Download Chapter 4

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. The two
scales in common use are the Fahrenheit and Celsius scales.
2. The freezing point of water is defined as 32°F or 0C, while the boiling point of water is
defined as 212°F or 100C.
3. The two scales are related by: TC = (5/9)  (TF − 32)
4. Neither scale (nor any other scale that defines its zero mark arbitrarily) has anything to do with
what temperature “is.” However, the Kelvin scale has its zero mark defined in a physical
meaningful way, as being the state of minimum atomic motion.
5. 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.
6. 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.
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. 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).
2. Frequency (f) is the number of repetitions per unit time. The units of frequency is given in
cycles/second or hertz (Hz).
3. The product of the frequency and wavelength of a wave equals the wave’s speed:  =   f.
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.
Advancing the Model: Measuring the Speed of Light
1. 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.
2. 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.
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 10−16 m.
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.
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).
3. According to Wien’s law: max (in nm) = 2,900,000 / T (in kelvin)
4. 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.
5. 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.
6. 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 and the 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.
4-6 The Bohr Model of the Atom
1. 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.
2. 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 move 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.
3. 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.
4. A photon is the smallest amount of electromagnetic energy of a particular wavelength.
5. 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.
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 EM 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.
4-7 The Doppler Effect
1. The Doppler effect is the observed change in wavelength of waves from a source moving
toward or away from the observer.
2. 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.
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. 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.
3.  =  − 0, where  is the observed wavelength of a line and 0 is its wavelength from a
stationary source.
4. 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.
Other Doppler Effect Measurements
1. The rotation rate of the Sun and the rotation rates of the planets and the rings of Saturn.
2. The motion of some binary stars.
3. Speeding cars by police radar.
4. The Earth’s motion around the Sun (from the annual variation in the Doppler shift observed in
stellar spectra).
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.