Chapter 5 The Nature of Light

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Chapter 5 The Nature of Light
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Guiding Ideas

• How fast does light travel (how is this
  measured)? c 300,00 km/s (in vacuum), Roemer
  1670 Jovian satellite timing over a year
• How does light behave like a wave? Interference
  effects
• How is the light from an ordinary light bulb
  different from the light emitted by a neon sign?
  Continuous vs. line radiation
• How can astronomers measure the surface
  temperatures of the Sun, stars, planets? Wiens
  Law
• What is a photon? Quantum nature of light, energy
  prop. to wavelength (duality of wave, particle
  picture)
• How can astronomers tell what distant celestial
  objects are made of? Spectral lines
  fingerprints of elements
• What are atoms made of? Structure of atoms (Bohr
  model)
• How does the structure of atoms explain what kind
  of light those atoms can emit or absorb? Bohr
  model of quantized electron orbits
• How can we tell if a star is approaching us or
  receding from us? Doppler effect

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Light travels through empty space incredibly
fast.

• Italian Galileo unsuccessfully attempted to
  measure the speed of light by asking an assistant
  on a distant hilltop to open a lantern the moment
  Galileo opened his lantern.

For hilltops separated by 10 km, time taken for
light is 30 microsec!
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Light travels through empty space at a speed of
300,00 km/s, called c

• In 1676, Danish astronomer Olaus Røemer
  discovered that the exact time of eclipses of
  Jupiters moons varied based on how near or far
  Jupiter was to Earth.
• This occurs because it takes varying amounts of
  time for light to travel the varying distance
  between Earth and Jupiter.

3108 km
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Light travels through empty space at a speed of
300,00 km/s, called c

• In 1850, Frenchmen Fizeau and Foucalt showed that
  light takes a short, but measurable, time to
  travel by bouncing it off a rotating mirror. The
  light returns to its source at a slightly
  different position because the mirror has moved
  during the time light was traveling a known
  distance.

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Light is electromagnetic radiation and is
characterized by its wavelength

• White light is composed of all colors which can
  be separated into a rainbow, or a spectrum, by
  passing the light through a prism.
• Visible light has a wavelength ranging from 400
  nm (blue) to 700 nm (red).

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Although Isaac Newton suggested that light was
made of tiny particles called PHOTONS 130 years
earlier, Thomas Young demonstrated in 1801 that
light has wave-like properties. He passed a beam
of light through two narrow slits which resulted
in a pattern of bright and dark bands on a
stream.
This is the pattern one would expect if light had
wave-like properties.
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Imagine water passing through two narrow openings
as shown below. As the water moves out, the
resulting waves alternatively cancel and
reinforce each other, much like what was observed
in Youngs Double Slit Experiment.
This is the pattern one would expect if light had
wave-like properties.
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Today, we understand that light has
characteristics of both particles and waves.
Light behaves according to the same equations
that govern electric and magnetic fields that
move at 300,000 km/s so light is also called
electromagnetic radiation.
Electromagnetic radiation consists of oscillating
electric and magnetic fields. The distance
between two successive wave crests is called the
wavelength and is designated by the letter l.
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Electromagnetic radiation is produced by stars at
a wide variety of wavelengths in addition to
visible light. Astronomers sometimes describe EM
radiation in terms of frequency, n, instead of
wavelength, l. The relationship is c l x
n Where c is the speed of light, 3 x 108 m/s
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A dense object emits electromagnetic radiation
according to its temperature.

• WIENS LAW The peak wavelength emitted is
  inversely proportional to the temperature.
• In other words, the higher the temperature, the
  shorter the wavelength (bluer) of the light
  emitted.

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BLACKBODY CURVES Each of these curves shows the
intensity of light emitted at every wavelength
for an idealized object (called a blackbody)
for several different temperatures. These are
called blackbody curves.
Note that for the objects at the highest
temperature, the maximum intensity is at the
shorter wavelengths and that the total amount of
energy emitted is greatest.
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Astronomers most often use the Kelvin or Celsius
temperature scales.
In the Kelvin scale, the 0 K point is the
temperature at which there is essentially no
atomic motion is called absolute zero. In the
Celsius scale, this point is 273º C and on the
Fahrenheit scale, this point is -460ºF.
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Wiens law and the Stefan-Boltzmann law are
useful tools for analyzing glowing objects like
stars

• Wiens law relates wavelength of maximum emission
  for a particular temperature
• lmax 0.0029 Tkelvins
• Stefan-Boltzmann law relates a stars energy
  output, called ENERGY FLUX, to its temperature
• ENERGY FLUX sT4
• ENERGY FLUX is measured in joules per square
  meter of a surface per second and s 5.67 X 10-8
  W m-2 K-4..

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A few other useful relationships

• Wiens law relates wavelength of maximum emission
  for a particular temperature.
• lmax 0.0029 Tkelvins
• Stefan-Boltzmann law relates a stars energy
  output, called ENERGY FLUX, to its temperature.
• ENERGY FLUX sT4
• ENERGY FLUX is measured in joules per square
  meter of a surface per second and s 5.67 X 10-8
  W m-2 K-4
• Energy of a photon (in terms of wavelength)
• E h c / l where h 6.625 X 10-34 J s
• or where h 4.135 X 10-15 cV s
• Energy of a photon (in terms of frequency)
• E h n where n is the frequency of light
• These two relationships are called Plancks law.

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Each chemical element produces its own unique set
of spectral lines.
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The brightness of spectral lines depend on
conditions in the spectrums source.
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The brightness of spectral lines depend on
conditions in the spectrums source.

• Law 1 A hot opaque body, such as a perfect
  blackbody, or a hot, dense gas produces a
  continuous spectrum -- a complete rainbow of
  colors with without any specific spectral lines.
  (This is a black body spectrum.)

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The brightness of spectral lines depend on
conditions in the spectrums source.

• Law 2 A hot, transparent gas produces an
  emission line spectrum - a series of bright
  spectral lines against a dark background.

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The brightness of spectral lines depend on
conditions in the spectrums source.

• Law 3 A cool, transparent gas in front of a
  source of a continuous spectrum produces an
  absorption line spectrum - a series of dark
  spectral lines among the colors of the continuous
  spectrum.

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Kirchhoffs Laws
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Features of the Suns spectrum created by passing
sunlight through a prism.
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Emission Line Spectra of A Few Common Elements
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The Electromagnetic Spectrum
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Electromagnetic Radiation Radio Waves (TV, ?
1m)
Antenna size 1m
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But, where does light actually come from?

• Light comes from the movement of electrons in
  atoms.

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Rutherfords Experiment (1915) Showed that Atoms
Are Largely Empty Space!
Alpha particles from a radioactive source are
channeled through a very thin sheet of gold foil.
Most pass through showing that atoms are mostly
empty space, but a few are rejected showing the
tiny nucleus is very massive.
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An atom consists of a small, dense nucleus
surrounded by electrons (Note Nucleus actually
much smaller)
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An atom consists of a small, dense nucleus
surrounded by electrons.

• The nucleus contains protons and neutrons
• All atoms with the same number of protons have
  the same name (called an element).
• Atoms with varying numbers of neutrons are called
  isotopes.

• Atoms with a varying numbers of electrons are
  called ions.

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Orbits of electrons
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Spectral lines are produced when an electron
jumps from one energy level to another within an
atom.
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Bohrs formula for hydrogen wavelengths

• 1/l R x 1/N2 1/n2
• N number of inner orbit
• n number of outer orbit
• R Rydberg constant (1.097 X 107 m-1)
• l wavelength of emitted or absorbed photon

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The wavelength of a spectral line is affected by
the relative motion between the source and the
observer.
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Doppler Effect Caused by Motion
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Doppler Shift

• Red Shift The distance between the observer and
  the source is increasing.
• Blue Shift The distance between the observer and
  the source is decreasing.
• Dl wavelength shift, Df frequency shift
• lo wavelength if source is not moving
• v velocity of source
• c speed of light

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Doppler Shift Example

• A spacecraft on its way to Mars transmits a
  signal at 100 MHz (1 MHz 106 Hz). It is
  received on Earth at 99.99 MHz. How fast is the
  spacecraft moving and in which direction?

Since observed frequency is lower, the spacecraft
is moving away from Earth.
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Chap 5 Key Ideas

• How fast does light travel (how is this
  measured)? c 300,00 km/s (in vacuum), Roemer
  1670 Jovian satellite timing over a year
• How does light behave like a wave? Interference
  effects
• How is the light from an ordinary light bulb
  different from the light emitted by a neon sign?
  Continuous vs. line radiation
• How can astronomers measure the surface
  temperatures of the Sun, stars, planets? Wiens
  Law
• What is a photon? Quantum nature of light, energy
  prop. to wavelength (duality of wave, particle
  picture)
• How can astronomers tell what distant celestial
  objects are made of? Spectral lines
  fingerprints of elements
• What are atoms made of? Structure of atoms (Bohr
  model)
• How does the structure of atoms explain what kind
  of light those atoms can emit or absorb? Bohr
  model of quantized electron orbits
• How can we tell if a star is approaching us or
  receding from us? Doppler effect

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PRS Quiz Nature of light and Spectra

• List the emission of red, green, and blue light
  in order of increasing wavelength
• Blue,green, red
• Red, green, blue
• Blue,red, green
• Green, red, blue
• Xrays travel at what speed? (c is the speed of
  light)
• Faster than c
• Slower than c
• At exactly c
• Depends on the energy of the x-ray
• The temperature of this room is closest to
• 290K
• 25K
• 273.1K
• 70K

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• A dilute hot gas (such as a neon beer sign) emits
• Emission line spectrum
• Absorption line spectrum
• Continuous spectrum
• Absorption lines superimposed on continuous
  spectrum
• Jupiter has a surface temperature of 120K and a
  blackbody spectrum which peaks at a wavelength of
  30 microns. Plutos blackbody spectrum peaks at
  60 microns. What is its surface temperature?
• 30K
• 60K
• 120K
• 240K
• The Doppler effect is a change of wavelength
  caused by
• Gravitational fields between emitter and observer
• Dilute hot gases in the path of the light
• Magnetic fields near the emitter
• Relative motion of the source or observer