You may recall that when mass is converted to energy, a giant multiplier comes into play. Einstein's famous equation says that the amount of energy is proportional to the amount of converted mass. But the latter is multiplied not just by the speed of light, but by its square.
Now the speed of light is already a big number: 300,000 kilometres per second. It takes light less than 1.3 seconds to get from here to the Moon. Multiply that figure by itself, and then by the amount of mass, and its no wonder that the 12 kiloton atomic bomb that destroyed Hiroshima consumed just six tenths of a gram of mass.
How big a bomb would one gram of mass make? Twenty kilotons.
But we're not blowing stuff up this issue. We're building things. For that we need our energy in a more useful form than explosive energy, so let us see what twenty kilotons amounts to in useful energy of the kind that powers our computers and airconditioners.
That twenty kilotons of explosive energy -- all created from the conversion of just one gram of mass -- equates to more than 20 million kilowatt hours of energy. Here in wintry Canberra, according to my electricity bill, that's nearly four thousand times the amount of electrical energy used by my family home in the last three months. Put another way, it's enough to power a thousand homes for a year.
Put yet another way, at retail electricity prices it is $2.8 million worth ... from the conversion of just one gram of mass into energy.
In an atomic bomb the nuclear reaction is supposed to proceed as quickly as possible. But with a nuclear power station the reaction has to be controlled. Remember, the essence of a nuclear reaction is a chain reaction. Some random atom in a block of fissile material spontaneously self-destructs and, in the process, shoots off a couple of neutrons. These strike other atoms making them self-destruct, shooting off more neutrons and so on.
With a nuclear reactor you do not want this chain reaction to run away exponentially like that, so basically you have your fissionable material in a convenient form which can be physically manipulated. A common form is the fuel rod. Then you can use other materials to control the flow of neutrons between them. This material needs to absorb neutrons. The more masking to the flow of neutrons that this material provides, the cooler the reactor becomes. Reduce the masking and things heat up.
After this, the rest of the system is pretty much the same as a gas or coal fired power station: you have a heat exchanger to transfer the heat to water. That becomes steam and drives a turbine which, in turn, rotates a generator.
I've been a bit vague about control rods and materials, but that's because there are multiple ways of doing the details. Including the type of fuel that's used.
As we saw with the atomic bomb, there were two quite different kinds used within a few days of each other back in 1945. The Hiroshima one (called 'Little Boy') used uranium while the Nagasaki bomb ('Fat Man') used plutonium.
And so it is with nuclear reactors. There are designs which use uranium-235, others with use the rarer U-233, some that work with plutonium, and some that work with thorium-232.
All produce waste, and some of that waste can be radioactive. But in some cases the waste can itself become fuel for a different kind of reactor. Way back in the early 1950s the 'Breeder Reactor' was developed. This is a nuclear reactor that actually produces more fuel than it consumes.
These haven't been popular for a number of reasons, including the fact that uranium is cheap. But they may become more popular over time because some kinds of breeder reactor can, with reprocessing of used fuel, end up reducing the total amount of radioactive waste to just one percent of a conventional design.
Back To the Bomb
Incidentally, there was one actual useful purpose, beyond death and destruction, realistically proposed for real nuclear bombs. This went under the name of 'Project Orion', and was a plan to power spaceships by using atomic bombs. As you read on, remember that this was a real proposal, not science fiction. Some of the design work was done by the eminent physicist Freeman Dyson.
The concept is simple. You drop a nuke out the back of the spaceship and set it off. The spaceship sits on a very large, very robust metal plate, connected with long dampers. The blast from the bomb pushes the spaceship.
The amount of energy available would have turned space travel on its head. Instead of making things light so that they could be carried aloft, the spaceship had to be heavily constructed to absorb the blasts without damage. The largest version thought to be feasible in 1958 -- with technology then available, mind you -- was four hundred metres in diameter, weighed over eight million tonnes, and was 'fuelled' by more than a thousand nukes.
In the end the proposals fell foul of various regulations, not least those to do with atomic fallout, and it all came to nought.