Question

If all energies are truly quantized, why is it possible to have a continuous spectrum from blackbody emitters?

Answer 1

Blackbody is macroscopic, composed of a large number of atoms. It is well known from band theory of solids that when atoms combine to form a solid, their energy levels split and the separation between these energy levels is finer when the number of atoms is larger. The typical number of atoms in a solid is of the order of 10^23. Therefore, the separation between energy levels is very fine and we have a 'quasi-continuous' energy band. Whenever a blackbody emits radiation, it corresponds to an electron jumping from higher energy state to a lower energy state and because of this an electron in excited state has a very large number of 'energy levels below', it can jump into any of the empty states giving a continuous spectrum.

or we can say a black body emit some radiation at each wavelength.When we plot the graph between radiation versus wavelength,It is obvious to get a continuous curve.