Why does an atom bother to glow?

In spontaneous emission of a photon from an atom, the energy of the emitted photon equals the difference in energy between the ground state and excited state of the atom. If the energy is equal, why does the atom bother emitting a photon at all?

Originally posted at Forbes!

All atoms in the periodic table have at least one electron orbiting around the nucleus of the atom, where the protons and neutrons hang out. Hydrogen is the simplest of all atoms, and as such is often used as the example – one proton in the center, with a single electron zooming around the proton. More complicated atoms are basically the same setup, but have both protons and neutrons in the center, and more electrons zooming around.

If any of the electrons around any atom get some energy tossed their way – maybe they got hit by some light that donated some of its energy – this electron can gain energy. However, the electron doesn’t just absorb a random amount of energy – up to a threshold, the electron tends to steal a fixed amount of energy from its donor photon. The amount of energy it can steal is dictated by the atom the electron is attached to. In the quantum world, this energy boost is often thought of as taking a step up an ‘energy ladder’. (The threshold I mention is an upper limit here; if the light is sufficiently energetic, it can give the electron enough energy to bounce right out of the atom.)

Depending on how much energy has been donated by our photon, the electron doesn’t have to move up only one step at a time – if your atom gets hit by a really powerful, super-energetic beam of light, you might jump up quite a few steps, all at once (if the photon is extra super energetic, this is when the electron is able to skip atom town, but we’ll assume that the photon wasn’t quite that energetic). But then what? Now we have an atom with at least one of its electrons in this ‘excited state’.

This is where spontaneous emission can come in. Spontaneous emission is when the electron, unprompted, lets go of a photon, which contains the extra energy that was holding the electron in the excited state. Similar to the step up the energy ladder, this process steps you down the energy ladder, and not always by a single step. And the question is correct- the photon is always equal in energy to the drop in energy of the photon. So why does the electron bother?

It might not bother, for some time – it depends on the atom, how excited it is, and what energy photon it needs to spit out. But there’s a formula you can write out that describes the probability that the electron will drop down to a lower energy state, and given enough time, it’ll definitely happen. If the electron needs to spit out a photon that falls within the visible spectrum, this will typically happen in less than a few millionths of a second.

The higher energy states are fundamentally less preferred than the lower energy states. The atom has a built-in preference to be in the ground state. You can think of it as similar to a potential energy argument. While you can balance a pen on its end, vertically, the pen prefers to be in a ground state of horizontal. It’s more stable laying down on the table than it is on its end, though it might balance on its end for quite some time, before some random jostling sends it tumbling down. So it is with electrons and their spontaneous emission of photons.

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