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In the last lesson we saw that the binding-energy-per-nucleon curve rises steeply from hydrogen, peaks at iron-56, and declines gently to uranium. This single feature explains both of the great energy-releasing nuclear processes of the twentieth century: fission (splitting heavy nuclei towards the peak) and fusion (joining light nuclei towards the peak). Together they power the reactors that supply a significant fraction of the world's electricity and the stars that light up the night sky. They are also, of course, the physics behind nuclear weapons.
This lesson covers section 6.4.3 of the OCR A-Level Physics A specification (H556), describing both processes qualitatively and quantitatively, and explaining why they are so hard to do in practice even though the energies involved are enormous.
Nuclear fission is the splitting of a heavy nucleus into two smaller nuclei, typically of roughly comparable mass, with the release of several neutrons and a large amount of energy. It was discovered in 1938 by Hahn and Strassmann, interpreted by Meitner and Frisch, and — with terrible speed — exploited for both weapons and power within a decade.
The classic fission reaction is the neutron-induced fission of uranium-235:
²³⁵₉₂U + ¹₀n → ²³⁶₉₂U* → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3 ¹₀n + energy
A slow ("thermal") neutron is absorbed by a U-235 nucleus, forming a highly excited U-236 compound nucleus. This excited nucleus is unstable and deforms into a dumbbell shape, eventually splitting into two unequal fragments — in this example, barium-141 and krypton-92. Three fast neutrons are also released, along with gamma photons and beta decay products from the fragments. The total energy release is about 200 MeV per fission event.
Key features of fission:
A \approx 95 and A \approx 140, not at the symmetric A \approx 118. The asymmetry is a shell-structure effect.N/Z ratio, which the fragments inherit), so they beta-decay through long chains to reach stability. This is the source of the long-lived radioactive waste from nuclear reactors.Because each fission releases 2–3 new neutrons, and each new neutron can in principle induce another fission, a chain reaction becomes possible. In a block of U-235, if on average at least one of the new neutrons from each fission goes on to cause another fission, the reaction will sustain itself. If more than one does, the reaction will grow exponentially.
The key quantity is the multiplication factor k, defined as the average number of neutrons from each fission that go on to cause a subsequent fission. Three regimes:
k < 1: subcritical. The chain reaction dies out.k = 1: critical. The reaction runs at a constant rate. This is the regime of a power reactor.k > 1: supercritical. The reaction grows exponentially. Controlled supercriticality is used in reactor startup; uncontrolled supercriticality is a nuclear explosion.The multiplication factor depends on:
For a given geometry and purity of fissile material, there is a minimum mass below which k < 1 and a chain reaction cannot be sustained. This is called the critical mass. For a bare sphere of pure U-235 metal, the critical mass is about 52 kg; for pure Pu-239 it is about 10 kg. Surrounding the fissile core with a tamper (a dense material that reflects escaping neutrons back in) reduces these figures significantly.
You do not need to memorise the numbers, but you should understand the qualitative reason: in a small sample, too many neutrons escape from the surface before causing further fission; in a large sample, enough are retained to sustain the reaction.
A nuclear power reactor runs a controlled, self-sustaining chain reaction at k = 1. The key components are:
_2O), heavy water (D_2O), and graphite are the common choices.k; withdrawing them raises k. Operators adjust them continually to keep k = 1.The thermal power of a typical reactor is around 3 GW, corresponding to about 10^{20} fissions per second. Each fission releases about 200 MeV, and the total is converted to electricity by a steam turbine cycle at ~33% efficiency, giving ~1 GW of electrical output.
Nuclear fusion is the joining of two light nuclei to form a heavier, more tightly bound nucleus, releasing energy. Fusion is how the Sun and other stars produce their energy: the net result of the proton-proton chain in the solar core is that four protons combine into one helium-4 nucleus, releasing 26.7 MeV per helium produced.
The simplest terrestrial fusion reaction — and the target of ITER and future commercial fusion reactors — is the deuterium-tritium (D-T) reaction:
²₁H + ³₁H → ⁴₂He + ¹₀n + 17.6 MeV
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