# Planck's distribution law

1. Aug 23, 2012

### johnnyies

1. The problem statement, all variables and given/known data

Estimate the energy density between 499.5 and 499.6 nm emitted by a blackbody at a temperature of 2000 K. Compare to the classical value predicted by the Rayleigh-Jeans law.

2. Relevant equations

http://en.wikipedia.org/wiki/Planck's_law

3. The attempt at a solution

now I know how to integrate the indefinite integral of the law by setting x = $\frac{hc}{KλT}$ (K = Boltzmann constant)

T = 2000K is substituted in and we use the same substitution for λ^5 of the equation.

However I do not understand how to numerically solve this with λ = 499.5 to 499.6, would we then substitute it to x = $\frac{hc}{KλT}$ and make x the new limits of integration?

2. Aug 23, 2012

### Mute

The fact that the wavelengths you are given are so close together suggests to me you just need to approximate the integral using

$$\int_{\lambda}^{\lambda+\Delta \lambda} d\lambda'~f(\lambda') \approx \Delta \lambda f(\lambda).$$