Fission and Fusion核裂变与核聚变

Big Idea · Structure and Properties (SAP)AP Science Practice 6 · Argumentation~35 min

Learning goals

  • Use the binding-energy curve to explain why both fission of heavy nuclei and fusion of light nuclei release energy
  • Write and check typical fission and fusion equations, and explain chain reactions and criticality
  • Compare the energy released by nuclear and chemical reactions

Before you start

  • Enthalpy change and thermochemical equations (2.10.5)
  • Types of radioactive decay (2.14.1)

Where do the sun and nuclear power plants get their energy?

Optional · not on the AP exam: this lesson is optional and only qualitative; AP Chemistry doesn’t test it. Chinese high schools teach fission and fusion in physics.

The chemical reactions of lesson 2.10 release energy from chemical bonds: old bonds break and new ones form. A nuclear power plant burns nothing, yet a small amount of uranium fuel generates electricity for a long time, and the sun has been shining for billions of years. Their energy comes from changes in the nucleus itself.

Binding energy

Pulling a nucleus apart into separate protons and neutrons takes energy; when protons and neutrons come together to form a nucleus, the same amount is released. This is the nucleus’s binding energy结合能. Divided by the number of nucleons (protons and neutrons are together called nucleons, so this is the mass number), it gives the binding energy per nucleon比结合能. The higher the binding energy per nucleon, the more tightly the nucleons are held and the more stable the nucleus.

By Einstein’s E = mc² (E is energy, m is mass, and c is the speed of light, 3.00 × 10⁸ m/s; c² is enormous, so a tiny mass corresponds to a lot of energy), releasing energy means losing mass: a nucleus weighs slightly less than its separate protons and neutrons. The difference is the mass defect质量亏损.

Nuclear energies are usually given in MeV. The eV (electron volt) is a very small unit of energy used for single atoms and nuclei: 1 eV = 1.60 × 10⁻¹⁹ J, and 1 MeV = 10⁶ eV.

Plotting binding energy per nucleon for many nuclei shows that:

  • very light nuclei such as ²H have low values, though ⁴He is especially stable;
  • nuclei with mass numbers around 56 to 62 (iron, nickel) have the highest values and are the most stable;
  • beyond that, heavier nuclei have lower values; uranium is only about 7.6 MeV.

So there are two ways for nuclei to become more stable and release energy: split a heavy nucleus into medium-sized ones, or join light nuclei together.

Fission

When uranium-235 is hit by a neutron, the nucleus splits into two medium-sized nuclei and releases 2 or 3 neutrons. This is nuclear fission核裂变. One common fission is:

X92235X2922235U+X01X2021n→X56141X2562141Ba+X3692X236292Kr+3 X01X2021n\ce{^{235}_{92}U + ^{1}_{0}n -> ^{141}_{56}Ba + ^{92}_{36}Kr} + 3\,\ce{^{1}_{0}n}

Check: mass number 235 + 1 = 141 + 92 + 3 = 236; atomic number 92 = 56 + 36.

The neutrons released can split more uranium nuclei, generation after generation: a chain reaction链式反应. If each fission causes k new fissions on average, then for k < 1 the reaction dies out; for k = 1 it runs steadily (a nuclear reactor, where control rods absorb extra neutrons); and for k > 1 it speeds up explosively (an atomic bomb). The smallest mass of uranium that can sustain a chain reaction is the critical mass.

Fusion

Joining two light nuclei into a heavier one is nuclear fusion核聚变. For example, deuterium and tritium fuse:

X12X2122H+X13X2123H→X24X2224He+X01X2021n\ce{^{2}_{1}H + ^{3}_{1}H -> ^{4}_{2}He + ^{1}_{0}n}

Nuclei are all positively charged and repel each other. Getting them close enough to fuse takes temperatures of more than ten million degrees, which is why fusion is also called a thermonuclear reaction. Inside the sun, hydrogen fuses into helium. Controlled fusion for electricity is being researched but isn’t in commercial use yet.

In the model below, switch between fission and fusion to see where the reactants and products sit on the binding-energy curve and how much energy is released. Then see how the number of fissions per generation changes for different values of k:

Try it: fission and fusion on the binding-energy curve

    Chain reaction: how many new fissions does each fission cause, on average?

    How much bigger is nuclear energy?

    From the binding energies, one uranium-235 fission releases about 173 MeV and one deuterium–tritium fusion about 17.6 MeV. Burning one carbon atom (C + O₂ → CO₂, ΔH = −393.5 kJ/mol) releases only about 4.1 eV. One nuclear reaction releases millions to tens of millions of times as much energy as one chemical reaction, which is why a small amount of nuclear fuel goes so far.

    How Chinese textbooks differ

    • In China, binding energy, fission, and fusion are taught in high school physics, with calculations in MeV and mass defect; US chemistry textbooks introduce them qualitatively in a nuclear chemistry chapter.
    • US textbooks often calculate the energy of a nuclear reaction from the mass defect with E = Δmc².

    Example 1: neutrons in a fission equation

    Uranium-235 can also split into xenon-140 and strontium-94: ²³⁵₉₂U + ¹₀n → ¹⁴⁰₅₄Xe + ⁹⁴₃₈Sr + x ¹₀n. Find x and check the atomic numbers.

    Step-by-step solution

    1. The rule. Nuclear reactions conserve mass number and atomic number. A neutron, ¹₀n, has mass number 1 and atomic number 0.

    2. Mass number: solve for x.

      235+1=140+94+x236=234+xx=2\begin{aligned} 235 + 1 &= 140 + 94 + x \\ 236 &= 234 + x \\ x &= \boxed{2} \end{aligned}

    3. Atomic number. Left: 92 + 0 = 92. Right: 54 + 38 + 2(0) = 92. Conserved.

    4. Conclusion. This fission releases 2 neutrons. As long as, on average, more than one neutron from each fission causes another fission, a chain reaction can keep going.

    5. Think about it. Neutrons have atomic number 0, so only the mass numbers can tell you how many there are; the atomic numbers check that the products are right.

    Example 2: fission and fusion per unit mass

    One uranium-235 fission releases about 173 MeV and involves 235 + 1 = 236 nucleons; one deuterium–tritium fusion releases about 17.6 MeV and involves 2 + 3 = 5 nucleons. Which releases more energy per nucleon?

    Step-by-step solution

    1. Why per nucleon? All nucleons have about the same mass, so energy per nucleon compares equal masses of fuel.

    2. Fission.

      173 MeV236≈0.73 MeV per nucleon\frac{173\ \text{MeV}}{236} \approx 0.73\ \text{MeV per nucleon}

    3. Fusion.

      17.6 MeV5≈3.5 MeV per nucleon\frac{17.6\ \text{MeV}}{5} \approx 3.5\ \text{MeV per nucleon}

    4. Compare. 3.52 ÷ 0.733 ≈ 4.8, about 5 times. For the same mass of fuel, fusion releases about 5 times as much energy as fission.

    5. Think about it. Per reaction, fission releases far more (173 MeV vs. 17.6 MeV); per unit mass the answer flips. On the curve, the jump from ²H and ³H up to ⁴He is especially large.

    6. A common mistake. Comparing 173 MeV with 17.6 MeV directly and concluding fission releases more. One fission uses almost 50 times as many nucleons as one fusion, so compare equal masses.

    Practice: fission, fusion, both, or neither?
    1. The main reaction inside the sun
    2. The reaction used in today’s nuclear power plants
    3. Started by a neutron and able to form a chain reaction
    4. Needs temperatures of more than ten million degrees
    5. A heavy nucleus splits into two medium-sized nuclei
    6. Light nuclei join to form a heavier nucleus
    7. The products have a higher binding energy per nucleon, so energy is released
    8. Mass number and atomic number are conserved
    9. Burning natural gas (methane)

    Common mistakes

    Mistake 1: “The higher the binding energy per nucleon, the less stable the nucleus.” It’s the reverse. Higher binding energy per nucleon means the nucleons are held more tightly and the nucleus is more stable; nuclei near iron and nickel are the most stable.

    Mistake 2: “Fission releases energy, so fusion must absorb it.” Fission of heavy nuclei and fusion of light nuclei both release energy, because both move toward the iron region at the top of the curve. Only fusing nuclei heavier than iron, or splitting nuclei lighter than iron, takes energy in.

    Mistake 3: “A nuclear reaction releases energy, so the mass number goes down.” The mass number (the number of nucleons) is conserved. What decreases is the nuclei’s mass (the mass defect), and only by a tiny fraction.

    Quick check

    In ²³⁵₉₂U + ¹₀n → ¹⁴⁰₅₄Xe + ⁹⁴₃₈Sr + x ¹₀n, what is x?

    Which nuclei have the highest binding energy per nucleon (are the most stable)?

    Summary

    • The higher the binding energy per nucleon, the more stable the nucleus; the peak is near iron and nickel. Fission of heavy nuclei and fusion of light nuclei both move toward the peak and release energy (mass defect, E = mc²).
    • Fission: ²³⁵U absorbs a neutron, splits into two medium-sized nuclei, and releases 2 or 3 neutrons, which can start a chain reaction (steady when k = 1). Fusion, such as ²H + ³H → ⁴He + n, needs extremely high temperatures.
    • One nuclear reaction releases millions of times more energy than one chemical reaction. Nuclear reactions conserve mass number and atomic number.
    On to AP (for later)

    AP Chemistry doesn’t cover nuclear energy. But in AP Unit 6 (thermodynamics) you’ll keep using the same idea, that products more stable than the reactants release the difference as energy, applied to chemical bond energies instead (lesson 2.10).

    Data sources: binding energies in the model come from the IAEA’s LiveChart of Nuclides.

    Practice this chapter: 2.14 · Intro to Nuclear and Organic Chemistry · 6 questions

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