Nuclear fission and chain reaction
A slow neutron splits uranium-235 into two medium nuclei, 2 or 3 neutrons and about 200 MeV. The new neutrons can split more nuclei: a chain reaction.
Fission of uranium-235, step by step
- 1A slow (thermal) neutron is captured by a ²³⁵₉₂U nucleus, forming an excited ²³⁶₉₂U* nucleus.
- 2The extra energy makes the nucleus wobble like a liquid drop, between a sphere and a dumb-bell shape.
- 3When the two ends move far enough apart, the electric repulsion between them beats the nuclear pull.
- 4The nucleus splits into two fragments of unequal mass, such as barium and krypton.
- 5Two or three neutrons fly out, with energies of a few MeV.
- 6★About 200 MeV is released, mostly as kinetic energy of the fragments, which turns into heat.
★ key step
Worked example: energy released from the masses
Find the energy released in ¹₀n + ²³⁵₉₂U → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3 ¹₀n. (Masses: ²³⁵U = 235.0439 u, ¹₀n = 1.00867 u, ¹⁴¹Ba = 140.9139 u, ⁹²Kr = 91.8973 u; 1 u = 931 MeV)
- Mass before = 235.0439 + 1.00867 = 236.05257 u.
- Mass after = 140.9139 + 91.8973 + 3 × 1.00867 = 235.83721 u.
- Mass lost Δm = 236.05257 − 235.83721 = 0.21536 u.
- Energy = 0.21536 × 931 MeV ≈ 200 MeV.
About 200 MeV per fission
Chain reaction
Each fission uses one neutron but gives out two or three. These can split more uranium nuclei, which give still more neutrons, and so on. This self-spreading process is a chain reaction. Some neutrons escape or are absorbed without causing fission. If, on average, exactly one neutron from each fission causes another fission, the reaction runs steadily: it is controlled and self-sustained. If more than one does, the number of fissions grows very fast: the reaction is uncontrolled. A nuclear reactor keeps it controlled; an atom bomb lets it run wild.
How an uncontrolled chain reaction grows
In a reactor, control rods absorb the extra neutrons, so that only one neutron from each fission goes on to cause another.
Controlled and uncontrolled chain reactions
Worked example: energy from 1 kg of uranium-235
Each fission of ²³⁵U releases 200 MeV. Find the energy released when 1 kg of ²³⁵U undergoes fission. (Avogadro number = 6.02 × 10²³ per mol, 1 MeV = 1.6 × 10⁻¹³ J)
- Moles in 1 kg = 1000 g ÷ 235 g/mol = 4.26 mol.
- Number of nuclei = 4.26 × 6.02 × 10²³ = 2.56 × 10²⁴.
- Energy = 2.56 × 10²⁴ × 200 MeV = 5.12 × 10²⁶ MeV.
- In joules: 5.12 × 10²⁶ × 1.6 × 10⁻¹³ = 8.2 × 10¹³ J.
- For comparison, burning 1 kg of coal gives about 3 × 10⁷ J (an example value), millions of times less.
About 8.2 × 10¹³ J
India's nuclear power stations, such as those at Tarapur, Rawatbhata (near Kota), Kaiga, Narora, Kakrapar and Kalpakkam, run controlled fission chain reactions to boil water and spin turbines for electricity.
5 marks: “What is nuclear fission? Write a balanced equation for the fission of ²³⁵U. Explain the chain reaction and distinguish between controlled and uncontrolled chain reactions.” Splitting of a heavy nucleus by a neutron into two medium nuclei with 2 or 3 neutrons and about 200 MeV: ¹₀n + ²³⁵₉₂U → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3 ¹₀n + Q. The released neutrons cause more fissions: a chain reaction. Controlled: one neutron per fission causes another (reactor). Uncontrolled: more than one, so fissions multiply (bomb).
2 marks: “Why is a chain reaction possible in the fission of uranium-235?” Each fission absorbs one neutron but releases two or three, which can cause further fissions.
1 marks: “Complete: ¹₀n + ²³⁵₉₂U → ¹⁴⁰₅₄Xe + ⁹⁴₃₈Sr + ?” 2 ¹₀n (A: 236 = 140 + 94 + 2; Z: 92 = 54 + 38).
One in, three out, 200 out: one slow neutron goes in; two or three neutrons and about 200 MeV come out.