MRIs

Although we didn't discuss this in too much detail, nuclei also have orbital levels. Just like in atoms, photons also get ejected from an excited nucleus, based on the difference of energies between two levels.

If you put a nucleus in an external magnetic field, we get what's called hyperfine splitting, where energy levels will split based on a proton's spin of +½ or –½¹². Not that we've talked about spin before; it's a quantum thing. Imagine it as an energy state. Usually a nucleus, just like an atom, is in its ground state. Why would it take the extra effort to occupy a state that requires more effort—a.k.a. more energy—on its part?

So, what happens if a photon with energy ΔE and frequency f collides on a nucleus, such that ΔE = E₂ − E₁? Yep: the nucleus jumps from a state of E₁ to E₂. It does that by flipping spins.(Who knew nuclear physics was so simple.) Once a proton flips spins, the nucleus becomes excited, and then subsequently flips back, emitting a photon of frequency f.

A nucleus, however, is always at the mercy of the electrons surrounding it. These electrons also have their own magnetic fields B_e. So protons can't readily absorb this magical photon of frequency f in the constant magnetic field B. Rather, we have to adjust the magnetic field B such that it cancels the electrons' magnetic field B_e. This is called nuclear magnetic resonance.

Now if we measure the exact energy needed to flip a proton, then we get information about a nucleus' surrounding electron distribution. This electron distribution, in turn, represents the molecular structure of matter.

This is how magnetic resonance imaging, MRI, works. A person is placed in an MRI scanner, which is in fact a large solenoid that produces a magnetic field B. The MRI scanner has a gradient, meaning that the magnetic field varies according to position, such that the nuclear magnetic resonance will vary with position too. The molecular structure of human tissue can then be imaged in high detail.

The main MRI signal comes from fat and water, since these compounds are highest in protons. Therefore, MRIs can be performed to map out soft tissue, as opposed to x-rays which map hard tissue. Amongst other various medical uses, this technique is highly used to trace out cancerous tumors in the brain and plan complicated and life-saving surgeries.

Physics saves the day again.