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Fission

Energy and power · level 8, lesson 2 of 6

A question to start

NASA's Kilopower test reactor had a uranium core about the size of a paper towel roll. A system like it could give up to 10 kW of electricity for at least 10 years. How can so little fuel give so much?

The idea

A uranium-235 nucleus that absorbs a neutron becomes unstable and splits in two. This is fission. The two pieces fly apart, and two or three new neutrons come out too. Each fission releases about 200 MeV, which is

\[200 \times 1.6\times10^{-13} \text{ J} = 3.2\times10^{-11} \text{ J}.\]

The new neutrons can split more nuclei: a chain reaction. In a reactor it is kept steady, so that each fission leads on average to exactly one more. Materials that soak up neutrons, in control rods or drums, set the rate.

neutronU-235two pieces more U-235

Where does the energy come from? The pieces, together, have slightly less mass than the uranium and the neutron that went in: about 0.09% less. That mass is the energy, by \(E = mc^2\).

Worked examples

1. A kilogram of uranium-235. It holds \(\dfrac{1000}{235} \times 6.02\times10^{23} = 2.56\times10^{24}\) nuclei. Splitting them all gives \(2.56\times10^{24} \times 3.2\times10^{-11} = 8.2\times10^{13}\) J, about 23 GWh of heat.

2. Against petrol. Petrol gives about 46 MJ per kg. \(8.2\times10^{13}/4.6\times10^7 \approx 1.8\) million times as much.

3. The mass lost. \(m = E/c^2 = 8.2\times10^{13}/(9\times10^{16}) = 9\times10^{-4}\) kg: under a gram from each kilogram.

4. Kilopower's fuel. Suppose a 10 kW unit turns a quarter of its heat into electricity. Its heat is 40 kW. Over 10 years, \(40{,}000 \times 3.16\times10^8 \text{ s} = 1.3\times10^{13}\) J, which splits only about 0.15 kg of uranium-235. The core holds more than that, because a reactor needs enough uranium to keep the chain going.

Try it

  1. What starts the fission of a uranium-235 nucleus?
  2. Why can a chain reaction grow very quickly if it is not controlled?
  3. Find the energy from splitting 1 g of uranium-235.
  4. A reactor gives 100 kW of heat for a year (\(3.16\times10^7\) s). What mass of uranium-235 does it split?
Answers
  1. It absorbs a neutron.
  2. Each fission gives out two or three neutrons, and each can cause another fission.
  3. \(8.2\times10^{10}\) J, about 23 MWh.
  4. \(100{,}000 \times 3.16\times10^7 = 3.2\times10^{12}\) J; \(3.2\times10^{12}/8.2\times10^{13} = 0.039\) kg, about 39 g.

Common mistake

"Only nuclear reactions turn mass into energy." Any release of energy lowers the mass. Burning fuel does too, but the change is about a million times smaller and far too small to weigh.

Where it leads