# Formula Wien's Displacement Law (Radiation Law) Temperature Wavelength

## Temperature

`$$ T $$`Unit

`$$ \mathrm{K} $$`

**Wien constant**. Note: \( \text{mK}\) is NOT "millikelvin", but the unit "meter times kelvin".

The sun has its radiation maximum at about a wavelength of \( \class{blue}{\lambda_{\text{max}}} = 500 \, \mathrm{nm} \) (nanometer: \(10^{-9} \, \mathrm{m}\)). With this wavelength we can estimate the temperature of the sun:`\begin{align}
T &~=~ \frac{2897.8 \,\cdot\, 10^{-6} \, \mathrm{m} \mathrm{K}}{ 500 \, \mathrm{nm} } \\\\
&~=~ \frac{2897.8 \,\cdot\, 10^{-6} \, \mathrm{m} \mathrm{K}}{ 500 \cdot 10^{-9} \, \mathrm{m} } \\\\
&~=~ 5796 \, \mathrm{K}
\end{align}`

The surface of the sun has a temperature of \( 5796 \, \mathrm{K} \). That is approximately \( 5523^{\circ} \, \mathrm{C}\).

## Wavelength

`$$ \class{blue}{ \lambda_{\text{max}}} $$`Unit

`$$ \mathrm{m} $$`

The surface of the star Sirius in the constellation 'big dog' has approximately a temperature of \( 10 \, 000 \, \mathrm{K} \). With Wien's radiation law we can determine the wavelength of the radiation which is emitted most by Sirius:`\begin{align}
\class{blue}{ \lambda_{\text{max}}} &~=~ \frac{2897.8 \,\cdot\, 10^{-6} \, \text{m} \text{K}}{ 10 \, 000 \, \mathrm{K} } \\\\
&~=~ 2.89 \cdot 10^{-7} \, \mathrm{m} \\\\
&~=~ 289 \, \mathrm{nm}
\end{align}`

So Sirius emits the most electromagnetic radiation, which has the wavelength 289 nanometers. This corresponds to extreme UV radiation.

## Wien's constant

`$$ 2897.8 \,\cdot\, 10^{-6} $$`