pages 4-11 only
The Electromagnetic Spectrum Jan 2020 1 THE ELECTROMAGNETIC SPECTRUM OBJECTIVES This exercise will allow you to visualize the range of the electromagnetic spectrum so that you can appreciate the width of all its different parts. In addition you will also use an animation to see the differences between continuous, emission and absorption spectra. You will also view spectral lines produced in the lab and identify the wavelengths of emission lines formed by different elements. EQUIPMENT Ruler with centimeter markings, colored pencils. The last page of this lab shows spectra from 5 elements. Please DO NOT print page 13 (last page) as it will waste your printer’s ink! Simply view page 13 online when asked to make measurements. INTRODUCTION The electromagnetic spectrum is the entire range of electromagnetic waves which are divided into different regions named as radio, infrared, visible, ultraviolet, x-rays and gamma rays. While all these waves travel at the speed of light (3 x 108 m/s) they do not have the same wavelength or frequency. Recall that the equation relating speed (c), frequency (f) and wavelength (λ) is c = f λ. Hence if any two variables are known, the third can be calculated. Any one of the following equations can be used to find the unknown quantity: c = f λ f = c/λ λ = c/f c = 3 x 108 m/s When these equations are used, it is important to keep track of units. If speed c is measured in meters per second (m/s), frequency will be in Hertz (Hz) and wavelength will be in meters (m). For example, let’s calculate the wavelength of yellow light if its frequency is given as 5 x 1014 Hz. λ = c/f = (3 x 108 m/s) / (5 x 10 14 Hz ) = 6 x 10-7 m The answer above can also be written as 60 x 10-8 m or 600 x 10-9 m or 6000 x 10-10 m You should use a calculator to help you do these calculations efficiently. If you need assistance, please check with your instructor. There is a reason why we are introducing all these different exponents. It is inconvenient to keep saying “10-7” so prefixes (shortcut words for the exponents) have been developed. The prefix for 10-9 is nano abbreviated as n. Hence the wavelength of yellow light can be written as 600 nanometers or 600 nm. Jan 2020 2 Another term also used with electromagnetic wavelengths is the “Angstom” abbreviated as Å which is 10-10 m. Hence the wavelength of yellow light can also be written as 6000 Å. The list below summarizes commonly used metric prefixes, their names and abbreviations. 10-9 nano n 10-6 micro µ 10-3 milli m 10-2 centi c 103 kilo k 106 mega (million) M 109 giga (billion) G 1012 tera (trillion) T 10100 googol (Yes! That’s the source of the name “Google” that you are familiar with. Strictly speaking, this is not a metric unit, but a whimsical word given by mathematicians.) This lab will show another important property of electromagnetic waves, which is that the range of each of the regions (radio, ir, visible, uv, x-ray and gamma ray) is not equal. Also, some regions include many familiar terms that you may not connect to an astronomy course, so here is an opportunity to learn how this course affects your daily life! Spectroscopy is a very important tool for astronomers. Each chemical element has its own distinctive fingerprint or bar code revealed by its spectral lines. Chemical compounds made up of two or more elements will show lines from each element, and the width and brightness of spectral lines gives additional information about the chemical constituents of objects. Since light is the only information we get from the stars, it is through spectral analysis that astronomers have figured out everything we know about stars, like their temperature, mass, size, etc. When sunlight passes through a prism or a diffraction grating, it breaks up into its component colors, which is the familiar band called a “spectrum.” In the nineteenth century scientists learned to make many different types of spectra which were examined in great detail with spectroscopes, which are instruments consisting of a prism or grating Jan 2020 3 to produce the spectrum and a small telescope to enlarge the colored spectrum and see its details. Three different types of spectra are summarized below. 1. A continuous spectrum shows a continuous band of colors, red merging into yellow, green and blue. It is produced by a dense gas or a luminous solid. You can easily see a continuous spectrum if sunlight passing through a hanging crystal makes a “rainbow” on a wall, or if you hold up the shiny surface of a CD to a light source. 2. An emission spectrum consists of a series of brightly colored lines, and each element shows specific colors in specific positions. It is produced by a low density gas if it is heated sufficiently. These types of spectra are easy to produce in the lab by passing electricity at a high voltage through a discharge tube containing the gas. Scientists have made accurate photographs of these types of spectra, and the position of the colored lines has been measured very accurately and converted to give their wavelengths. 3. An absorption spectrum looks like a continuous spectrum, but it has dark lines on it. It is produced when a cool, low density gas is placed between the light source and the spectroscope. It is noticed that the location of the dark lines depends on the nature of the intervening gas. For example if the intervening gas is oxygen, the absorption spectrum will show dark lines in the same position showed by an emission spectrum of oxygen. To understand how spectra are produced, recall that each chemical element has its own number of protons, neutrons and electrons. The protons and neutrons are tightly bound in the tiny nucleus and do not contribute to forming spectra. It is the movement of electrons which produces spectra. The electrons in an atom are organized in different orbitals or shells and each orbital has its own energy level. The energy levels are also like rungs on a ladder, so an electron can be in level 1 or level 2, but not on level 1.5. The energy levels of electrons in atoms are said to be quantized, i.e. each level has a discrete value associated with it. Also, the energy increases the further away the electron lies from the nucleus, meaning that energy levels further away from the nucleus have a higher value. Just as it takes energy to climb a ladder from rung 2 to rung 4, an electron has to absorb energy to go from energy level 2 to energy level 4. Similarly, just as you decrease your potential energy if you climb down from rung 5 to rung 2, the electron decreases its energy if it moves from energy level 5 to energy level 2. The excess energy between level 5 and 2 will be emitted as a photon. A photon is a tiny packet of electromagnetic energy, or simply put a particle of light. The photon’s energy is related to its frequency by the equation E = hf and frequency f is related to wavelength by c= fλ Let’s first explain how an emission spectrum is produced. If oxygen gas is placed in a discharge tube and a high voltage is applied to the tube, the electrons in the gas will be energized and move to higher energy levels. But not wanting to stay there, they will move back to their original energy levels and emit the photons they had previously Jan 2020 4 absorbed. This produces an emission spectrum with many colored lines at specific positions. Each line’s position indicates its wavelength, which can be related to the frequency and the difference in the energy level of the electron. While an emission spectrum is produced by a gas at low density, a continuous spectrum is produced by a luminous solid or a dense gas which has millions more electrons that are available to make many millions of chaotic jumps. This will give rise to many millions of photons at different wavelengths. Think of the continuous spectrum containing all wavelengths compared to the emission spectrum which contains only specific wavelengths. If the light from a continuous spectrum passes through a cooler gas like oxygen, the oxygen atoms will absorb their preferred photons. The result will be a continuous spectrum deficient in certain photons, indicated by the dark lines. This is the absorption spectrum. It is noticed that absorption lines occur at the same wavelengths as emission lines since each indicates the presence or absence of photons with a specific energy and frequency. Measuring the positions of the dark lines indicates that the intervening gas was oxygen. PRE-LAB QUESTIONS 1. The speed of x-rays is a. Faster than light b. Slower than the speed of gamma rays c. Same as the speed of radio waves d. Same as the speed of seismic waves 2. Use the equation f = c/λ to calculate the frequency of radio waves whose wavelength is 50 m. a. 0.6 Hz b. 6 x 106 Hz c. 6 Megahertz d. Both b and c are correct 3. Use the equation λ = c/f to calculate the wavelength of ultraviolet light whose frequency is 2 x 1015 Hz. a. 1.5 x 107 m b. 1.5 x 10-7 Hz c. 1.5 nm d. 1.5 x 10-7 m Jan 2020 5 4. Which of the following units is the smallest? a. Millimeters b. Centimeters c. Nanometers d. Kilometers 5. The wavelength of blue light is 450 nm. This can be written as a. 450 x 10-9 m b. 4.5 x 10-7 m c. 4500 A d.