## Saturday, June 10, 2006

### Astronomical Data - Part 1b: Where Does Light Come From?

In my last post on this topic, I gave a very abbreviated overview of the nature of light and pointed out that it is both a particle that carries discreet energies in the form of a photon, yet also exhibits the interference patterns characteristics of waves.

Yet, in this, I made the assumption that the light, in whatever form it is, already existed. But that light had to come from somewhere. And that's the topic of this post.

In short, light comes from atoms. That's the quick answer, but before I try to give the more complete one, let's review some basic concepts that you may or not remember from high school.

Source

This is the basic model of an atom with which you're probably familiar.

In this we see the nucleus (although represented millions of times too large) which contains protons and neutrons (the red and blue balls in the center). Around the nucleus is a swarm of electrons. In a normal atom, the number of negatively charged electrons is the same as the number of positively charged protons which makes the atom neutral.

However, while you're probably familiar with this model of the atom, it's also very outdated. While it's easy to picture electrons orbiting in that manner, it's actually incorrect.

With pretty little circular orbits like that you'd expect that you could just make the orbit a little larger and still have no problems. There shouldn't be any preferred orbits. But as you're probably expecting by now, that's not the case.

In fact, electrons are only able to be in very specific orbits which are conveniently called "orbitals". And not all orbitals are created equal. In fact, none of them are.

To get a better feel for this, let's take consider the simplest case we can; the hydrogen atom. This atom has a single proton in the nucleus, and is orbited by one electron. Can't get any simpler than that.

The smallest orbit that an electron is called the "s orbital". When electrons are in this state, they have the least amount of energy possible, which is why this level is often referred to as the "ground state". The s orbital is able to hold at most, two electrons.

Beyond the s orbital, the next smallest orbit that electrons can possess is called the "p orbital". When electrons are in this orbital, or any other besides the s orbital, they're said to be excited which basically means they have extra energy (kinda like that excited little kid who'd never been on an airplane before that I sat next to this morning). But unlike hyperactive children, these electrons don't have energy in the sense that they're bouncing off the walls.

Instead, you can think of this energy as a sort of potential energy. Potential energy is something that you're probably quite familiar with, even though you may not realize it. The most common instance we see of it, is with objects that are raised some distance from the ground. If an object is raised, it accumulates potential energy due to it's height. The higher an object is, the more potential energy it has.

If you want to see just how much potential energy an object has in a case like this, drop it. The potential energy will be converted to kinetic energy (energy of motion). Common sense will tell you that a rock dropped from the top of a cliff is going to end up hitting the ground a lot harder than that same dropped from your hand.

The reason for this is that the rock dropped from the higher point had more potential energy. Since energy must be conserved, when the rock falls, it has to convert that energy to kinetic energy.

The same sort of thing happens with our little electron. If we have an electron in the p orbital, that's like having the rock raised off the ground. However, just as a rock will fall if unsupported, so too will an electron. If that electron is in the p orbital and there aren't two electrons filling that s orbital to support it, then that electron will fall back down to the s orbital.

Since the p orbital was the one with higher energy (the excited state), that means that the electron is going to have to convert that potential energy into another form. But instead of picking up speed like our hypothetical rock, the electron does something a little different; It spits out a photon.

This photon will have the exact same energy as the electron lost as it fell down.

But remember how light can't just be thought of as a particle? Here's a great place to think of it as a wave again. Waves are described by two main properties: their amplitude (the height of the wave) and their wavelength (the distance between successive waves). What important to know here is that the smaller the wavelength, the higher the energy of that wave is.

That means that if you have a really energetic photon/wave, it will have a very short wavelength. These are things like x-rays, gamma rays. They have lots of energy and can do serious damage to your cells the same way a highly energetic kid can do serious damage to a china shop. That's the reason you try to limit your exposure to such wavelengths. On the other hand, if there's a small change in the energy, the wavelength will be long giving you things like micro waves and radio waves.

If you're really following everything here, what you should realize is that these falling electrons are responsible for creating photons of every sort we observe; from radio waves to cosmic rays. In reality, it's all dictated by a rather simple formula that gives the energy of a photon in relation to its wavelength:

In which lambda is the wavelength, c is the speed of light (3 x 108 m/s), and h is just a number, known as Planck's constant (6.6 x 10-34 m2kg/s).

However, you might have spotted a problem here. So far we only know that the electron can go from the p orbital to the s. Every time this happens, it will release a consistent amount of energy, which would correspond to a single wavelength. That means the entire universe should be monochrome! This obviously contradicts what we see since the world is filled with pretty colors and all those other wavelengths that we can't even see with our eyes.

You're probably expecting that there must somehow be more transitions with different energies. And you'd be right. Beyond the p orbital, there are several more including the d and the f orbitals.

So when you start putting everything together, you'll eventually start getting a picture like this:

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In this schematic diagram, you'll see the ground state at the bottom. Above it is each excited state. What you'll notice is that each next excited orbital is closer to the previous one than the one before it. Thus, they start to bunch up. Eventually they bunch up so much, they're not really going anywhere, hence that top line labeled with the infinity symbol.

We'll come to that in a moment, but for now, what you may be realizing is that, even with all these additional orbitals, we still haven't figured out how to get every different wavelength out there. Since there's only those discreet transitions it can make, it can still only produce photons at very specific wavelengths. We haven't solved the problem at all!

But that's where that last line with the infinity symbol comes in. What that line represents is the "ionization energy" for hydrogen. If an atom is ionized, that just means that it's lost an electron somehow. That means the atom as a whole will have more protons than it does electrons and it need to find a new electron to be neutral again.

Fortunately, electrons aren't too hard to find. And when an electron falls into one of those orbitals from past that ionization line, it can fall from any distance. That means it can fill in all those "gaps" that electrons jumping from all those bound orbitals just can't do. So now, we can successfully explain light of any wavelength out there!

So now that we know where light comes from, we can be prepared for my next post on this topic, which we receive this light. However, as we'll see, it's not quite as simple as catching a net and refusing to let it go until it tells us where it came from. Light takes a long way to get here, and there's dozens of things astronomers have to compensate for before they're able to get any useful information. The process of getting rid of all the junk is known as "data reduction".

Thus, my next post on this astronomical data topic will deal with a brief history of how astronomers have captured this light, with emphasis on how we capture and "reduce" it with modern instrumentation.

My last section I wanted to cover is how we actually learn so many things from a lonely photon. To bridge these two sections, I think it may be useful to digress into a brief discussion on astrophotography which of course, wouldn't be complete without many beautiful pictures.

So that's it for today on this topic. I hope you've found it enlightening (no pun intended).