Different radiation intensities from a black body

Question

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?

Answer 1

TL;DR: The density of electromagnetic modes increasing with frequency, while the number of photons contained in each mode drops with frequency.

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.