Questions on fission and fusion

Question 1

Describe what happens in induced nuclear fission.

Accepted Answer

A heavy nucleus, such as uranium-235, absorbs a slow (thermal) neutron and becomes unstable (1); it splits into two smaller nuclei, releasing two or three neutrons and a large amount of energy (1).

Question 2

Explain what is meant by a chain reaction in a fissile material.

Accepted Answer

Neutrons released by one fission are absorbed by other nuclei and cause further fissions (1); each fission releases more neutrons, so the reaction sustains itself and can grow (1).

Question 3

State what is meant by the critical mass of a fissile material.

Accepted Answer

The minimum mass for a self-sustaining chain reaction (1); on average at least one neutron per fission goes on to cause another fission rather than escaping from the material (1).

Question 4

State what is meant by a thermal neutron.

Accepted Answer

A slow neutron, with kinetic energy comparable to that of particles in thermal motion, which uranium-235 captures far more readily than a fast neutron (1).

Question 5

State the two number balances that must hold in any nuclear reaction equation.

Accepted Answer

The total nucleon (mass) number is the same before and after the reaction (1); the total proton (atomic) number is the same before and after (1).

Question 6

State the form in which most of the energy released in a fission event appears.

Accepted Answer

As kinetic energy of the two fission fragments (1).

Question 7

In one fission reaction, ²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + x ¹₀n. Determine the value of x and show that the proton numbers balance.

Accepted Answer

Nucleon numbers: 235 + 1 = 141 + 92 + x (1) 236 = 233 + x, so x = 3 neutrons (1) Proton numbers: 92 + 0 = 56 + 36 = 92, so they balance (1).

Question 8

A single fission event converts a mass of 3.5 × 10⁻²⁸ kg into energy. Calculate the energy released in joules and in MeV. c = 3.0 × 10⁸ m s⁻¹, 1 MeV = 1.60 × 10⁻¹³ J

Accepted Answer

E = mc² = 3.5 × 10⁻²⁸ × (3.0 × 10⁸)² (1) E = 3.15 × 10⁻¹¹ J (1) E = 3.15 × 10⁻¹¹/(1.60 × 10⁻¹³) = 197 MeV (1)

Question 9

Explain why very high temperatures are needed for nuclear fusion to occur.

Accepted Answer

The fusing nuclei are both positively charged, so they repel each other electrostatically (1); they must approach to within the very short range of the strong nuclear force to fuse (1); only at very high temperatures do the nuclei have enough kinetic energy to work against that repulsion and get close enough (1). Beyond what this question requires: even at stellar temperatures the average nucleus falls hundreds of times short of the top of the barrier, and fusion proceeds because quantum tunnelling carries the fastest nuclei through it.

Question 10

A fusion reaction releases 17.6 MeV of energy. Calculate the energy released in joules and the mass converted into energy. c = 3.0 × 10⁸ m s⁻¹

Accepted Answer

E = 17.6 × 10⁶ × 1.60 × 10⁻¹⁹ = 2.82 × 10⁻¹² J (1) m = E/c² = 2.82 × 10⁻¹²/(3.0 × 10⁸)² (1) m = 3.13 × 10⁻²⁹ kg (1)

Question 11

Explain why the fragments produced by the fission of uranium-235 are radioactive, and state the type of decay they undergo.

Accepted Answer

The fragments form with roughly the same neutron-to-proton ratio as uranium-235 (1); nuclei of their smaller size are stable at a lower neutron-to-proton ratio, so the fragments are neutron-rich and lie above the line of stability (1); they therefore decay by beta-minus emission, often in chains, until stability is reached (1).

Question 12

In one fusion reaction, two deuterium nuclei form helium-3 and a neutron:
²₁H + ²₁H → ³₂He + ¹₀n
Nuclear masses: ²₁H 2.01355 u, ³₂He 3.01493 u, neutron 1.00867 u. Calculate the energy released, in MeV.
1 u = 931.5 MeV

Accepted Answer

Mass before = 2 × 2.01355 = 4.02710 u (1) Mass after = 3.01493 + 1.00867 = 4.02360 u, so Δm = 0.00350 u (1) E = 0.00350 × 931.5 = 3.3 MeV (1)

Question 13

A reactor core produces thermal power at a steady 600 MW. Each fission releases about 200 MeV. Calculate the number of fissions occurring each second. Go on to determine the mass converted into energy in one day of operation.
1 MeV = 1.60 × 10⁻¹³ J, c = 3.0 × 10⁸ m s⁻¹, 1 day = 86 400 s

Accepted Answer

Energy per fission = 200 × 1.60 × 10⁻¹³ = 3.2 × 10⁻¹¹ J (1)
Rate = P/E = (600 × 10⁶)/(3.2 × 10⁻¹¹) = 1.9 × 10¹⁹ fissions per second (1)
Energy in one day = 600 × 10⁶ × 86 400 = 5.2 × 10¹³ J (1)
m = E/c² = 5.2 × 10¹³/(3.0 × 10⁸)² = 5.8 × 10⁻⁴ kg (about 0.6 g) (1)

Question 14

Each fission of a uranium-235 nucleus releases about 200 MeV. Estimate the energy released by the complete fission of 1.0 kg of uranium-235. N_A = 6.02 × 10²³ mol⁻¹, 1 MeV = 1.60 × 10⁻¹³ J

Accepted Answer

Number of nuclei in 1.0 kg = N_A × 1000/235 = 2.56 × 10²⁴ (1)
Energy per fission = 200 × 1.60 × 10⁻¹³ = 3.20 × 10⁻¹¹ J (1)
Total energy = 2.56 × 10²⁴ × 3.20 × 10⁻¹¹ (1)
E = 8.2 × 10¹³ J (1)

Question 15

Compare nuclear fission and nuclear fusion in terms of the fuel used, the conditions required and the products formed.

Accepted Answer

Fuel: fission uses heavy nuclei such as uranium-235; fusion uses light nuclei such as hydrogen isotopes (1). Conditions: fission needs slow neutrons and a critical mass, and proceeds at ordinary temperatures (1); fusion needs extremely high temperatures and densities to bring nuclei close against electrostatic repulsion, with quantum tunnelling doing the rest (1). Products: fission gives radioactive fragments plus neutrons; fusion gives helium with far less long-lived radioactive waste (1).

Question 16

Use the binding energy per nucleon curve to explain why energy is released in both fission and fusion.

Accepted Answer

In both processes the products have a higher binding energy per nucleon than the original nuclei (1); fusion moves light nuclei up the steep rise of the curve, and fission moves heavy nuclei towards the peak near iron-56 (1); the increase in binding energy per nucleon corresponds to a decrease in mass, and the equivalent energy is released (1).

Question 17

The fusion of deuterium and tritium releases 17.6 MeV from nuclei totalling five nucleons. The fission of uranium-235 releases about 200 MeV from 236 nucleons (the nucleus plus the absorbed neutron). A journalist writes that fission must release more energy per kilogram of fuel, because 200 MeV is far greater than 17.6 MeV. Deduce whether the journalist is correct.

Accepted Answer

Equal masses of fuel contain almost equal numbers of nucleons, so energy per kilogram is compared using energy per nucleon (1)
Fusion: 17.6/5 = 3.52 MeV per nucleon (1)
Fission: 200/236 = 0.85 MeV per nucleon (1)
Fusion releases about 4 times more energy per kilogram of fuel, so the journalist is not correct (1)

Question 18

A fixed mass of fissile material can be formed into different shapes. Suggest why a sphere is the shape most likely to sustain a chain reaction.

Accepted Answer

Neutrons are lost by escaping through the surface of the material (1); a sphere has the smallest surface area for a given volume (1); so the smallest fraction of neutrons escapes and the largest fraction remains to cause further fissions, making a self-sustaining chain most likely (1).