Radioactivity

Lessons

Senior 6 · Chemistry

Radioactivity

5 lessons

Lesson 4 of 5

Nuclear Fission and Fusion

25 min

Barium where there should be none

In December 1938, in Berlin, the chemists Otto Hahn and Fritz Strassmann bombarded uranium with neutrons and expected to make elements slightly heavier than uranium. Careful chemical separations showed instead that one product was barium, an element with little more than half the mass of uranium. Lise Meitner, Hahn's long-time colleague, who had fled Germany that summer, and her nephew Otto Frisch explained the result early in 1939: the uranium nucleus had split in two. They called the process fission, and calculated that each split released about 200 MeV, millions of times more than any chemical reaction. Within a few years fission was powering reactors.

Definition

Nuclear fission: the splitting of a heavy nucleus, usually after it absorbs a neutron, into two medium-sized nuclei (fission fragments) and two or three neutrons, with the release of a large amount of energy. Example: ${}^{235}_{92}\mathrm{U} + {}^{1}_{0}\mathrm{n} \rightarrow {}^{141}_{56}\mathrm{Ba} + {}^{92}_{36}\mathrm{Kr} + 3\,{}^{1}_{0}\mathrm{n}$ .

Chain reaction: a self-sustaining series of fissions in which neutrons released by one fission cause further fissions.

Critical mass: the smallest mass of fissile material in which a chain reaction can sustain itself, because enough of the neutrons released cause further fissions instead of escaping.

Nuclear fusion: the joining of two light nuclei to form a heavier nucleus, with the release of energy. Example: ${}^{2}_{1}\mathrm{H} + {}^{3}_{1}\mathrm{H} \rightarrow {}^{4}_{2}\mathrm{He} + {}^{1}_{0}\mathrm{n}$ .

Fission equations

A uranium-235 nucleus can split in many different ways; more than a hundred different fragment nuclides are known. Two common examples:

{}^{235}_{92}\mathrm{U} + {}^{1}_{0}\mathrm{n} \rightarrow {}^{141}_{56}\mathrm{Ba} + {}^{92}_{36}\mathrm{Kr} + 3\,{}^{1}_{0}\mathrm{n}

{}^{235}_{92}\mathrm{U} + {}^{1}_{0}\mathrm{n} \rightarrow {}^{140}_{54}\mathrm{Xe} + {}^{94}_{38}\mathrm{Sr} + 2\,{}^{1}_{0}\mathrm{n}

Both balance: mass numbers $236 = 141 + 92 + 3 = 140 + 94 + 2$ , atomic numbers $92 = 56 + 36 = 54 + 38$ . The fragments are neutron-rich (they keep the high $\frac{N}{Z}$ of uranium), so they lie above the band of stability and are themselves β⁻ emitters. This is why spent nuclear fuel is intensely radioactive.

The chain reaction

Each fission releases 2 or 3 neutrons. If, on average, more than one of them causes another fission, the number of fissions grows in each generation (Figure 4.1), and the energy release runs out of control, as in a nuclear weapon. If exactly one does, the reaction runs steadily, as in a power reactor. There, the fuel is uranium enriched to a few per cent of uranium-235; a moderator (water or graphite) slows the neutrons so that uranium-235 captures them more easily; and control rods of boron or cadmium absorb surplus neutrons to keep the rate constant. Senior 6 Physics describes the reactor itself.

Figure 4.1: A branching chain reaction (one neutron from each fission shown going on in each direction; fragments drawn only for the first two generations).

Fusion

Light nuclei release energy when they join, because the product is more tightly bound than the reactants (the binding energy per nucleon rises from hydrogen up to iron, then falls slowly for heavier nuclei; see Senior 6 Physics). Fusion powers the Sun, where hydrogen nuclei combine through several steps whose overall result is:

4\,{}^{1}_{1}\mathrm{H} \rightarrow {}^{4}_{2}\mathrm{He} + 2\,{}^{0}_{+1}\mathrm{e}

(two neutrinos and gamma photons also leave). Nuclei repel each other strongly, so fusion needs temperatures of about $10^{7}$ to $10^{8}\,\mathrm{K}$ and a way of holding the hot plasma together. The Sun uses its own gravity; experimental reactors called tokamaks use magnetic fields.

Worked example 1: completing fission equations

Problem. (a) How many neutrons are released in ${}^{235}_{92}\mathrm{U} + {}^{1}_{0}\mathrm{n} \rightarrow {}^{144}_{56}\mathrm{Ba} + {}^{89}_{36}\mathrm{Kr} + x\,{}^{1}_{0}\mathrm{n}$ ? (b) Identify X in ${}^{235}_{92}\mathrm{U} + {}^{1}_{0}\mathrm{n} \rightarrow {}^{137}_{52}\mathrm{Te} + \mathrm{X} + 2\,{}^{1}_{0}\mathrm{n}$ .

Solution. (a) $A$ : $236 = 144 + 89 + x$ , so $x = 3$ . Check $Z$ : $92 = 56 + 36$ . ✓

(b) $A = 236 - 137 - 2 = 97$ ; $Z = 92 - 52 = 40$ , which is zirconium: X is ${}^{97}_{40}\mathrm{Zr}$ .

Worked example 2: energy from the mass defect of a fusion reaction

Problem. Calculate the energy released in ${}^{2}_{1}\mathrm{H} + {}^{3}_{1}\mathrm{H} \rightarrow {}^{4}_{2}\mathrm{He} + {}^{1}_{0}\mathrm{n}$ . Masses: ${}^{2}\mathrm{H}$ 2.014102 u, ${}^{3}\mathrm{H}$ 3.016049 u, ${}^{4}\mathrm{He}$ 4.002603 u, n 1.008665 u; $1\,\mathrm{u} \equiv 931.5\,\mathrm{MeV}$ .

Solution.

\Delta m = (2.014102 + 3.016049) - (4.002603 + 1.008665) = 5.030151 - 5.011268 = 0.018883\,\mathrm{u}

E = 0.018883 \times 931.5 = 17.6\,\mathrm{MeV} \text{ per reaction}

Per kilogram of fuel this is about $3.4 \times 10^{14}\,\mathrm{J}$ , roughly four times the energy per kilogram of uranium-235 undergoing fission.

Worked example 3: fission against combustion

Problem. Each fission of uranium-235 releases about 200 MeV. Calculate the energy released by the fission of 1.0 g of uranium-235, and the mass of methane ( $\Delta_\text{c}H = -890\,\mathrm{kJ\,mol^{-1}}$ , $M = 16.0\,\mathrm{g\,mol^{-1}}$ ) that would have to burn to release the same energy.

Solution. Nuclei: $\frac{1.0}{235} \times 6.022 \times 10^{23} = 2.56 \times 10^{21}$ .

E = 2.56 \times 10^{21} \times 200 \times 10^{6} \times 1.602 \times 10^{-19}\,\mathrm{J} = 8.2 \times 10^{10}\,\mathrm{J}

Moles of methane: $\frac{8.2 \times 10^{10}}{8.90 \times 10^{5}} = 9.2 \times 10^{4}\,\mathrm{mol}$ ; mass $= 9.2 \times 10^{4} \times 16.0 = 1.5 \times 10^{6}\,\mathrm{g}$ , about 1.5 tonnes. One gram of uranium-235 matches one and a half tonnes of methane.

Fission and fusion compared

	Fission	Fusion
Process	heavy nucleus splits	light nuclei join
Typical fuel	uranium-235, plutonium-239	deuterium and tritium (isotopes of hydrogen)
Conditions	slow neutrons; critical mass	about $10^{8}\,\mathrm{K}$ and confinement
Energy per reaction	about 200 MeV	17.6 MeV (D–T), but more per kilogram of fuel
Waste	long-lived radioactive fission products and actinides	mainly helium; reactor walls made radioactive by neutrons
Status	used in power stations since the 1950s	experimental; no power station yet

Warning

Common mistakes

Forgetting the neutron that starts the fission on the left-hand side; it counts in the mass-number balance.
Saying fusion and fission both release energy "because mass is destroyed". In both, the products are more tightly bound than the reactants; the small decrease in mass appears as energy, $E = \Delta m\,c^2$ .
Thinking a power reactor can explode like a nuclear weapon. Reactor fuel is only slightly enriched and the chain reaction is controlled; reactor accidents are about overheating and the release of radioactive material.

Tip

To remember which way energy flows: nuclei "want" to be like iron. Big nuclei release energy by splitting towards iron; small nuclei release energy by joining towards iron.

Science ABC: Nuclear Fission v Nuclear Fusion, Differences and Similarities Explained. Watch for why the fission of a heavy nucleus and the fusion of light nuclei both release energy.

✦

Practice

Distinguish between nuclear fission and nuclear fusion, with a balanced equation for each.
Complete: ${}^{235}_{92}\mathrm{U} + {}^{1}_{0}\mathrm{n} \rightarrow {}^{90}_{38}\mathrm{Sr} + {}^{143}_{\ \ ?}\mathrm{Xe} + x\,{}^{1}_{0}\mathrm{n}$ . Find the atomic number of xenon and $x$ .
Explain what is meant by a chain reaction, and how control rods keep it steady in a reactor.
Explain why fission fragments are radioactive, and which type of decay they usually undergo.
Calculate the energy released in ${}^{2}_{1}\mathrm{H} + {}^{2}_{1}\mathrm{H} \rightarrow {}^{3}_{2}\mathrm{He} + {}^{1}_{0}\mathrm{n}$ , given ${}^{3}\mathrm{He}$ 3.016029 u and the masses in worked example 2.
Why does fusion need very high temperatures, while fission of uranium-235 happens best with slow neutrons?
Evaluate this statement: "Fusion power stations would produce no radioactive waste at all."

Show answersHide answers

Fission: a heavy nucleus splits, e.g. ${}^{235}_{92}\mathrm{U} + {}^{1}_{0}\mathrm{n} \rightarrow {}^{141}_{56}\mathrm{Ba} + {}^{92}_{36}\mathrm{Kr} + 3\,{}^{1}_{0}\mathrm{n}$ . Fusion: light nuclei join, e.g. ${}^{2}_{1}\mathrm{H} + {}^{3}_{1}\mathrm{H} \rightarrow {}^{4}_{2}\mathrm{He} + {}^{1}_{0}\mathrm{n}$ .
$Z = 92 - 38 = 54$ ; $x = 236 - 90 - 143 = 3$ .
Neutrons from each fission cause further fissions, so the process sustains itself. Control rods absorb neutrons; they are moved in or out so that, on average, exactly one neutron from each fission causes another.
They keep the high neutron-to-proton ratio of uranium, so they lie above the band of stability and decay by β⁻ emission (often followed by γ).
$\Delta m = 2 \times 2.014102 - (3.016029 + 1.008665) = 0.003510\,\mathrm{u}$ ; $E = 0.003510 \times 931.5 = 3.27\,\mathrm{MeV}$ .
Fusing nuclei are both positive and must overcome strong electrical repulsion, which needs very high kinetic energies. A neutron has no charge, so it meets no repulsion; slow neutrons stay near the uranium-235 nucleus longer and are captured more readily.
Not quite: the fuel and the product (helium) are not long-lived waste, but tritium is radioactive and the neutrons make the reactor's structure radioactive. The waste is much shorter-lived and smaller in amount than from fission, but it is not zero.

Sources and credits

Image: Hahn and Meitner in 1912.jpg, unknown author, via Wikimedia Commons, in the public domain.
Image: The Sun by the Atmospheric Imaging Assembly of NASA's Solar Dynamics Observatory, NASA/SDO (AIA), via Wikimedia Commons, in the public domain as a work of NASA.
Atomic masses: Atomic Weights and Isotopic Compositions, NIST (public data).
Video: Nuclear Fission v Nuclear Fusion: Differences and Similarities Explained, Science ABC, embedded from YouTube.
The text, tables, chain-reaction drawing, worked examples and Practice items were written and drawn by Ganzaa.

1Barium where there should be none

2Fission equations

3The chain reaction

4Fusion

5Fission and fusion compared

Barium where there should be none

Fission equations

The chain reaction

Fusion

Fission and fusion compared