## Multiwavelength Milky Way: Radiation Laws

### The laws of light, energy, and temperature

I. The Stefan-Boltzmann law

II. Wien's law

III.Planck's law

#### Blackbody Radiation laws

I. The Stefan-Boltzmann law

II. Wien's law

**blackbody** - an object which absorbs all radiation falling upon it, and
does not *reflect* any. All radiation emitted by a blackbody is due to its
temperature. A star is a near perfect blackbody.

I. The amount of energy radiated by an object is related to its temperature. The
hotter the object, the more energy it releases. This idea is represented by the
**Stefan-Boltzmann law**

where **Energy Flux** (F) is the amount of energy emitted every second, **σ** (Greek symbol __sigma__) is the
Stefan-Boltzmann constant (equal to 5.67 x 10^{-8} watts meter^{-2} K^{-4}), and **T** is temperature in degrees kelvin (K). This law is best applied to a blackbody.
The law says, for example, if you double an object's temperature, the amount of energy it
releases increases by a factor of 16.

The Stefan-Boltzmann law is named after two Austrian physicists, Josef Stefan and Ludwig Boltzmann.

II. An object emits radiation at several wavelengths. However the *peak* wavelength
emitted depends on the object's temperature. The cooler the object, the longer the wavelength
at which most of the radiation is emitted. This is known as **Wien's law**

where **λ** (Greek symbol __lambda__) is wavelength, **C** is a constant, and
**T** is temperature. If wavelength is measured in meters and
temperature is measured in degrees kelvin, then C = 0.0029 (if wavelength is measured in
nanometers, C = 29 x 10^{5}). This law is also best applied
to a blackbody such as a star. The peak wavelength helps determine an object's color. If an object peaks
in the ultraviolet portion of the electromagetic spectrum, more of its emitted radiation
is on the violet/blue end of the visible spectrum than on the red end, so we see the
object as being blue in color.

Wien's law is named after a German physicist, Wilhelm Wien.

Blackbody curves are used to illustrate the Stefan-Boltzmann law and Wien's law. A hot object has a high curve (more total energy, Stefan-Boltzmann Law), which peaks at a short wavelength (Wien's Law). A cooler object has a low curve (less total energy), which peaks at a longer wavelength.

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#### Planck's Law

Light at a particular wavelength has a specific energy. This can be described as

where **E** is energy, **h** is Planck's constant, **c** is the speed of light, and
**λ** (Greek symbol __lambda__) is wavelength. Planck's constant, **h**, is equal to
6.625 x 10^{-34} joules sec, which is the same as 4.135 x 10^{-15} eV sec (eV stands for "electron volt," and is a unit of energy like the joule is). This equation shows the relationship
between the wave-like and particle-like nature of light, and is named after a German
physicist, Max Planck. Planck's Law tells us that longer wavelengths have a lower energy than short wavelengths.

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**Noteworthy:**

In connection with COBE and the TARP (Technology And Research Partnership) project, two high school students have written a short discussion on
Blackbody radiation and Wien's Law.

**Related Online Resources:**

About Temperature - definition, history, and theory

Blackbody Radiation Graphs -
Plots and Quicktime movies for blackbody temperatures 500K-26,000K.

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