# Is Plancks function a distribution one?

• epik

#### epik

In many textbooks Plancks law or function is also referred to as Plancks distribution.
But is it a true distribution function?

I was reading a textbook where it was describing Maxwell-Boltzmann distribution
(which is a true distribution function since its integral across the range equals 1 )
and a few pages later it was comparing it with Plancks distribution pointing out how similar they look.

But is Plancks law a true distribution function?

Usually Planck's law is defined so that it is normalized to total power per unit area, rather than 1, which would have made it a probability distribution. But if you ignore the probability definition, it is a distribution.

Usually Planck's law is defined so that it is normalized to total power per unit area, rather than 1, which would have made it a probability distribution. But if you ignore the probability definition, it is a distribution.

But the form of the Plancks function that gives radiance (Energy/time/area/steradian/wavelength or frequency) is not a probability density function,right?

Usually Planck's law is defined so that it is normalized to total power per unit area, rather than 1, which would have made it a probability distribution. But if you ignore the probability definition, it is a distribution.

Ok,I got what you said.It is a distribution and should be treated as one.The reason its integral is not 1 is because it is multiplied by a factor to give irradiance, radiance etc.

Thanks.