1446 Introductory Astronomy II

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1446 Introductory Astronomy II

• Chapter 4
• Radiation, Spectra the Doppler Effect
• R. S. Rubins
  Fall, 2009

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Thermal Radiation 1

• Every object in the universe emits EM radiation,
  and also absorbs EM radiation from its
  surroundings.
• A blackbody is an object which absorbs all the EM
  radiation falling on it.
• An ideal blackbody is a cavity with a small
  aperture.
• A black material, such as soot, is a perfect
  absorber in the visible region, but necessarily
  at other wavelengths.
• An object at a constant temperature, emits the
  same amount of energy as it absorbs.
• Thus, a good absorber is a good emitter, and vice
  versa.
• An object absorbing more energy than it emits
  becomes hotter, one emitting more energy, becomes
  cooler.

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Thermal Radiation 2

• An ideal emitter emits thermal (or blackbody)
  radiation in a combination of wavelengths that
  depending only on its temperature.
• Thus, the temperature of a distant thermal
  emitter can be determined simply from the
  radiation it emits.
• Since stars are almost perfect thermal radiators,
  their temperatures may be obtained from
  Earth-based measurements.

An ideal blackbody (or thermal emitter) is a
cavity with a small aperture.
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Thermal Radiation from Stars
UV
IR
visible
Peak in IR
Peak in visible
Peak in UV
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Thermal Radiation 3

• Solids or liquids become red hot at about 2000 K,
  white hot at about 5000 K and blue hot above 8000
  K.

12,000 K, peak in UV
6000 K, peak in visible
3000 K, peak in IR
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Color Sensitivity of the Eye
blue
red
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Sunlight Thermal Radiation at 5800 K
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Thermal Radiation 4

• Three results for thermal (or blackbody)
  radiation
• As an object gets hotter, it emits more energy
  per second (or power) at all wavelengths
• Wiens Law
• As the temperature increases, the peak of the
  intensity vs. wavelength curve moves to shorter
  wavelengths i.e.
• ?maxT constant or ?2/?1 T1/T2 .
• Stefan-Boltzmann Law
• The total EM energy emitted per second (or
  power) is proportional to the fourth power of the
  temperature i.e.
• P constant x T4 or P2/P1 (T2/T1)4 .

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Spectral Types 1
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Spectral Types 2
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Spectral Types 3
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Spectral Types 4
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Emission Line-Spectrum of Sodium
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Absorption Line-Spectrum of Atomic Hydrogen
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Absorption and Emission Spectra

• Upper spectrum absorption lines from the Sun.
• Lower spectrum emission lines of vaporized iron.

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Ernest Rutherford

• He was born on a farm in New Zealand in 1871.
• He shared the 1908 Nobel Prize in Chemistry for
  finding that one radioactive element can decay
  into another.
• In 1907, at Manchester University, England, he
  suggested that his graduate student, Ernest
  Marsden, look for a-particles scattered
  backwards, when fired at a gold target.
• Gold was chosen for this experiment, because it
  can be rolled very fine, and has a relatively
  massive nucleus.
• He was astonished when Marsden obtained a
  positive result.
• This result was in conflict with J. J. Thomsons
  plum pudding model of the atom - leading
  Rutherford to propose the nuclear atom in 1911.

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Nuclear Atom 1
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Nuclear Atom 3
H atom
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Nuclear Atom 2
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Bohr Model 1The negative electron orbits the
positive nucleus.
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Bohr Model 2

• Radius of the nth allowed orbit
• rn n2 r1,
• where the lowest (or ground) state has n 1
  and r1 0.05 nm.
• n ( 1, 2, 3, etc.) is the principal quantum
  number.
• e.g. the radius of the 3rd lowest state (n3) is
  r3 9r1 0.45 nm.
• Non-radiative orbits
• According to Bohrs hypothesis, the electron
  orbits the nucleus without radiating EM energy.
• This result conflicts with classical EM theory,
  which requires an accelerating charge to radiate
  EM energy.

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Bohr Model 3
Photon absorption
Photon emission
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Bohr Model 4
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Bohr Model 5
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Bohr Model 6
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Bohr Theory and H Spectra

• The Balmer emission lines are transitions to the
  n2 level.

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Emission Line-Spectra of some Elements
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Representation of a Many-Electron Atom
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Electronic Charge Clouds

• Improved representations of electronic orbits for
  excited n2 states of an H atom.
• The quantum mechanical solutions represent the
  probability distributions (or charge clouds).
• The darker the shade of blue, the higher is the
  probability of finding the electron in that
  region.

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Doppler Effect 1

• The Doppler effect is the change of wavelength
  (and frequency) which occurs when the source of
  waves and the observer are in relative motion.
• Wavelength ? and frequency f of a wave moving
  with speed v are related by the equation v f ?,
  so that higher frequency means shorter
  wavelength, and vice-versa.
• When the source and observer approach each other,
  the frequency increases and the wavelength
  shortens this is known as a blueshift.
• When the source and observer move apart, the
  frequency decreases and the wavelength lengthens
  this is known as a redshift.
• Note only for visible wavelengths are the actual
  shifts towards the blue or the red.

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Doppler Effect 2
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Radial and Transverse Doppler Effects
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Barnards Star Transverse (Proper) Motion
Transverse motion of Barnards star
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Calculating the Radial Velocity

• If ? is the wavelength of a spectral line
  observed from a star with a radial velocity v,
• ?o is the wavelength of the that spectral
  line observed in the lab,
• then, if v ltlt c,
• (? ?o )/ ?o v/c.
• An approaching source gives a blueshift, since ?lt
  ?o, so that v/c is negative.
• A receding source gives a redshift, since ?gt?o,
  so that v/c is positive.
• Example If a spectral line measured in the lab
  at 400 nm, appears at 396 nm when measured from a
  star, the stars velocity is given by v/c (396
  400)/400 4/400 0.01.
• Thus, v 0.01 c towards the Earth
  (blueshift).

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