# Different radiation intensities from a black body

I am a high school student and was wondering about the radiation curve of a black body. Why do the emitted wavelengths from a black body have different intensities? What happens at the atomic level that makes some wavelengths stronger than others resulting in a radiation peak?

• Commented Jan 4, 2023 at 9:58

According to the Planck's law, the spectral radiance is given by $$B(\nu, T)=\frac{2\nu^2}{c^2}\frac{h\nu}{\exp\left(\frac{h\nu}{k_B T}\right)-1}$$ The factor $$\nu^2$$ originates from the density of states, i.e., the density of electromagnetic modes per frequency interval, which increases with frequency, $$\nu$$. On the other hand, factor $$h\nu/\left[\exp\left(\frac{h\nu}{k_B T}\right)-1\right]$$ is nearly constant at low frequencies and decays expinentially when $$h\nu\gg k_BT$$: $$h\nu/\left[\exp\left(\frac{h\nu}{k_B T}\right)-1\right]\approx h\nu\exp\left(-\frac{h\nu}{k_B T}\right)$$. Thus, at small frequencies the radiance increases, but then drops - hence there is a peak in between. In essence, it is the competition between the density of electromagnetic modes increasing with frequency, while the number of photons contained in each mode drops with frequency.