Describe two features of energy levels for an electron in a crystal.

When we dive into the microscopic universe of crystals, things get intriguing, particularly regarding how electrons behave. Unlike isolated atoms, electrons in a crystal don't stick to one clearly defined energy level. Instead, they're part of a social network of atomic interactions, resulting in continuous 'energy bands'. Imagine a concert stadium where every seat represents a possible energy level. In a single atom, an electron would have an assigned seat. But in a crystal, the party gets bigger, and the electrons can choose from a range of closely spaced seats, or energy levels, if you will.

Why does this happen? Because the atoms in a crystal are so snugly packed together that their energy levels begin to merge, forming bands. This overlap is like musical notes from different instruments blending to create chords. The new 'chords' in a crystal are these energy bands, where electrons have more flexibility to move and groove around.

Now that we understand energy bands, let's chat about the 'no-fly zones' of electron activity known as band gaps. Picture that concert stadium again but now imagine certain rows are cordoned off. No one can sit there, period. In the crystal world, band gaps are these off-limits rows, representing energy levels that electrons are forbidden from occupying.

There are two VIP sections in a crystal – the 'valence band', which is full of electron fans, and the 'conduction band', which is where electrons would love to jump when they get some energy to party harder. The band gap, then, is like a rope separating these sections. The width of the rope – or the size of the band gap – is super important. It dictates if we've got a solid material that's an insulator (high-fiving from afar because the rope is too wide), a semiconductor (a manageable leap across), or a conductor (where the rope is super thin or non-existent, so electrons move freely).

Electrical conductivity is all about how well a material can carry an electric charge, and it's tied up with the ideas of energy bands and band gaps we've already chatted about. Materials are categorized based on their electron dance skills – how well electrons can move from the valence band to the conduction band.

Starting with insulators, these are the wallflowers of the electron dance. They have such wide band gaps that electrons can't easily jump across. It's like having a chasm between them and the dance floor. Next up, we have semiconductors which are a bit braver. They have smaller band gaps, so with a bit of energy – like some heat or light – electrons can make the jump and get moving. Lastly, conductors are the life of the party. Their band gaps are so tiny, or non-existent, that electrons can freely hop to the conduction band and get the electric current flowing with ease.