Key Ideas

The Nature of Light: Light is electromagnetic radiation. It has wavelike properties described by its wavelength λ and frequency ν, and travels through empty space at the constant speed c = 3.0 × 10⁸ m/s = 3.0 × 10⁵ km/s.

Thermal energy: The thermal energy of a material comes from the kinetic energy of its microscopic particles (atoms and molecules). The hotter a material, the faster its particles move, and the greater its thermal energy.

Blackbody Radiation: A blackbody is a hypothetical object that emits a continuous spectrum; the hotter the object, the greater the emission. Stars closely approximate the behavior of blackbodies, as do other hot, dense objects.

• The intensities of radiation emitted at various wavelengths by a blackbody at a given temperature are shown by a blackbody curve.
• Wien’s law states that the dominant wavelength at which a blackbody emits electromagnetic radiation is inversely proportional to the Kelvin temperature of the object: λ_max (in meters) = (0.0029 K m)/T.
• The Stefan-Boltzmann law states that a blackbody radiates electromagnetic waves with a total energy flux F directly proportional to the fourth power of the Kelvin temperature T of the object: F = σ T⁴.

Photons: Light is made of particles called photons. Each photon has a wavelength equal to the wavelength of the light that the photons make up.

• Planck’s law relates the energy E of a photon to its frequency ν or wavelength λ: E = hν = hc/λ, where h is Planck’s constant. The shorter the wavelength a photon has, the higher its frequency and the larger its energy.

Kirchhoff’s Laws: Kirchhoff’s three laws of spectral analysis describe conditions under which different kinds of spectra are produced.

• A hot, dense object such as a blackbody emits a continuous spectrum covering all wavelengths.
• A hot, transparent gas produces a spectrum that contains bright (emission) lines.
• A cool, transparent gas in front of a light source that itself has a continuous spectrum produces dark (absorption) lines in the continuous spectrum.

Atomic Structure: An atom has a small dense nucleus composed of protons and neutrons. The nucleus is surrounded by electrons that only occupy certain orbits or energy levels.

• When an electron jumps from one energy level to another, it emits or absorbs a photon of corresponding energy (and hence of a specific wavelength).
• The spectral lines of a particular atom correspond to various electron orbital transitions between energy levels in the atom. Each atom has a unique “spectral fingerprint.”

The Doppler Shift: The Doppler shift enables us to determine the line-of-sight (radial) velocity of a light source from the displacement of its spectral lines.

• The spectral lines of an approaching light source are shifted toward short wavelengths (a blueshift); the spectral lines of a receding light source are shifted toward long wavelengths (a redshift).
• The size of a wavelength shift is proportional to the radial velocity of the light source relative to the observer.