# Science

BLACKBODY CURVES LAB
Adapted from Astronomy Lab Manual AST1002C for Distance Learning by Prof. M. Werhner
Background

A body in a constant radiation field will reach temperature equilibrium where the amount of energy being absorbed equals the amount of energy being emitted (radiated). All bodies do not absorb or emit energy in the same way. Some are more reflective than others. Theoretically it is possible for a body to absorb all the energy that falls on it, this theoretical body is called a blackbody. A blackbody will absorb all wavelengths which strike it and, hence, it is totally opaque. It does, however, emit all of the radiation it absorbs so that it does not necessarily appear black. Stars are considered good absorbers of all wavelengths and are good approximations of a blackbody. A working definition of a blackbody is: something which absorbs all the energy it receives, heats up to a certain temperature, and then reradiates the energy with a characteristic spectrum defined by that temperature.

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Figure 1. Planck Radiation curves for three temperatures, with the wavelengths of the visible segment of the electromagnetic spectrum shaded. Energy (Planck Function) on the vertical axis plotted against wavelength (in Ångstroms). From: http://burro.astr.cwru.edu/Academics/Astr221/Light/blackbody.html

Planck’s Law

In the 18th Century experimental physicists determined the character of the radiation emitted from hot bodies at various temperatures. Figure 1 shows the Planck radiation curves for the radiation emitted by hot bodies at three different temperatures. Note that each body emits radiation at all wavelengths but the peak radiation (which determines the apparent color of the luminous body) depends on the temperature (given in Kelvin (K)). Also note that the hotter the temperature the further towards the blue end of the spectrum (shorter wavelengths) the peak of the radiation curve is. Max Planck found that if he assumed the electromagnetic radiation emitted consisted of not waves but discrete packets of energy (photons) he could mathematically duplicate the curves shown in Figure 1. This became known as Planck’s Law. It states (among many other things) that:

1. A blackbody emits radiation at all wavelengths in varying amounts

2. A hotter body gives out more energy at every wavelength than a cooler body

3. The hotter the body is, the bluer is the preponderance of radiation emitted by the body (i.e. the apparent color of a body is an indication of the temperature of the body)

Wien’s Law

Wien’s law is a follow on from Planck’s radiation law. It states the relationship between the temperature of a blackbody and the wavelength at which it emits most of its radiation.

where T = temperature (in Kelvin) and λ = wavelength (in Ångstroms)

For astronomers this means that using a photometer (light meter) and a series of filters attached to telescope the energy distribution of a star may be observed. The wavelength value of the peak of this energy distribution (blackbody curve) is then inserted into Wien’s Law to determine the star’s temperature.

Question

1. Use the seven Wien’s curves in the graph below to calculate the temperature of each star they were generated by. Remember it is the wavelength at peak energy emission that is required to plug into Wien’s equation (above), the dashed line is there as a guide for the peaks. Complete the table below the graph. Note 1 nanometer (nm) = 1 billionth of a meter. There are 10 Ångstroms in 1 nanometer. Complete the color column with a relative estimate of which end of the electromagnetic spectrum the star is emitting at, blue, yellow, red, etc.

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Peak Wavelength (nm)

Peak Wavelength

(Ångstroms)

Temperature

(Kelvin)

Color

(estimation)

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