In my introductory chemistry class, we are learning about the basics of quantum mechanics. We were introduced to the concept of emission and absorption spectra. Our textbook describes how electrons can only exist at certain energy levels, and the packets of energy absorbed and emitted as they transition between these levels give rise to absorption and emission spectra.
The book then goes on to describe a black body as a hypothetical object that can absorb and emit at all wavelengths. I understand that this is only a hypothetical object, but how does that even make sense if electrons can only exist at certain energy levels? Furthermore, the book immediately goes on to describe things such as the Stefan-Boltzmann law and Wien's law and all kinds of graphs of how temperature and intensity and wavelength of a black body relate to each other. But if a black body is theoretical, how do we even know these relations?
I am just completely confused about the entire concept of a black body.
Best Answer
This was the first question I asked my astrophysics mentor when I interned at Jet Propulsion Lab. It's a great question many people fail to ask for a long time.
When you have an individual atom, you get a distinct set of electron energy levels where you can excite a gas and have it jump back down an energy level. To first order this also works well to describe light observed from very weakly interacting states of matter (like gases). However things get trickier at the condensed states where interactions now matter.
Basically what happens here is that when you bring independent atoms close together, the wavefunctions for their electrons couple together, and you get energy level splitting, which basically means that two atoms which individually had 2 energy levels at $\epsilon_i $ you instead end up with two distinct energy levels at $\epsilon_{i+\delta} $ and $\epsilon_{i-\delta} $. This splitting occurs throughout the solid state and as N atoms enter the solid state it creates what is called an energy band, which resembles a continuum. The details are all material dependent so a nice baseline model would allow for us to ask essential questions and then study how the system in question deviates from the model. That's where the black body comes in. It assumes an equal density of states throughout the entire medium, with this "quantized" continuum framework that QM demands.
Cultural enrichment: The average energy of $\epsilon_{i+\delta}$ and $ \epsilon_{i-\delta} $ is not $\epsilon_{i} $ , but slightly less. You may know the case of two atoms in a subclass of this interaction as bonding and anti-bonding orbital.
Enrichment 2: You can use the statistical mechanics of a harmonic oscillator to model black body radiation.