ATE (How does the Hydrogen bomb work?)

This is the third in a series of answers to questions put to me by students at a local secondary school. The sheet of paper they gave me was titled "Ask the Expert", but I don't really feel like "an expert" let alone "the expert" so I've changed the post title to ATE.

J asks "How does a hydrogen bomb work?"

Given the serious resources needed to put any of what follows into practice, I'm confident that J, or anyone else who reads this, will not be in any better position to actually make a bomb than they were before.

Look at an atom and you'll find that it has a very dense positively charged nucleus surrounded by a cloud of negatively charged electrons. If the nucleus was the size of a tennis ball then the atom as a whole would be about 10km across. 

The nucleus is made from positively charged protons and, as their name suggests, neutrally charged neutrons. Since like charges repel, and the closer you put them the harder they repel, there must be an even stronger force (helpfully known as the strong nuclear force) that stops the protons in the nucleus simply blasting the whole thing apart. This is the reason why there's a limit to how many protons a nucleus can contain and explains why bigger stable nuclei tend to have a larger proportion of neutrons (they provide extra glue to hold it all together).

You may recall the most famous equation in physics (E = mc²). This is a consequence of Einstein's special theory of relativity and quantifies the fact that mass and energy are interchangeable. Measure the mass of all the fuel and air that goes into a coal fired power station and compare this with the mass of all the ash and flue gases that come out and you'll find that a little bit less comes out than goes in. Put this mass into the famous equation and you'll get the total energy (heat and electricity) that the power station produced.*

If you compare the mass of a nucleus with the masses of its component parts (i.e. all the protons and neutrons) you find that the nucleus weighs less than the sum of its parts. If you wanted to pull the nucleus apart you'd have to supply this missing mass (energy) and so it represents what's called the binding energy of the nucleus. If you look at a whole load of different nuclei and divide the total binding energy of each by the number of nucleons (the collective term for protons and neutrons) you get the binding energy per nucleon.

Plot a graph of this binding energy per nucleon against the size of the nucleus and you get an interesting curve.

The nuclei of light atoms such as Hydrogen and Helium are on the left and of large atoms like Uranium are on the right. You'll notice that if you were to stick two light nuclei together to make a bigger one then the binding energy per nucleon would increase. This happens all the way up to Iron (Fe). Similarly, if you could persuade a really big nucleus to split into two or more parts then the binding energy per nucleon would also increase. The first process, putting two nuclei together, is known as fusion. The second, when a big nucleus falls apart, is know as fission. 

In a conventional hydro electric power station, falling water turns a turbine and produces power. The water ends up closer, more tightly bound, to the earth than it was at the start. So, increasing the water's binding energy releases energy that's used by the turbine. Similarly if two light nuclei fuse, or a heavy nucleus splits, then energy is released. Lots of it.

The first nuclear bombs were purely fission devices. It turns out that there are particular isotopes of Uranium and Plutonium that are largely stable until hit by a neutron, at which point they fall apart. This not only releases tremendous amounts of energy but also spits out a few more spare neutrons. If one of these should hit another nucleus then that too will split and, if there's enough material (a critical mass) and its in the right shape, you can get an explosive chain reaction. 

Choose the right nuclei, and fission is relatively easy. Find ways to control the reaction so it doesn't get out of hand and you can have a nuclear power station. Fusion is much more difficult for the simple reason that to get two nuclei to fuse you've got to get them very close together and, because they're both positively charged, they really don't like this. But, it can be done provided that they're moving fast enough to overcome the repulsive electrical force. 

Now you can speed up a nucleus in two ways. One at a time in a particle accelerator, or a whole bunch of them by simply raising the temperature. Deuterium is an isotope of Hydrogen which contains a proton and a neutron rather than just a proton. To get two Deuterium nuclei to fuse takes a temperature of around 100 million degrees. The interior of the Sun is as hot as this, and its enormous gravity stops everything flying apart, but these conditions are much harder to achieve on Earth.

But, there is one place where we can get temperatures and pressures high enough to initiate a fusion reaction and that's inside a conventional fission powered nuclear bomb. So a Hydrogen bomb is simply a fission device with the right isotopes of Hydrogen carefully packed around it in such a way that, when the fission bomb goes off, they hang around long enough to start fusing into Helium.

*A 1GW station produces 1 x 10⁹ J of electrical energy per second. It's about 40% efficient so this is about 40% of the total energy produced. Hence the total energy = 1 x 10 ⁹ / 0.4 = 2.5 x 10⁹ J. In a year this adds up to a total of 1.3 x 10¹⁵ J. The speed of light c = 3 x 10⁸ m/s so putting this much energy into the equation E = mc² gives a mass of 0.015kg (about 6 ounces). Just think of all the coal trains going in, and all the gases coming out, and I think you'll agree this might be quite difficult to measure.