What nuclear means

I am designing an ion thruster, and nuclear physics got onto my reading list through it: the power for a serious electric drive in deep space comes from a reactor or a decaying isotope, and anything that flies above the atmosphere lives in radiation. This essay and the ones that follow are notes from that work, written as I learn it.

Radiation and ionization

Nuclear physics is the study of what comes out of the nucleus of an atom, and what it does to whatever it hits. What comes out is called radiation. Interesting things happen when this radiation has enough energy to knock electrons off atoms. We call them ionizing radiation.

Radiation is anything that travels and carries energy. Light is radiation. Radio is radiation. A thrown stone is radiation if you want to be strict about it. The word has no menace in it.

Ionizing means able to knock an electron off an atom. An atom that has lost an electron is called an ion, and the event is an ionization. That is all. Chemistry is entirely about the electrons around an atom, so radiation that removes electrons changes chemistry, and radiation that cannot remove electrons does not. Ionizing radiation rearranges the molecules in a living cell. Below the threshold, radiation can at most heat molecules or lift their electrons to a higher energy without removing them. Ultraviolet does the second to DNA, and an excited base sometimes bonds to its neighbour. That is sunburn, and it happens without a single ionization. I have written it up separately in How ultraviolet burns you.

So the question about any radiation is one question: does each piece of it carry enough energy to remove an electron, yes or no?

The threshold

An electron is held to its atom by a definite amount of energy. For the single electron in hydrogen it is 13.6 electron volts. For xenon, the propellant in my thruster, it is 12.1. For most molecules it is 7 to 10. Breaking a chemical bond without removing an electron takes less, about 3 or 4, and that is where chemical damage starts. An electron volt is the energy an electron picks up crossing one volt; it is a tiny unit, about 1.6 × 10⁻¹⁹ joules, and it is the natural currency of chemistry.

Light arrives in packets called photons, and each photon’s energy is set by its colour, nothing else. Short wavelength, high energy. The rule is simple enough to carry in your head: energy in electron volts equals 1240 divided by the wavelength in nanometres. Red light at 650 nanometres is 1.9 electron volts. Blue at 450 is 2.8. Ultraviolet at 300 is 4.1. A dental X-ray is up to about 60,000. A gamma ray from caesium-137 is 662,000.

Now the part that trips people up. Brightness does not help. A floodlight is a very large number of photons, each carrying 2 electron volts. None of them can remove an electron that is held by 13.6, and ten billion of them cannot do it either, because they arrive one at a time. A dim ultraviolet lamp, each photon carrying 5 electron volts, breaks chemical bonds all day. This was Einstein’s 1905 paper, the one he got the Nobel prize for, and it is why sunburn comes from ultraviolet and not from the much brighter visible light beside it.

One photon at a time. Slide along the spectrum and watch what a photon does when it reaches the atom. Below about 4 electron volts the atom only warms up. Turn the brightness up as far as it goes: still nothing leaves. Past about 7 electron volts a single photon starts taking electrons with it.

A microwave oven runs at 2.45 gigahertz. That is a wavelength of 12 centimetres and a photon energy of ten millionths of an electron volt. A phone is in the same range. Neither is within a factor of a million of removing an electron. They can heat you, which is what the oven is for, but heat is all they can do.

The counter

Arguments about radiation should be settled by an instrument, and the instrument costs less than a phone. A Geiger counter is a brass tube full of gas with a wire down the middle and about 500 volts between the wire and the wall. When one ionizing particle passes through, it knocks electrons off a few gas atoms. The voltage drags those electrons toward the wire, they knock off more on the way, and within a microsecond a single ionization has become a measurable pulse of current. The counter turns that pulse into a click and a flash. One click, one ionizing event. It cannot tell you what kind of particle it was, but it cannot be fooled about whether there was one.

A counter you can hold things up to. With nothing nearby it clicks about twenty times a minute. Switch on the light bulb, the microwave, the phone: nothing changes. Bring out a sealed check source, choose the isotope, and slide it toward the tube. The rate climbs as one over the distance squared, and it depends on what the isotope emits: the tube counts betas and gammas but its brass wall stops alphas, so a smoke-detector americium disc barely registers. Turn the sound on if you want the real experience.

Two things the counter settles in thirty seconds. Microwaves do not emit ionizing radiation. Phones do not emit ionizing radiation. Both are radiation, both are below the threshold by a factor of a million, and the counter does not move. If a claim about radiation cannot survive a Geiger counter, it is not a claim about ionizing radiation.

Twenty clicks a minute from nowhere

The counter clicks with nothing near it. That background is real ionizing radiation, and it is worth knowing where it comes from, because it sets the scale for everything else.

Cosmic rays arrive from space and shower the atmosphere with secondary particles; the dose roughly doubles every 1,500 metres you go up. The ground contains uranium, thorium and potassium, and so does every brick and granite worktop made from it. The air contains radon, a gas that leaks out of the ground as uranium decays, and radon is the largest natural source for most people on Earth. And you are radioactive: the potassium in your body includes potassium-40, and about 4,400 of those atoms decay inside you every second, with another 3,000 carbon-14 decays alongside.

The unit for dose is the sievert, which weights the energy deposited in tissue by how much biological damage that kind of radiation does. It is a large unit. Doses in ordinary life come in millisieverts, thousandths of a sievert. The world average from natural sources is 2.4 millisieverts a year.

A year of dose. World-average natural sources, in millisieverts. Move to altitude, move to granite country, add the X-rays and scans you had. The limit for dose added to the public by a nuclear facility is 1 millisievert a year on top of this. A radiation worker may take 20.

Medicine gives most people far more dose than any power station ever will. A single CT scan is three years of natural background. Take the scan if you need it. The numbers are what matter, not the word.

Why the nucleus is different

So far everything has been about electrons, and electrons are the business of chemistry. Here is why the nucleus is a different business.

Burning a carbon atom in coal releases about 4 electron volts. That is a chemical bond rearranging: electrons moving between atoms. Splitting one uranium-235 nucleus releases about 200 million electron volts. The nucleus is bound about a million times more tightly than its electrons are, and when you rearrange it, you get paid at that scale. It takes almost nothing to start. A neutron drifting in at thermal speed is enough to tip the nucleus over a barrier of about 6 MeV, and the 200 MeV comes out as the two halves fly apart.

Einstein’s other 1905 result says where the energy came from. The fragments of a split uranium nucleus weigh a little less than the nucleus did, about one part in a thousand, and the missing mass left as energy at the rate of c² joules per kilogram. For coal the same accounting holds, but the mass that disappears is one part in ten billion, too small to weigh.

Energy from a mass of fuel. Log scale: each gridline is a thousand times more. Slide the mass and all four bars move together. One kilogram of uranium-235, fully split, is the energy of about three million kilograms of coal, or twenty kilotons of TNT. The same kilogram turned entirely into energy would be a thousand times more again.

This ratio, fifty million to one atom for atom and three million to one kilogram for kilogram, is the whole reason the subject exists. It is why a submarine can run for twenty years on a lump of metal the size of a wastepaper basket, why a reactor’s lifetime fuel fits in a swimming pool, why the bombs were possible, and why a probe heading out of the solar system has run on about a dozen kilograms of plutonium for nearly fifty years. Every argument about nuclear power, weapons, medicine and propulsion is downstream of this one number.

The four kinds of nuclear radiation - Alpha, Beta, Gamma, Neutrons

What comes out of a nucleus is a short list. Space adds a fifth kind that matters for anything that flies: protons from the sun and from cosmic rays. They behave like alphas with half the charge, and I will come back to them.

Each one loses energy by a different mechanism, and the mechanism sets the shape of the path and how far it goes. The question to ask of each is: what does it collide with, and how heavy is it compared with what it hits?

Alpha is a helium nucleus: two protons, two neutrons, charge +2, mass of about 7,300 electrons. It ploughs through the electron clouds of the atoms it passes, knocking electrons loose thousands of times per micrometre. Each collision is with something 7,300 times lighter, so it barely deflects the alpha and takes only a sliver of its energy. The track is dead straight, densely ionizing, and ends abruptly when the energy runs out: a few centimetres of air, a sheet of paper, the dead outer layer of your skin. A cannonball through fog. Harmless outside you. Dangerous inside you, because all of that energy lands in a few cells.

Beta is a fast electron, charge −1. It scatters off other electrons of exactly its own mass, and off nuclei, and a collision with an equal mass can throw it through a large angle. So the path zigzags, and the total distance travelled is much longer than the depth reached. Betas from one source also leave with a spread of energies, which is why they stop at different depths. A ping-pong ball in a room full of ping-pong balls. A few metres in air, a few millimetres of aluminium.

Gamma is a photon, no charge, no mass, energies from tens of thousands to millions of electron volts. It does not lose energy gradually. It flies in a straight line until one event happens: it is absorbed outright, or it scatters once off an electron and continues at a new angle with less energy. Nothing slows it in between. So the track is a straight line of random length, and all that matter changes is the odds per centimetre of that one event. A beam thins out exponentially with depth. Dense matter thins it fastest: 5 centimetres of lead absorbs about 998 of every 1,000 caesium-137 gammas, and the other two come through untouched.

Neutrons have no charge, so the electrons do not exist for them. A neutron only interacts when it hits a nucleus. Off a heavy nucleus like lead it bounces away in some new direction with almost no energy loss, so lead scatters it about but barely slows it. Off a hydrogen nucleus, which has the same mass, it is one billiard ball striking another: a big deflection and on average half its energy gone. About twenty such collisions bring a fast neutron down to the speed of the surrounding atoms, after which a nucleus captures it. That is why the shielding for neutrons is water, paraffin and concrete, all full of hydrogen, and why the track inside them is a jagged random walk. Neutrons are what keep a reactor going, and in practice they are the only one of the four that makes other material radioactive.

What stops what, and why the tracks look different. Six of each kind, fired at paper, aluminium, lead and water. Switch slabs off to see what each one really needs. Alphas run straight and all die in the paper at the same depth. Betas zigzag and die in the paper or the aluminium, depending on the energy they left with. Gammas fly straight until one chance event absorbs them, mostly inside the lead, with the odd one getting through. Neutrons pass the lead barely slowed and random-walk to a stop in the water. Charged particles have a range; neutral ones have a probability.

Takeaway

Radiation is anything that travels with energy.
Ionizing radiation carries enough energy per particle to remove an electron, and the threshold is about ten electron volts.
A Geiger counter detects it one event at a time and is the go to device to detect ionizing radiation.
Background radiation is 2.4 millisieverts a year and comes mostly from the ground, the air and your own body.
The nucleus pays out at a million times the scale of chemistry, which is the whole reason anyone cares.
There are four kinds of nuclear radiation, each stopped by something different.