Alpha particles

Here's a photograph of a little demonstration cloud chamber:

To the right in the chamber, diagonally across the picture, there's a tungsten welding rod. These rods work better if traces of other substances are added to them and this one has a small amount of thorium oxide. Thorium is a naturally occurring radioactive substance so these welding rods are very slightly radioactive, not enough to endanger the lives of welders - obviously! - but enough to be interesting in the cloud chamber.

Thorium is chemical element number 90. It has chemical symbol Th. The isotope we find in nature is ²³²Th, "thorium-232". From webelements.com we find that its half-life is 14 billion years - it stays radioactive for a long, long time, but at a low level.

Look at the two misty streaks heading left from the welding rod. Each of these is the path of a single alpha particle, a nucleus of the element helium, ejected forcibly from a thorium nucleus when it spontaneously decays. As it travels through the air in the chamber the fast-moving alpha particle knocks electrons out of atoms, leaving a trail of ions behind it. The chamber, cooled well below room temperature, contains alcohol vapour as well as air. Each ion becomes the centre for the formation of a little droplet of liquid alcohol and the path of the alpha particle becomes visible as a string of liquid droplets. The cloud chamber, Nobel-prize winning invention of the Scot CTR Wilson, doesn't quite show us individual electrons and ions but it does let us see where they go and how they move.

Let's do some sums. Alpha-particles emitted in radioactive decay all have more or less the same energy, depending only on which radioactive nucleus we started from. There's a table at this link, telling us that an alpha particle emitted by ²³²Th has an energy of 3.8111 MeV.

The eV - "electron-volt" - is the convenient unit of energy in the subatomic world. We need 14.5 eV of energy to completely liberate an electron from a nitrogen atom and make it into an ion - ionise it; 13.2 eV for an oxygen atom. The average energy of a photon of sunlight is about 2 eV. "M" stands for "mega": one million. So just one of these ²³²Th alpha's will ionise hundreds of thousands of atoms.

(Yes, we call them "alpha's" in a familiar way. Maybe even α's, using the Greek symbol. They're our friends.)

As an α travels away from the nucleus that spawned it, through the air of the laboratory, it loses energy by knocking electrons out of atoms. Each ion created robs the α of roughly 30 eV. How far can it go in air?

The answers to such questions are well known, even available online. From the NIST ASTAR program, available online, we learn that a 4 MeV α stops in a column density of 0.003 grams per square centimetre of air. We need to think about how much material the α meets, and this is best expressed as the amount of material in a cylinder of 1 cm² area. This hypothetical cylinder should include 0.003 grams. If it's very tenuous, like the air we might meet in the stratosphere, the cylinder has to be very long. At sea level where the air is much denser, it will be shorter. But it needs to include 0.003 grams. Air at sea level has a density of just over 0.001 grams per cubic centimetre, so the α will travel (0.003 grams per cm²)÷(0.001 grams per cm³) = 3 cm - slightly over an inch, just as we see in the picture.

In solar flares, ions sometimes get accelerated to energies of MeV and beyond, by strong electric fields, not in radioactive decay. The same ideas apply. How far will they go? How much will they heat up the solar atmosphere in the process? In the cloud chamber we can see much of the relevant physics, even for this remote and exotic application.