Light

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Light

• Waves
• Photons
• Atomic structure
• Line emission/absorption
• Doppler shift
• Temperature
• Luminosity
• Flux

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Waves

• Sounds waves have crests and troughs
• The pitch or tone of a sound is determined by how
  fast those crests and troughs arrive at your ear.
• Since sound travels at constant speed, how fast
  the crests and troughs arrive at your ear is
  inversely proportional to the distance between
  successive crests the wavelength.

Demo 3B22.30
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Waves

• Properties wavelength, frequency, speed

wavelength ? frequency speed
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Electromagnetic spectrum
The spectrum of a particular star is how much
light it produces at each wavelength.
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Photon energy

• From Einstein, we known that light comes in
  discrete packets called photons and the energy of
  each photon is set by its frequency

h Plancks constant 6.63?10-34 Js
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Photon energy
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Atoms
electron
nucleus
p
e-
n
proton
neutron
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The size of an Atom

• Although it is the smallest part of the atom,
  most of the atoms mass is contained in the
  nucleus.
• The electrons do not orbit the nucleus they
  are smeared out in a cloud which give the atom
  its size.

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Periodic Table of the Elements
atomic number protons (defines element)
atomic mass no. protons neutrons (defines
isotope)
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The particles in the nucleus determine the
element isotope.
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Electron Orbitals

• The number of electrons for a neutral atom is
  equal to the number of protons
• The chemical properties of an atom are determined
  by the configuration of electrons
• The position of each electron is indefinite and
  describes a smeared out probability distribution
  or orbital centered on the nucleus

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Electron orbits
From quantum mechanics, only certain orbits are
allowed. Each orbit has a specific energy.
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Bohr Model of the Hydrogen Atom
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How atoms emit light
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Spectral lines of hydrogen

• Energy difference of levels determines the
  photon energy.
• Only certain energies are possible the
  spectral lines of H.

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Rydberg formula for Hydrogen Lines
(1 A 0.1 nm)
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Spectral lines

• Each element (hydrogen, helium, neon, mercury,
  iron, ) has its own particular set of energy
  levels and its own set of spectral lines.
• Demonstration 7B10.10

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Uses of spectral lines

• Because each element has it own unique pattern of
  spectral lines, the spectral lines from stars can
  be used to determine the composition, or the
  relative number of atoms of each elements, of the
  stars

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Kirchhoffs Laws
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Absorption spectrum of a star
Demonstration 7B11.15
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Composition of a typical star
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Uses of spectral lines

• We can also use spectral lines to determine the
  velocity and rotation of a star via the Doppler
  effect.

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Doppler effect

• The buzzer makes a constant pitch
• When the buzzer is moving towards you, the waves
  get bunched up the pitch sounds higher.
• When the buzzer is moving away, the waves get
  spread out the pitch sounds lower.

Demo 3B40.10
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Doppler effect
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The Doppler Effect
?0 wavelength of line at rest ?obs observed
wavelength of line V velocity of object (
receding)
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Measuring Rotational Velocity
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Uses of spectral lines

• We can use the spectrum of an object to determine
  it temperature.

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Temperature
lower T
higher T

• Temperature is proportional to the average
  kinetic energy per molecule

k Boltzmann constant 1.38?10-23 J/K
8.62?10-5 eV/K
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Temperature vs. Heat
lower T
higher T

• Temperature is proportional to the average
  kinetic energy per molecule
• Heat (thermal energy) is proportional to the
  total kinetic energy in box

less heat
more heat
same T
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Wiens law

• Cooler objects produce radiation which peaks at
  lower energies longer wavelengths redder
  colors.
• Hotter objects produce radiation which peaks at
  higher energies shorter wavelengths bluer
  colors.
• Wavelength of peak radiation
• Wien Law ?max 2.9 x 106 / T(K) nm

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A objects color depends on its surface
temperature

• Wavelength of peak radiation
• Wien Law ?max 2.9 x 106 / T(K) nm

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Luminosity of a Black Body Radiator

• Stephan-Boltzmann Law an opaque object at a
  given temperature will radiate, per unit surface
  area, at a rate proportional to the surface
  temperature to the fourth power
• P/m2 ?T4
• ? Stephan-Boltzman constant
• 5.67?10-8 W/m2 K4
• T surface temperature
• P/m2 power radiated per square meter

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Luminosity of a Black Body Radiator

• For the spherical object, the total power
  radiated the total luminosity is
• L 4?R2?T4
• T temperature
• ? Stephan-Boltzman constant
• 5.67?10-8 W/m2 K4
• R radius

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Luminosity of a Black Body Radiator
Suppose the radius of the Sun increased by a
factor of 4 but the rate of power generated by
fusion remained the same, how would the surface
temperature of the Sun change?
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Flux and luminosity

• Luminosity - A star produces light the total
  amount of energy that a star puts out as light
  each second is called its Luminosity.
• Flux - If we have a light detector (eye, camera,
  telescope) we can measure the light produced by
  the star the total amount of energy intercepted
  by the detector divided by the area of the
  detector is called the Flux.

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Flux and luminosity

• To find the luminosity, we take a shell which
  completely encloses the star and measure all the
  light passing through the shell
• To find the flux, we take our detector at some
  particular distance from the star and measure the
  light passing only through the detector. How
  bright a star looks to us is determined by its
  flux, not its luminosity. Brightness Flux.

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Flux and luminosity

• Flux decreases as we get farther from the star
  like 1/distance2

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How your eye sees light and color
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Rods and cones on the retina sense light
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Rods and cones

• Cones are color sensors
• There are cones for red, green, and blue
• The color ones perceives depends on the firing
  rates of the red vs. green vs. blue cones
• Cones need relatively bright light to work
• Rods give finer, more detailed vision
• Rods can work with less light
• At night, color vision is less effective because
  only the rods function

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Sensitivity of cones
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A star will produce light overlapping the
response of all three cones. The color of the
star depends on how strong its spectrum is in the
ranges covered by the different cones.
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A star will produce light overlapping the
response of all three cones. The color of the
star depends on how strong its spectrum is in the
ranges covered by the different cones.
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A star will produce light overlapping the
response of all three cones. The color of the
star depends on how strong its spectrum is in the
ranges covered by the different cones.
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Review Questions

• What is the wavelength of the n 3 to n 2
  transition of Hydrogen?
• An emission line identified with the 468.6 nm
  line of He is found in an stars spectrum at
  481.0 nm. What is the speed and direction of
  motion of the star?
• We measure the surface temperature of a star to
  be 15,000 K and its luminosity to be 12 times
  that of the Sun. What is the stars radius in
  meters and in terms of solar radii?