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 FINDING EMITTED RADIATION AND WAVELENGTH OF MAXIMUM EMISSION

METEOROLOGIST JEFF HABY

All objects emit radiation. All objects also emit a variety of wavelengths of radiation. However, the temperature of the object determines the most common range of wavelengths emitted.

The radiation emitted from an object can be expressed as the Energy emitted per unit time (Power) through an area of the object. The metric units for this expression are Watts per meter squared (W/m^2). The equation that relates emitted Watts per area to the temperature of the object is:

Emission = T^4 * Stefan-Boltzmann constant

T^4 = Temperature in Kelvins to the fourth power

Stefan-Boltzmann constant = 0.0000000567 Wm^-2K^-4

For example, the sun has a surface temperature of about 6,000 K. Find the emission from the sun

Emission = 6,000^4 K^4 * 0.0000000567 Wm^-2K^-4

Emission = 6,000 * 6,000 * 6,000 * 6,0000 K^4 * 0.0000000567 Wm^-2K^-4 = 73,483,200 Wm^-2

The equation that relates the wavelength of maximum emission to the temperature of the object is:

Wavelength of max emission (um) = 2897 umK / Temperature

um = micron, which is a millionth of a meter ( 0.000001 m or can be written 10^-6 meters)

2897 umK = constant that relates max emission to Temperature

Temperature = Kelvins

Although energy will be emitted in a variety of wavelengths this equation finds what the most common emitted wavelength is. The relationship between temperature and wavelength is that as temperature goes up the wavelength gets shorter and as the temperature goes down the wavelength gets longer. Thus, warmer objects emit shorter wavelengths and colder objects emit longer wavelengths.

For example, what is the wavelength of maximum emission for the sun?

Wavelength of max emission (um) = 2897 umK / 6,000 K

Wavelength of max emission (um) = 0.48 um