Wien's Peak Law

Wien's peak law, or Wien's displacement law is used to find the peak (or most probable) wavelength or frequency of the plank function for any given temperature.

Wien's Peak Law for Frequency
$$\frac {h \nu _p}{kT} \approx 2.82$$

$${h \nu _p} = 3kT$$

This result is found by differentiating plank's law in frequency with respect to frequency and solving for the maximum. This results in a transcedental equation and solving that, will result in the equations above

Wien's Peak Law for Wavelength
$$\frac {hc}{\lambda _p kT} \approx 4.97$$

$$\frac {h \nu _p}{kT} \approx 4.97$$, using $$\nu _p \lambda _p = c$$

$$h \nu _p = 5kT$$