Nuclear fission

The Ebn curve is flat at about 8.0 MeV for 30 < A < 170 and lower on either side. The more tightly bound a system, the less its total mass, so turning less tightly bound nuclei into more tightly bound ones releases energy: in fission of a heavy nucleus or fusion of light ones.

Coal and petroleum rely on chemical reactions involving energies of electron volts; nuclear reactions involve MeV. So, for the same amount of matter, nuclear sources give about a million times more energy: fission of 1 kg of uranium gives about 10¹⁴ J, burning 1 kg of coal about 10⁷ J.

Bombarding nuclei with particles such as protons, neutrons or alpha-particles opens up reactions beyond natural decay. The most important neutron-induced one is fission.

A neutron striking ²³⁵₉₂U forms ²³⁶₉₂U, which splits into two intermediate-mass fragments, for example ¹⁴⁴₅₆Ba + ⁸⁹₃₆Kr + 3 neutrons (Eq. 13.10), or ¹³³₅₁Sb + ⁹⁹₄₁Nb + 4 neutrons (Eq. 13.11). Another outcome is ¹⁴⁰₅₄Xe + ⁹⁴₃₈Sr + 2 neutrons (Eq. 13.12).

The fragments are radioactive and emit β particles one after another until they reach stable end products.

The energy released (Q value) is about 200 MeV per fission. Estimate: a nucleus of A = 240 (Ebn ≈ 7.6 MeV) splits into two of A = 120 (Ebn ≈ 8.5 MeV), a gain of about 0.9 MeV per nucleon, so 240 × 0.9 = 216 MeV in all.

This energy appears first as kinetic energy of the fragments and neutrons, and ends up as heat in the surroundings. Nuclear reactors that make electricity run on fission; uncontrolled fission is the source of an atom bomb's energy.

In a nuclear reaction the numbers of protons and of neutrons are each conserved (Example 13.4). The energy comes from the difference in total binding energy between the two sides, which shows up as a difference in mass.