Ch. 4: Radiation and Spectra

4.1 The Nature of Light

  1. Maxwell's theory of electromagnetism
    1. Atoms are made of positive (protons) and negative (electrons) charges.
    2. Charges feel electric forces, moving charges feel magnetic forces.
    3. Oscillating charges produce electric and magnetic (electromagnetic) waves.
    4. Maxwell calculated that the speed of electromagnetic waves is the same as the speed of light.
    5. On that basis, light was inferred to be an electromagnetic wave.
    6. Radiation is electromagnetic waves.
  2. Wave-like characteristics of light
    1. Electromagnetic waves don't require a medium (such as air or water) to move through -- they can propagate through empty space.
    2. All electromagnetic waves move at the speed of light.
    3. Electromagnetic waves can have different wavelengths (different colors of light have different wavelengths).
    4. Representation of a typical wave. [insert figure of a wave, with crests, troughs, and wavelength labelled]
    5. In order of decreasing wavelength: radio waves, infrared, visible light, ultraviolet, x-rays, gamma rays.
    6. Frequency (measured in hertz, Hz) measures how many cycles (waves) occur each second.
    7. c = λf, c = speed of light, λ = wavelength, f = frequency.
  3. Light as a photon
    1. Light sometimes behaves like a particle we calla photon.
    2. A photon can be thought of as a piece of a wave.
    3. A photon carries a specific amount of energy, depending only on its frequency.
  4. Propagation of light
    1. Light moves away from a source in all directions.
    2. The apparent brightness decreases like the inverse square of the distance from the source. When twice as far from a source, the apparent brightness is the inverse of 2 squared, or 1/4.

4.2 The Electromagnetic Spectrum

  1. For convenience, we divide the electromagnetic spectrum into categories based on wavelength.
  2. The categories are:
    1. gamma rays
      1. wavelength, λ < 0.01nm
      2. highest energy radiation
      3. cosmic gamma rays are absorbed in the atmosphere
      4. detection requires instruments in space
    2. x-rays
      1. wavelengths between 0.01nm and 20 nm
      2. less energetic than gamma rays, more energetic than light, able to penetrate tissue
      3. cosmic x-rays are absorbed in the atmosphere
      4. detection requires instruments in space
    3. ultraviolet
      1. wavelengths between x-rays and visible light
      2. mostly absorbed by ozone in the atmosphere
      3. responsible for tans, sunburns, and skin cancer
    4. visible light
      1. wavelengths between 400 nm (violet color) and 700 nm (red color)
      2. most solar radiation in this range
      3. easily penetrates the atmosphere
      4. "white" light is a mixture of all colors
      5. the colors in light can be separated with a prism
    5. infrared
      1. wavelengths between visible light and radio waves
      2. responsible for "heat" radiation, can be felt on the skin
      3. much is absorbed in the atmosphere
      4. detection requires instruments on mountains, planes, or in space
    6. radio waves
      1. all wavelengths longer than infrared
      2. includes microwaves, shortwaves, radar waves, FM, TV, and AM radio waves
      3. some radio waves penetrate the atmosphere, others don't
  3. Each category of radiation tells us things about the source.
  4. Different techniques are used to detect the different categories of radiation:
    1. radio waves -- antennas
    2. infrared -- cooled infrared detectors (like night scopes)
    3. visible -- eyes, photographic film, CCD's (digital cameras)
    4. ultraviolet -- UV film, CCD's
    5. x-rays -- x-ray film, x-ray silicon sensors
    6. gamma rays -- crystals
  5. Radiation laws and temperature
    1. Objects emit radiation due to their temperature.
    2. A blackbody is an object that absorbs all incident radiation.
    3. At a given temperature, a blackbody emits a particular spectrum of radiation.
    4. All wavelengths of radiation are emitted, but in varying amounts that depend on the temperature.
    5. The most abundantly emitted wavelengths depend on the temperature -- hotter objects emit more of their radiation at shorter wavelengths.
    6. Hotter objects emit more radiation at all wavelengths than colder objects.
    7. The most abundantly emitted wavelength is given by λmax = (3×106)/T where T is the temperature in kelvins, and λmax is the wavelength in nanometers. This is known as Wien's Law.
    8. The total energy emitted in radiation is E = σT4, where σ is a constant number called the Stefan-Boltzmann constant, T is the temperature in kelvins, and E is the energy in joules.
    9. If the temperature doubles, the amount of energy emitted increases by 24 or 16 times!

4.3 Spectroscopy in Astronomy

  1. Optical Properties of Light
    1. reflection: light reflects from shiny surfaces -- mirrors
    2. refraction: light is bent when passing from one medium to another -- eyeglasses, magnifying glasses, binoculars
    3. dispersion: different wavelengths (pure colors) of light are bent (refracted) by different amounts. A prism or diffraction grating separates light into its component colors. White light is an equal mixture of all colors and yields a complete rainbow. In general, light is a mixture of wavelengths (pure colors). A spectrometer is a device for measuring the component wavelengths of light.
  2. The Value of Stellar Spectra
    1. Temperature: a star emits a continuous blackbody spectrum according to its surface temperature.
    2. Upon closer inspection, many dark bands (missing wavelengths) are seen interrupting the continuous spectrum.
    3. The dark bands correspond to colors absorbed by certain gases.
    4. Different gases absorb different colors -- the dark bands tell us what gases are present to absorb those wavelengths.
  3. Types of Spectra
    1. continuous spectrum: due to the temperature of the object -- independent of its composition!
    2. absorption line spectrum: dark bands superimposed on the continuous spectrum, depends on the atoms and molecules between source and observer.
    3. emission line spectrum: series of bright lines corresponding to the emission lines of cool atoms and molecules. The bright lines emitted have the same wavelength (color) as the dark absorption lines for that substance.
    4. The series of lines (spectral lines)associated with a particular atom or molecule is unique. Like a signature, fingerprint, or DNA identifies a particular person, spectral lines identify atoms and molecules.
    5. Helium was discovered by noting a set of perviously unknown spectral lines from the Sun. The name Helium is derived from Helios, the Greek word for Sun.

4.4 The Structure of the Atom

  1. Probing the Atom
    1. Atoms are composed of a positively charged nucleus surrounded by negatively charged electrons (solar system model).
    2. Charges come in certain quantities; the charge of an electron is the exact opposite of the charge of a proton.
    3. We refer to charges in units of the proton charge (called e), therefore the charge on a proton is +1e and the charge on an electron is -1e.
    4. Atoms of different elements differ in the amount of charge in the nucleus: H has +1e, He has +2e, Li has +3e, Be has +4e, B has +5e, C has +6e, N has +7e, and O has +8e.
    5. The number of electrons around the nucleus determines the ionization state of the atom. Neutral atoms have as many electrons as the nucleus charge. Singly ionized atoms have 1 electron less than the nucleus charge.
  2. The Atomic Nucleus
    1. The nucleus is much smaller than the atom itself and is composed of protons and neutrons.
    2. The neutrons carry no charge.
    3. The number of protons determines the charge in the nucleus and hence the type of atom.
  3. The Bohr Atom
    1. The model of an atom with a small, massive nucleus orbited by electrons looks much like our solar system with the nucleus playing the role of the Sun and the electrons playing the roles of planets.
    2. This model gets many physical details wrong. While any radius is permitted for a planet's orbit, there are only certain orbits allowed for electrons.
    3. Associated with these restricted orbits (called states) are particular energy levels of the atom (this is called quantization).
    4. When atoms absorb or emit light, they move from one energy level to another. The light can have only certain specific energies.
    5. The energy in a piece of light (a photon) depends on its wavelength (or frequency if you prefer). Energy = (Planck's constant)×(frequency)
    6. The restriction of the electrons to certain energy levels results in emission and absorbtion lines in atoms. That is, an atom can emit or absorb only specific frequencies (wavelengths) of light.
    7. The possible wavelengths for a particular atom is called its atomic spectrum.
    8. The spectrum from each type of atom is different.

4.5 Formation of Spectral Lines

  1. The Hydrogen Spectrum
    1. We can use the Bohr model of the hydrogen atom to understand how light is emitted and absorbed from atoms.
    2. A beam of white light is a mixture of all frequencies.
    3. Hydrogen atoms can absorb photons that have the correct energy to move their electrons from one energy level to another -- the photon energy equals the difference in the energy of the two levels.
    4. These photons are removed from the beam. They are later emitted when the electrons return to the lower energy levels, but the emission is in a random direction, not necessarily the original beam direction.
    5. The set of frequencies/wavelengths emitted or absorbed by hydrogen atoms is called the hydrogen spectrum
    6. Other atoms are more complicated by the presence of more electrons and more energy levels, but the same general picture holds.
    7. The set of frequencies/wavelengths emitted or absorbed (spectrum) by each type of atom is unique, like a fingerprint. Knowing the spectrum, astronomers can identify the atom(s) that created it.
  2. Energy Levels and Excitation
    1. The lowest possible energy level of an atom is called its ground state.
    2. Any higher energy level is called an excited state.
    3. An atom can absorb energy (a photon) and move from the ground state to an excited state. Later it will emit a photon, lose energy, and return to the ground state.
    4. Because the emission is in a random direction, a beam of white light develops dark bands of missing frequencies. When the beam of light is diffracted, the resulting spectrum is called an absorption spectrum.
    5. Relatively cold atoms are normally in the ground state. Hot atoms can be in excited states (due to collisions with other atoms, not photons). The most prominent spectral lines will be different in the two cases.
  3. Ionization
    1. Generally, atoms have as many electrons as protons.
    2. An ion is an atom with a different number of electrons than protons.
    3. Removing an electron from an atom is called ionization.
    4. An atom with fewer electrons than protons is a positive ion.
    5. A positive ion can attract an electron, to become a neutral atom. As the electron falls into the energy levels of the atom, photons are emitted.
    6. The spectra of ions are different from the spectra of their neutral atoms

4.The Doppler Effect

  1. Motion Affects Waves
    1. The Doppler effect is named after Christian Doppler
    2. He pointed out in 1842 that if a light source is moving, its waves will be compressed or spread out, depending on the relative motion.
    3. Figure 4.19 shows how the waves are changed by motion of the source.
    4. From the figure we can see that if the source is moving towards or away from the observer (radial motion), the waves will be doppler shifted.
    5. If the source moves perpendicular to the observer, there is no doppler shift.
  2. Color Shifts
    1. When the source moves towards you, the waves are compressed, and the wavelength becomes shorter. This causes the color of the light to change slightly towards the blue and is therefore known as a blueshift.
    2. When the source moves away, the waves are stretched, and the wavelength becomes longer. This causes the color of the light to change slightly towards the red and is known as a redshift.
    3. Even for radiation that is not in the visible, we still use the terms blueshift and redshift to describe the shortening and lengthening of the wavelength caused by motion.
    4. The greater the motion, the larger the change in wavelength.
    5. v/c = delta lambda/lambda, so measuring the change in wavelength allows us to determine the radial velocity of a source.
© Robert Harr 2005