CHAPTER 4
Light and the Electromagnetic Spectrum
CHAPTER OUTLINE
4-1 The Kelvin Temperature Scale / Tools of Astronomy: Temperature Scales
1. We started measuring temperatures long before we understood what temperature is.
2. The two scales in common use are the Fahrenheit and Celsius scales. The freezing point of water is defined as 32°F or 0C, while the boiling point of water is defined as 212°F or 100C. The two scales are related by: TC = (5/9) (TF − 32)
3. The commonly used temperature scale in science is the Kelvin scale. The Kelvin scale has its zero mark defined in a physical meaningful way, as being the state of minimum atomic motion.
4. On the Kelvin scale, the “absolute zero” corresponds to the lowest possible temperature. The scale is related to the Celsius scale by: TK = TC + 273. Notice that temperature differences on the Kelvin and Celsius scales are the same.
5. Temperature is a fundamental quantity. It is a good approximation to say that given an object’s temperature we can calculate the average speed of each of its constituent particles, that is, temperature is a measure of their average kinetic energy.
6. Kinetic energy is an object’s energy due to motion. For an object of mass m and speed, its kinetic energy is equal to (1/2)m2.
4-2 The Wave Nature of Light
1. Our understanding of light changed many times over the years. Two lines of thought came to us from the ancient Greeks. Aristotle pictured light as an “aethereal” motion while others considered light as a stream of very small, fast-moving particles.
2. Newton theorized that light consists of tiny, fast-moving particles. He showed that color is a fundamental property of light and that a prism does not add color to light.
3. A spectrum is the order of colors or wavelengths produced when light is dispersed, as by a prism.
Characteristics of Wave Motion
1. Like acts as a wave.
2. The wavelength () of a wave is the distance from a point on the wave to the next corresponding point (e.g., from one crest to the next crest).
3. Frequency (f) is the number of repetitions per unit time. The units of frequency is given in cycles/second or hertz (Hz).
4. The product of the frequency and wavelength of a wave equals the wave’s speed: = f. This equation applies to all types of waves, including light and sound waves.
Light as a Wave
1. White light is made up of light of many wavelengths, all traveling at the same speed. The speed of light in vacuum (c) is about 300 million meters/second (3.00 108 m/s).
2. The approximate vacuum wavelength range of visible light is 380 nm (for violet) to 720 nm (for red). A nanometer (nm) is a unit of length = 10−9 m = 10 Angstrom (Å) (a non-SI unit).
3. The frequency of a 700 nm red light is f = 4.3 1014 Hz, while that of a 400 nm violet light is f = 7.5 1014 Hz.
4. The color we see is not a property of the light itself but a manifestation of the system that senses it, that is our eyes, nerves, and brain.
4-3 The Electromagnetic Spectrum
1. The electromagnetic spectrum is the entire array of electromagnetic waves and extends from long wavelength, low frequency radio waves to short wavelength, high frequency gamma rays.
2. The frequency range from radio waves to gamma rays is from below 102 to above 1024 Hz. The corresponding wavelength range is from above 106 m to below 10−16m.
3. Based on frequency or wavelength, the EM spectrum is usually broken into these regions: radio (AM/FM/microwave), infrared, visible, ultraviolet, X-rays, gamma rays.
4. These waves are called “electromagnetic” because they consist of combined, perpendicular, electric and magnetic fields that result when a charged particle accelerates.
5. Our atmosphere is transparent to visible light and to part of the radio spectrum, but most of the rest of the EM spectrum is blocked to some degree. Astronomers refer to windows in the Earth’s atmosphere (the visual and radio windows) that allow certain wavelengths to pass.
Advancing the Model: Measuring the Speed of Light
1. The first accurate measurement of c was made by the Danish astronomer Ole Roemer. Around 1675, he attributed the differences between the observed and anticipated times for eclipses of Jupiter’s moons to the time required for light to travel from Jupiter to Earth.
2. In 1849, physicist Armand Fizeau obtained a more accurate measurement in a laboratory using mirrors and rotating wheel.
3. The speed of light in vacuum is now defined to be c = 299,792.458 km/s. Light has a smaller speed when going through other transparent media.
4-4 The Colors of Planets and Stars
Color from Reflection—The Colors of Planets
1. Planets have their colors because the material on their surfaces or in their clouds absorbs some of the wavelengths of sunlight and reflects a combination of wavelengths that appear, for example, as the rusty red of Mars or the blue of Neptune.
Color as a Measure of Temperature
1. An intensity/wavelength graph (the thermal spectrum) of an object emitting electromagnetic radiation can be used to detect its temperature.
2. The peak of the intensity/wavelength curve (max) for a light-emitting object falls at a wavelength that depends upon the object’s surface temperature (T). This relationship isWien’s law: max (in nm) = 2,900,000 / T (in kelvin)
3. Wien’s law was derived from theoretical calculations in the late 19th century, when scientists studied ideal objects called blackbodies. A blackbody is a theoretical object that is a perfect absorber and emitter of radiation. The intensity/wavelength curve of a blackbody is called the blackbody curve. Almost all objects of interest in astronomy can be approximated as blackbodies.
4. Stefan (in 1879) and Boltzmann (in 1884) showed that the energy emitted per second and per square meter of the surface by an object of temperature T (in kelvin) is proportional to the fourth power of the temperature: energy flux T4.
5. The Stefan-Boltzmann law allows us to find the radius of a star, since from observations we can find the temperature and total energy emitted by the star each second.
4-5 Types of Spectra
Kirchhoff’s Laws
1. A continuous spectrum contains an entire range of wavelengths rather than separate, discrete wavelengths. The heated filament of a lamp andthe glowing piece of iron in the blacksmith’s forge are examples of a continuous spectrum.
2. In 1814 Fraunhofer analyzed the solar spectrum and found a number of dark lines across the continuous spectrum. It was later discovered that the dark lines are caused by absorption.
3. In the mid-1800s it was discovered that if gases are heated until they emit light, a spectrum made up of bright lines appears. It was also found that each chemical element has its own distinctive pattern of lines.
4. In the 1860s Kirchhoff formulated a set of rules that summarize how the three types of spectra are produced:
(a) A hot, dense glowing object (a solid or dense gas) emits a continuous spectrum.
(b) A hot, low-density gas emits light of only certain wavelengths—a bright line spectrum.
(c) When light having a continuous spectrum passes through a cool gas, dark lines appear in the continuous spectrum.
5. The connection between Kirhhoff’s laws and the nature of matter was not made until 1913, when Niels Bohr proposed a new model of the atom.
4-6 The Bohr Model of the Atom
1. Three postulates of the Bohr atom:
(a) Electrons in orbit around a nucleus can have only certain specific energies. (An electron is the negatively charged particle that orbits the nucleus—the central massive part—of an atom.)
(b) An electron can transit from one energy level to another changing the energy of the atom.
(c) The energy of a photon determines the frequency of light that is associated with the photon.
2. According to the Bohr model, light is emitted (and absorbed) in tiny bursts of electromagnetic energy called photons. When an electron moves from an outer to an inner orbit, light is emitted. When an electron moves from an inner to an outer orbit, light is absorbed.
3. A photon is the smallest amount of electromagnetic energy of a particular wavelength.
4. The equation that relates a photon’s energy (E) with its frequency (f) is: E = hf, where h is Planck’s constant.
Emission Spectra
1. The Bohr model of the atom can be used to explain why only certain wavelengths are seen in the spectrum emitted by a hot gas.
2. The ground state is the lowest energy state of an atom.Excited states are the energized states of an atom.
3. An emission spectrum (as from a heated, low-density gas) is made up of discrete wavelengths rather than a continuous band of wavelengths.
4. Emission spectra provide a valuable tool for identifying elements, since each has a unique spectral “fingerprint.”
Continuous and Absorption Spectra of the Stars
1. The photosphere (the visible surface of the Sun) emits a continuous spectrum, even though it is more like a gas than a solid. As atoms are pushed together, their energy levels are broadened and begin to overlap.
2. The Sun’s spectrum shows absorption lines because light must pass through the Sun’s relatively cooler atmosphere as well as the Earth’s atmosphere.
3. An absorption spectrum is a continuous spectrum except for certain discrete wavelengths; it is the dark line spectrum of Kirchhoff’s laws.
4. During a total solar eclipse the emission spectrum of the Sun’s atmosphere can be observed. This is the re-emitted light (sent out in all directions) that results after the cool gases in the Sun’s atmosphere have absorbed radiation.
5. Examination of the complex spectrum of a star can tell us what elements are in the star’s atmosphere.
Tools of Astronomy: The Balmer Series
1. The bright lines in the hydrogen spectrumbecome progressively closer as they approach the blue end of the spectrum.
2. The lines in the hydrogen spectrum are called Balmer series after Johann Jacob Balmer who found the mathematical relationship for them in 1885.
3. The Balmer series is easily explained by the Bohr model, since there is less difference between the energy levels as orbits get farther from the nucleus. The wavelengths correspond to the energy of photons that cause electrons to jump between the energy levels.
4. Hydrogen also has lines in the ultraviolet part of the spectrum, these are called the Lyman series. Another series in the infrared portion of the spectrum is called the Paschen series.
Advancing the Model: Evidence for the Wave-Particle Duality of Light
1. In the 1660s, Hooke proposed a simple wave theory in which light was the manifestation of fast oscillations in the aether. Newton favored the particle model for light, in which the particles induce oscillations in the aether; his preference of a particle model was based on misunderstandings about how waves behave.
2. Both the particle and wave models for light explained reflection and refraction of light.
3. Around 1801, Young showed using a simple experiment that light diffracts. The interference of light clearly showed its wave nature.
4. In the 1860s, Maxwell succeeded in unifying what was then known about electricity and magnetism. His model allowed the existence of waves that combine electromagnetic effects and move at a speed very close to the then known value for c. These are transverse waves, with the electric and magnetic fields perpendicular to each other and to the wave’s direction of propagation.
5. In 1888, Hertz produced radio waves in his lab, which confirmed all the properties of light known at the time.
6. In 1900, Max Planck discovered an equation that fit the blackbody curve. In an effort to understand its meaning, he was forced to accept that electromagnetic waves can only have discrete energy values that are integer multiples of a minimum value, called a quantum of energy.
7. In 1905, Einstein used the quantum idea to explain the photoelectric effect. Light was considered to be a stream of massless particles (photons).
8. In 1922, Compton provided evidence that light indeed shows its particle nature when it interacts with matter.
9. Light has a wave-particle duality. When it propagates through space, light can be described by a wave model (as shown by the double-slit experiment). When it interacts with matter, light can be described by a particle model (as shown by the photoelectric effect and the Compton effect).
4-7 The Doppler Effect
1. It is most well known as the change in pitch of sound waves when a speeding car or train blowing its horn passes by. In front of the moving source one hears higher frequency (shorter wavelength) sound. Behind the source one hears lower frequency (longer wavelength) sound.
2. The Doppler effect is the observed change in wavelength of waves from a source moving toward or away from the observer.
3. Even though the source of the waves is moving, the waves still travel at the same speed in all directions.
4. The wavelengths of the waves in front of the moving source are shorter than they would be if the source was stationary, and the wavelengths behind the moving source are longer.
5. The sound does indeed get louder as a siren approaches, but this is not what the Doppler effect is about.
6. If the source moves at a uniform speed, the frequency is observed to be higher than the source’s (but constant in value) as the source approaches and lower than the source’s (but constant in value) as it recedes.
The Doppler Effect in Astronomy
1. The Doppler effect is also applicable for EM waves.
2. Light from an object coming toward us has a wavelength shorter than normal. We say the light is blueshifted. (By “normal” we mean the wavelength as measured by someone traveling with the source.)
3. Light from an object moving away from us has a wavelength longer than normal. We say the light is redshifted.
4. Except for very distant galaxies, most redshifts or blueshifts caused by the Doppler effect are very small.
5. It is the spectral lines (usually the absorption lines) that make the Doppler effect a powerful tool.
The Doppler Effect as a Measurement Technique
1. The Doppler effect can be used not only to detect motion of a star toward or away from us but also to determine the star’s radial velocity relative to Earth.
2. Radial velocity is velocity along the line of sight, toward or away from the observer. Tangential velocity is velocity perpendicular to the line of sight. The Doppler effect allows us to measure only the radial component of an object’s velocity.
3. Measuring the amount of the shifting of stellar spectral lines () allows us to determine the radial velocity of the star relative to the Earth: / 0 = /c. This equation is valid for speeds much slower than c.
4. = − 0, where is the observed wavelength of a line and 0 is its wavelength from a stationary source.
Other Doppler Effect Measurements
1. The rotation rate of the Sun and the rotation rates of the planets and the rings of Saturn can be measured with the Doppler effect.
2. The motion in a binary star system, in which a pair of stars are gravitationally bound so that they orbit one another, can be measured with the Doppler shift as each star moves alternately toward and away from us.
3. The annual variation in the Doppler shift observed in stellar spectra provides evidence for the Earth’s motion around the Sun.
4. Police radar measures motorists’ speeds by bouncing waves from their cars and detecting the Doppler shift in the reflected waves
Relative or Real Speed?
1. The speed measured by the Doppler effect is the speed of the object relative to the speed of the Earth.
2. All speeds are relative to something. All motion (or non-motion) is relative, too.
3. The understanding of the relativity of motion is called Galilean relativity or Newtonian relativity. Einstein’s theory of relativity goes much further than this.
4-8 The Inverse Square Law of Radiation
1. According to the inverse square law of radiation, radiation spreading from a small source decreases in intensity as the inverse square of the distance from the source.
2. The force of gravity also follows an inverse square relationship with distance.