Thermal Sources

The power radiated by thermal sources is a function of their temperature.  We divide thermal sources into two classes, black-body radiators and line sources.

Kirchoff's laws of spectroscopy characterize thermal emission of light from matter.

bulletA continuous spectrum is emitted by a luminous solid, liquid, or a very dense gas.
Examples: an incandescent light bulb, glowing coals in the fireplace, element of an electric heater.
bulletAn emission-line spectrum is emitted by a thin, luminous gas.
bulletAn absorption-line spectrum is produced when white light passes through a cold gas.

Quantum mechanics governs the internal structure of atoms and allows us to elaborate on Kirchoff's Laws.

bulletIsolated atoms of any element absorb or emit light only at specific wavelengths.  Atoms are isolated in a thin gas.
bulletEvery element has its own distinctive pattern of wavelengths at which absorption or emission can occur.  The absorption or emission lines which occur in a spectrum therefore allow us to deduce which chemical elements are present.
bulletThe relative strengths of emission or absorption lines of a given element depend on the temperature of the gas absorbing or emitting the light.  We therefore have a means of determining the temperature of a gas.  By comparing the strengths of emission or absorption lines of different elements, we can deduce quantitatively the relative abundance of each element.
bulletIf we compress a gas, then the internal properties of individual atoms are affected by the electronic properties of neighboring atoms and the absorption or emission lines are no longer sharp, but broadened.  The widths of the absorption or emission lines can give us information the density of the gas.  If the light emitting material is compressed even more, then all the emission lines blur together completely into a featureless spectrum. This is called a black-body spectrum.

Radiation laws govern the properties of the continuous spectrum.

Radiation laws

The primary law governing radiation is the Planck Radiation Law, which gives the intensity of radiation emitted by a blackbody as a function of wavelength for a fixed temperature.  The Planck law gives a distribution, which peaks at some wavelength.  The peak shifts to shorter wavelengths for higher temperatures, and the area under the curve grows rapidly with increasing temperature.  The diagram below shows the intensity distribution predicted by the Plank law in J/(m2s) for blackbodies at various temperature.

A blackbody is a body that absorbs all the radiation that falls onto it.  It does not reflect any radiation.  It reaches thermal equilibrium with its surroundings, and in thermal equilibrium emits exactly as much radiation it absorbs.  It has emissivity = 1.  Emissivity measures the fraction of radiative energy that is absorbed by the body.

The Wien Law gives the wavelength of the peak of the radiation distribution, λmax = 3*106/T.  Here λ is measured in units of nanometer (10-9 m) and T is in Kelvin.

The Stefan-Boltzmann Law gives the total energy being emitted at all wavelengths by the body.

Radiated power = emissivity * σ * T4 * Area

Here σ is the Stefan-Boltzmann constant, σ = 5.67*10-8 W/(m2K4).  Light colored or reflective objects have low emissivity.  They do absorb a smaller percentage of the incoming radiation than do dark objects, and also emit radiation less readily.

The Wien law explains the shift of the peak to shorter wavelengths as the temperature increases, while the Stefan-Boltzmann law explains the growth in the height of the curve as the temperature increases.  This growth is very abrupt, since it varies as the fourth power of the temperature.

The Planck radiation law tells us the intensity of the radiation emitted by a hot object as a function of wavelength.  The Wien Law gives the wavelength of the peak of the distribution.  The surface temperature of the sun is 5800oC = 6073 K.  The wavelength of the peak of the distribution therefore is 494 nanometer.  This wavelength lies in the yellow region of the visible spectrum.

In an incandescent light bulb a filament is heated to approximately 2500oC = 2773 K.  This is the maximum temperature that a tungsten filament can stand without evaporating quickly.  Compared to the sun, such a filament emits a greater fraction of its radiation in the infrared region of the electromagnetic spectrum.  The wavelength of the peak of the distribution is 1082 nanometer.  This wavelength lies in the infrared region of the spectrum.

Sunlight and light from an incandescent bulb contain all the colors of the visible spectrum.  But the intensity distribution over the different colors is different.  Sunlight appears brilliant white while a light bulb looks yellowish.