Excited Energy levels of Hydrogen vs Solids

Question

My question has to do with Excited Energy Levels. I keep reading and learning that all objects/most solids emit infrared radiation. But to emit radiation, an object's particles must first enter a higher energy orbital (electrons) which will then immediately lead to the atom returning to its ground state, releasing the energy of the level jump from ground state to level 2 in eV in the form of a photon wave.

BUT! When I looked for information about energy levels of elements, I could only find hydrogen, and when I plugged in the energy for: l=hc/E where l is wavelength, h is Plancks constant, c is the speed of light, and E is energy of the photon.

The wavelength came up to be 1.121x10^-7! That is in the ultraviolet range! That means that it takes a ton of EM Energy to emit a photon wave! This doesn't make sense unless solids require much less energy to move up orbitals.

Is this true? What happened to Infrared or Radio? And how do I find out about energy levels of solid elements and understand the data?

Answer 1

A solid material is a lot more complicated than the hydrogen atom, but you can imagine a larger atom as being similar to a hydrogen atom with many electrons occupying the energy levels. The hydrogen energy levels are $E_n=-{13.6\,\text{eV} \over n^2}$, so you can see that as you go to higher energies, the difference between the levels gets smaller. For example, $13.6 \,\text{eV}*(10^{-2}-11^{-2}) \approx .024 \,\text{eV}$ is infrared.

In addition, molecules and solids also have energy levels associated with the vibrations of the constituent atoms relative to each other, which tend to be significantly lower than those of the hydrogen atom.

On top of that, there are various ways that the energy levels can be broadened into a range of values. Any state that has a finite lifetime will also have a nonzero linewidth (range of possible energies), to satisfy with the energy-time uncertainty relation, $\Delta E\Delta t \ge \hbar/2$. This is why we sometimes talk about solid materials like conductors have energy bands rather than levels.