We've all heard of carbon-dating; it's practically a household word these days. No, it's not when two carbon atoms start to date (although, that's super cute), but rather, the scientific method that allows archeologists to declare how old stuff is. Stuff could be anything, a bone, dinosaur poop, a clay pot.
There are a few isotopes of carbon on Earth. The most abundant and stable one is Carbon-12, which is 99% of all the Carbon on the planet. Carbon-14 is formed on Earth as high energy cosmic-rays from outer space interact with our atmosphere, where carbon dioxide resides. The most prominent production of C-14, accounting for 99.63% of it, occurs as thermal neutrons interact with nitrogen, as seen here:
On Earth, both C-14 and C-12 are absorbed by living organisms in the form of carbon dioxide, CO2. Throughout its life, a living organism maintains a steady ratio between these two isotopes of carbon, with an extremely small percentage of C-14.
A living organism will also keep a balanced amount of C-14 throughout its life. Remember that C-14 is an unstable isotope with a half-life of t1/2 = 5,730 years. It β-decays back to the stable N-14.
C-12, on the other hand, is a stable isotope. When an organism dies, its levels of C-12 remain the same, however, since it's well, dead, it no longer intakes C-14 and C-14 decays, so the ratio of C-12 to C-14 begins to change at death.
By measuring the ratio of C-12 to C-14 and knowing the half-life of C-14, scientist calculate the age of a specimen. That's cooler than Indiana Jones, right there.
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 Be. 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 Be. 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.
The Expansion of the Universe
Remember absorption spectra? We said we could use it identify what a star was made out of, or even a planet's atmosphere. We weren't lying, but that's only the beginning of it.
Let's go back to the Doppler Effect in our study of sound waves13. The siren of a police car moving towards us has a higher pitch. As the car moves away, the pitch drops. When a sound pitch "drops," the frequency decreases. That makes sense. The police car is moving away from us, so the sound waves have to travel a little more distance to reach our ears. Their wavelength increases.
The same thing happens with objects that give off light. In the 1920's, an astronomer named Edwin Hubble studied distant galaxies and analyzed their light. He came to the remarkable conclusion that their absorption spectrum was shifted to longer wavelengths, and that the exact shift depended on the exact distance to the galaxy. Longer wavelengths means redder colors. This phenomenon is called redshift.
If light from galaxies is redshifted, then they are moving away from us at velocities v proportional to their distance d from Earth. With math, Hubble wrote the Hubble law: v = Hod, where Hois the Hubble constant. Its exact value varies from 15 to 30 kilometers per second per million light years.
If the universe is expanding, then there was a point in the distant past when it was a lot smaller. The Hubble Law hints at the fact that all galaxies originated from the same place. This is where the idea of the Big Bang comes from. The universe could've been created with a huge explosion– an explosion so powerful that we're still observing its (accelerating) effects.