Wien's Tail

Wien's Tail or Wien's approximation is used to describe the spectrum of electromagnetic radiation from a blackbody. The equation accurately describes the short wavelength limit but fails to fit experimental data for long wavelengths. It's compliment is Rayleigh-Jean's Law, which accurately describes long wavelengths but fails to describe short wavelengths

Think low wavelength, high frequency

Equations

For wavelength $\lambda$, the law can be expressed as:

$B _\lambda (T) = \frac {2hc^2}{\lambda^5} e ^ {- \frac {hc}{\lambda kT}}$

For frequency $\nu$, the law can be expressed as:

$B _\nu (T) = \frac {2h \nu^3}{c^2} e ^ {- \frac {h \nu}{kT}}$

Recognizing the Wien Tail

We can simplify Plank's Law when the following inequality holds:

$\frac {h\nu}{kT} \gg 1$