavelengths are present, it's called a continuous spectrum. A continuous spectrum shows all the colors of visible light.
There's another way of separating out the different wavelengths of visible light, and that is to use a diffraction grating. A diffraction grating is just a piece of glass or plastic with thousands of microscopic grooves etched into it. This has the same effect as a prism, that is, spreading out the light in order of wavelength. If you bought a new copy of the textbook, it should have come with a piece of diffraction grating in the inside back cover. Try holding it up to your eye and looking at various kinds of lights through it. But don't look at the sun through it! (Looking directly at the sun can cause permanent damage to your eyes.)
Thus far we have described some of the properties of light. To understand how scientists use information from light, it is important to know how light is produced. Light is emitted when charged particles, such as electrons, are accelerated. Since electrons are found in atoms, we'll now need to review a few things about atoms.
The visible spectra observed from stars, or from clouds of gas in space, are not continuous spectra. To understand how these other spectra are created we first need to examine the structure and behavior of atoms, for it is ultimately from atoms, or subatomic particles, such as electrons, that light is emitted.
Each atom contains a nucleus having one or more protons and perhaps some neutrons as well. Any electrons that the atom might have surround the nucleus at varying distances. Atoms are often drawn as though the electrons are in circular orbits around the nucleus, like the orbits of the planets.
This diagram is not exactly the way atoms really are, but it's good for describing various properties of atoms.
Protons have a positive electric charge. Electrons have a negative electric charge. Neutrons have neither a positive nor a negative charge; they are electrically neutral. When an atom has the same number of protons and electrons, it has no net electric charge; it is neutral.
The simplest atom is hydrogen. Its nucleus consists of only one proton. A hydrogen atom also has one electron. It is the number of protons in an atom that determines what chemical element it is. With one proton, it's hydrogen; two protons, helium; three protons, lithium; and so on.
If you have two atoms with the same number of protons, but different numbers of neutrons, then you have two different isotopes of the same chemical element. The one with more neutrons will have a greater mass (heavier weight) than the other one. For example, there's an isotope of hydrogen, called deuterium, which has one neutron in its nucleus. This makes it heavier than normal hydrogen, which has no neutrons.
These two isotopes of hydrogen (normal hydrogen and deuterium, respectively) are denoted by 1H and 2H, where the superscript indicates the atomic mass. (Note that the superscript indicating the atomic mass is placed on the left instead of the right to avoid confusion with mathematical exponents.) The atomic mass is the number of particles in the nucleus (protons plus neutrons).
Normal helium (4He) has two protons and two neutrons in its nucleus. But there's a lighter isotope of helium, 3He, that has one less neutron. We'll discuss 4He and 3He further when we talk about the nuclear reactions that produce energy inside the sun.
Most atoms on our planet are neutral. That is, they have the same number of electrons as protons. If you remove one or more electrons from an atom, you've created an ion that's not electrically neutral. It has a net positive charge because you've removed negatively charged electrons. The process of creating an ion is called ionization.
The electrons in an atom can be in any of a number of "orbits" or energy levels. These energy levels represent the only levels where an electron can exist in an atom. It's sort of like tossing a beanbag up onto a staircase. The beanbag can land on one step or another, but never between steps. The idea that the electrons could be only in discrete, or quantized, energy levels was a radical idea when first proposed about a century ago. But it was necessary to explain the observed spectra, and the idea turned out to be correct.
To get an electron to go up to a higher energy level, you must add a specific amount of energy to the atom. When an atom has an electron in one of the higher energy levels, the atom has more energy than usual and is said to be in an excited state.
There are two ways of exciting an atom, that is, two ways of giving it just the right amount of energy for the electron to move up to a higher energy level.
One situation in which atoms can become excited by the first of the above methods (i.e., by absorption of a photon) occurs when white light (containing all wavelengths) passes through a cool gas. In this case, the atoms in the gas will absorb certain wavelengths (those with precisely the right amount of energy to excite the atoms).
After the light goes through the cool gas, you can send it through a prism and look at the spectrum. See figure 1-21. Most of the colors will be there, except for some dark lines at the wavelengths that were absorbed by the atoms. This type of spectrum is called an absorption spectrum.
The wavelength of the photon absorbed during the transition between two energy levels is unique. It's different from the wavelength of the photon emitted during the transition between any other two energy levels. That's because the amount of energy between levels is different for every pair of energy levels.
Furthermore, the amount of energy between two energy levels is different for different chemical elements. So, while the transition from the third energy level to the second energy level will result in the emission of a photon with a particular wavelength, that wavelength will be different for hydrogen compared to helium.
In short, if you know the wavelength of a photon emitted by an atom, you can tell both the energy levels that the electron jumped between as well as what kind of atom (that is, what chemical element) emitted the light.
Stars produce absorption spectra. This is because the interior is hot and dense, and therefore emits light of all wavelengths. But then that light has to travel through the cooler, outer layers of the star. While moving through this cooler gas, certain wavelengths will be absorbed, and you will observe an absorption spectrum. From the wavelengths of the absorption lines in the spectrum, you can determine which chemical elements emitted the light. Thus, the absorption spectrum from a star is like a fingerprint, identifying the chemical composition of the star.
The analysis of spectra was a tremendous leap forward in astronomy. As we shall see, spectra can be used not only to determine the composition of stars, they can also be used to determine many other properties of the stars, including the stars' temperatures and velocities.
Suppose you have an excited atom, i.e., an atom with an electron in one of the higher energy levels. If you leave the atom alone, sooner or later the electron will jump back down to a lower energy level. When that occurs, a photon will be emitted, carrying away exactly the same amount of energy as was absorbed earlier to make the atom excited in the first place.
In other words, the wavelengths that were initially absorbed are the same wavelengths that get emitted. This is true because the same amount of energy that is absorbed when an atom gets excited is released when the electron jumps back down. Since the energies are the same, the wavelengths (and colors) will be the same.
If the atom is in, say, the fourth energy level, it could get back down to the lowest energy level via any of the intervening energy levels. One way would be for it to jump down from the fourth energy level to the third, then from the second, and finally from the second to lowest energy level (the ground state). Alternatively, the electron could skip levels, and, for example, jump from the fourth energy level directly down to the ground state. The electron could also jump from the fourth energy level to the third level and from there directly to the ground state, and so forth.
Each time the electron makes a transition from one energy level to a lower level, a photon is emitted. So, if the electron goes from the fourth energy level to the ground level in three jumps, the atom will emit three photons. The sum of the energies of these photons will equal the energy that was needed to get the electron up to the fourth energy level in the first place.
If you look at the spectrum of light from a cloud of hot glowing gas, instead of seeing all wavelengths of light like a continuous spectrum, you'll see only lines of certain colors. See figure 1-23. Those are the wavelengths that were emitted by the various electron transitions between energy levels. This spectrum is called an emission (or bright-line) spectrum.
As with the absorption spectrum, the wavelengths of the emission lines are unique to the particular chemical element and to the particular pair of energy levels within the atom. So, the emission spectrum can be used to unambiguously identify the chemical composition of the glowing gas.
When do you know when you'll get each type of spectrum? A German physicist, Gustav Kirchhoff, formulated three rules of spectroscopic analysis based on experimentation with spectra. The three rules, describing when you will get each kind of spectrum, are as follows:
Reading: Zeilik, chapter 6
Astronomers observe astronomical objects to learn about them and to test hypotheses. The key tools in making these observations are telescopes.
We aren't certain who invented the telescope. It's often credited to Hans Lippershey, a Dutch optician who had one in 1608, although it seems that Zacharias Janssen, another Dutch optician, made one in 1604. You can read about this discussion at http://nebula.honors.unr.edu/~fenimore/wt202/apple, "Who Really Invented the Telescope?" by University of Nevada–Reno honors student Jessica Apple. For a somewhat more enhanced history of the telescope, you might visit http://es.rice.edu:80/ES/humsoc/Galileo/Things/telescope.html, "The Telescope Web site," from Rice University; and http://www-isds.jpl.nasa.gov/cwo/cwo_54ga/html/cd/telescop.htm, "History of the Telescope," from NASA's JPL Information Systems Development Support Web site.
Telescopes that are used with visible light are called optical telescopes. There are two main types of optical telescopes—reflecting telescopes and refracting telescopes.
A refracting telescope, or refractor, the first kind of telescope invented, uses a large lens—the objective lens, or simply, the objective—to collect and focus the light.
Parallel rays of light passing through the objective lens will converge to a focus, then go out the back of the telescope either into an eyepiece, camera, or some other type of detector. An eyepiece is a small lens that straightens out the diverging light rays so you can view the image with your eye.
The distance between a lens and the focal point is the focal length of the lens. The objective lens has a long focal length, and the eyepiece has a short focal length. This combination of focal lengths results in the telescope magnifying the image, making it possible to see smaller or fainter objects.
Instead of a lens, a reflecting telescope, or reflector (invented by Isaac Newton in the 1660s), uses a large mirror to collect and focus the light. This is considered the objective. One type of reflector is the Newtonian reflector, in which the converging light rays are deflected out the side of the telescope tube where you can place an eyepiece.
Another type of reflector, the Cassegrain reflector, also uses a large mirror to collect and focus the light. In this case, however, a smaller, secondary mirror reflects the converging light rays again. The light then goes back down the telescope and out a small hole in the back of the telescope where you can attach an eyepiece or some more sensitive detector, such as a photometer (which precisely measures very small changes in brightness) or a spectrometer (which records a spectrum).
One problem with some refractors is that different wavelengths of light refract at slightly different angles. This causes a small amount of color separation in the image. Reflectors don't have this problem because all wavelengths of light reflect at the same angles.
For a large telescope, a reflector is less expensive than a refractor. One reason for this is that the large lens in a refractor must be made of very high quality glass so that light passing through it isn't affected by imperfections in the glass. Imperfections in the glass out of which the large mirror of a refractor is made are not so serious. This is so because only the surface of the mirror is used, and as long as that is smooth and the right shape, the telescope should work perfectly well.
It's difficult to make a very large refracting telescope. This is because it's necessary to support the objective lens only by the edges, as light has to pass through the center of it. The largest refracting telescope in the world has a 40-inch objective.
The ability to see faint stars, and large numbers of stars, is determined by the light-gathering power of a telescope. The area of the objective determines the light-gathering power of a telescope. The area of a circle (and the light-gathering power of a circular objective) is proportional to the square of the diameter. The lens in one of your eyes is about 1/3 inch in diameter. Using your eyes, you can see about 6,000 stars. But if, instead, you use a telescope with a 5-inch diameter objective, you can then see half a million stars! So, having a large telescope can make a big difference in what you can see.
The ability to see fine detail (for instance, to distinguish two stars that are extremely close together) is called resolving power, and is proportional to l/d, where l is the wavelength of the light and d is the diameter of the objective. The smaller l/d, is, the better the resolving power. However, for any telescope on the ground, the actual resolving power is limited by the atmosphere to about one second of arc, i.e., the apparent size of dime viewed from a distance of two miles. This limitation is a result of turbulence in the earth's atmosphere that blurs any light coming though.
The magnification of a telescope is equal to the focal length of the objective divided by the focal length of the eyepiece. So, you can change the magnification of a telescope simply by changing eyepieces.
Interestingly, professional astronomers very rarely look through a large telescope these days. This is because there are now a variety of detectors that are more sensitive than the human eye. If you want to see what a typical mountaintop observatory site looks like, visit http://www.ifa.hawaii.edu/mko/, "Mauna Kea Observatories" from the University of Hawaii Institute for Astronomy (IfA).
We can learn a great deal about astronomical objects by analyzing the non-visible radiation that they emit. Consequently, scientists have built detectors specifically for other types of radiation, for instance, ultraviolet (UV), x-rays, infrared (IR).
However, not all parts of the electromagnetic spectrum can get through the earth's atmosphere and make it to the ground. In fact, the only two kinds of electromagnetic radiation than can easily make it to the ground are visible light and radio waves. (Although a little UV radiation gets through the atmosphere—enough to give you a sunburn or skin cancer—most of it is blocked by the ozone layer.) The regions of the electromagnetic spectrum to which the atmosphere is transparent are sometimes referred to as spectral windows, through which we can detect radiation from astronomical objects. To detect other types of radiation, you have to get your telescope above the atmosphere.
The reason that certain parts of the electromagnetic spectrum cannot get through the earth's atmosphere is that various gases in the atmosphere absorb those wavelengths of light. You may already know that ozone (O3) blocks a lot of the ultraviolet radiation coming through the atmosphere. The ozone also absorbs x-rays and gamma rays. Water vapor (H2O) and oxygen (O2) absorb microwaves, and water vapor and carbon dioxide (CO2) absorb a lot of infrared radiation.
One problem with radio telescopes is that, as a result of the long wavelength of radio waves, the resolving power will be mediocre. In other words, the quantity l/d is too large. To compensate for the long wavelength, the diameter of the telescope is made very large. That helps get l/d down to a reasonable range.
Another way to get better resolving power is to use two or more radio telescopes as an interferometer. This is an arrangement whereby the signals from the radio telescopes are combined in such a way that they interfere with each other in such a way that causes the waves to either reinforce each other (causing constructive interference) or cancel each other out (causing destructive interference). The resulting combined signal contains information about details that wouldn't be visible with one of the radio telescopes alone.
It's not necessary to have the radio telescopes in an interferometer physically joined together. They can operate independently, with the signal from each one being stored in a computer. The data from the telescopes can then be combined and analyzed in a computer. The fact that the radio telescopes in an interferometer don't have to be connected allows us to have the radio telescopes on opposite sides of a continent. This arrangement is called Very Long Baseline Interferometry (VLBI).
Making observations of radio waves is very useful if the object(s) you're trying to observe are obscured by intervening dust. Indeed, there's a lot of dust in the Milky Way. When astronomers first mapped out the spiral structure of the Milky Way galaxy, they did it by using radio waves rather than visible light.
Infrared radiation is useful if you want to observe moderately warm objects such as planets. Telescopes located on the earth's mountaintops can observe a little infrared radiation, but the best infrared observations are made from above the atmosphere, using a telescope in space.
Having a telescope in space is desirable for several reasons. You can observe parts of the electromagnetic spectrum that cannot reach the ground. You'll also have better resolving power than with a telescope on the ground. Note however, that a telescope in space doesn't get you significantly closer to the stars and planets. For example, the Hubble space telescope is in an orbit very close to the earth.
The Hubble space telescope was a giant leap forward in observational astronomy. Pictures of astronomical objects could be obtained with details 1/10 the size of the finest detail on any previous visible-light images, and spectra could be obtained from some of those fine details. You can see some of the fabulous photos from the Hubble Space Telescope at http://oposite.stsci.edu/pubinfo/pictures.html, "Hubble Space Telescope Pictures," from the Space Telescope Science Institute.
Some of the most important problems that astronomers hope to tackle with the Hubble space telescope are questions of cosmology—the study of the large-scale structure and evolution of the universe as a whole. In the early part of the twentieth century, an astronomer named Edwin Hubble worked on some of these cosmological problems. It was for him that the Hubble Space Telescope was named.
In 1905, Albert Einstein published a modification of Newton's laws known as the special theory of relativity. It was "special" in the sense of being restricted—in this case, restricted to uniform motion, that is, no acceleration. Einstein later (in 1916) published the general theory of relativity, which deals with accelerations and gravity.
For low velocities, as we encounter in day-to-day life, the special theory of relativity gives essentially the same results as Newton's laws. Only in extreme conditions—velocities approaching the speed of light—does the deviation from Newton's laws become significant.
The special theory of relativity is based on two postulates:
The first of these postulates tells you that any experiment you perform will have the same results regardless of whether you are standing still or performing the experiment in an airplane moving at a constant velocity of 500 miles per hour. The postulate also implies that if you're in a closed room (no windows or other contact with the outside) such as an elevator or a bathroom on an airplane, there is no experiment you could do to determine your speed.
The second postulate is rather strange, because it implies that light behaves differently from ordinary objects like baseballs. If a baseball pitcher can throw a ball with a speed of 80 mi/hr, and throws it from a vehicle moving 40 mi/hr, the ball can end up with a speed of 120 mi/hr. But according to the second postulate, that wouldn't happen with light. Light will always be measured to have the same speed, regardless of the motion of the source of the light or the observer.
These two postulates have some very interesting consequences. One is that no object can be accelerated to, or beyond, the speed of light. The reason is that at very high (relativistic) speeds, an object's mass increases, which means that it will require more force, and more energy, to accelerate it further. It would require an infinite amount of energy to accelerate an object to the speed of light. That's why it could never happen.
Another consequence of special relativity is that, when clocks move fast, especially at relativistic speeds, they slow down. This phenomenon has been experimentally verified. Furthermore, this is true of all kinds of clocks, including biological clocks. So, if you were to take a journey into space at relativistic speeds, and then return to the earth, you would find when you got back that you did not age as much as everyone else who stayed here.
A further result of special relativity is Einstein's famous equation, E = mc2. This equation tells how much energy, E, you'd get if you converted some mass, m, completely into energy. Recall that the value of c, the speed of light, is 3 ´ 108 m/s. The equation also tells how much mass you would get if you converted some energy into mass. Places where mass actually gets converted into energy include nuclear power plants, atomic bombs, and the sun's core.
Here's an example of how this equation works:
Suppose you had two kilograms (2 kg) of mass that you were going to convert completely into energy. How much energy would you get? To find out, you would start with E = mc2, and substitute 2 kg for m and 3 ´ 108 m/s for c:
E = mc2
E = (2 kg)(3 ´ 108 m/s)2
Square the speed of light:
E = (2 kg)(9 ´ 1016 m2/s2)
Multiply the two quantities:
E = 18 ´ 1016 kg-m2/s2
Notice that we've kept track of all the units, and ended up with units of kg-m2/s2. What does kg-m2/s2 mean? It means joules! So, the amount of energy you get by converting 2 kg of mass completely into energy is 18 ´ 1016 joules (or 1.8 ´ 1017 joules).
But, just how much energy is that? Is it a lot? To find out, let's see for how long that much energy could keep a 100-watt light bulb shining. Divide that amount of energy (18 ´ 1016 joules) by the rate at which a 100-watt light bulb uses energy (100 joules/sec):
(18 ´ 1016 joules)/(100 joules/sec) = 18 ´ 1014 sec
But how long is 18 ´ 1014 sec? To find out, let's divide it by the number of seconds in a year, 3 ´ 107 sec/yr:
(18 ´ 1014 sec)/(3 ´ 107 sec/yr) = 6 ´ 107 yr
So, if you convert 2 kg of mass completely into energy, it will be enough energy to keep a 100-watt light bulb shining for 6 ´ 107 yr, or 60 million years! That's a lot of energy! The fact that, when you convert mass into energy, you can get out an enormous amount of energy is one reason why nuclear power plants can produce lots of energy at competitive prices.
Report broken links or any other problems on this page
to course-admin@info.umuc.edu.
Be sure to include the name of the course and module in your e-mail.
Copyright © by University of Maryland
University College.