E.4 Fission

Practice Worksheet — name: ______________________ date: ____________

Formulas for this topic

Mass–energy equivalence

E = \Delta m\,c^{2}

Section A — Multiple choice

A1. The purpose of the moderator in a fission reactor is to:

A Absorb excess neutrons to stop the reaction
B Slow neutrons so they are more likely to induce fission in U-235
C Speed up neutrons to increase collision energy
D Cool the reactor core

A2. In one fission of U-235, about 200 MeV is released. This energy appears mainly as:

A Gamma radiation
B Kinetic energy of the fission fragments
C Kinetic energy of the emitted neutrons
D Mass of the products

A3. A chain reaction is self-sustaining when, on average:

A Every neutron produced causes a fission
B At least one neutron per fission goes on to cause another fission
C Three neutrons are produced per fission
D The moderator absorbs no neutrons

Section B — Short answer

B1. One fission reaction is $^{235}_{92}\text{U} + n \to\ ^{144}_{56}\text{Ba} + ^{89}_{36}\text{Kr} + 3n$ . Show that the equation balances, and explain the origin of the released energy. [4 marks]

B2. Explain why fission products are radioactive, referring to the neutron-to-proton ratio. [3 marks]

B3. Outline two challenges in the management of spent nuclear fuel and one strategy used to address them. [3 marks]

Answer key

For worked explanations, interactive practice and more free resources, visit www.newtonine.com

Section A

A1: Slow neutrons so they are more likely to induce fission in U-235 — Fast fission neutrons are inefficient at inducing further fissions in U-235; slowing them to thermal speeds (by collisions with water or graphite nuclei) raises the capture probability enormously. Absorbing neutrons is the CONTROL RODS' job — a distinct role, and a favourite MCQ confusion.

A2: Kinetic energy of the fission fragments — The mutual Coulomb repulsion of the two positively charged fragments converts most of the released energy (~165 MeV) into their kinetic energy, which becomes heat in the fuel. Neutrons and gammas carry the smaller remainder.

A3: At least one neutron per fission goes on to cause another fission — Criticality is bookkeeping: of the 2–3 neutrons released, losses to absorption and escape must leave exactly one (on average) to trigger the next fission. More than one → supercritical growth; fewer → the reaction dies away.

Section B

B1: Nucleons: $235 + 1 = 236 = 144 + 89 + 3$ . ✓ Protons: $92 = 56 + 36$ . ✓ The products have greater binding energy per nucleon than uranium, so the total rest mass decreases; the mass defect appears as energy via $E = \Delta mc^2$ , mostly as fragment kinetic energy.

B2: Heavy nuclei need a high neutron-to-proton ratio for stability ( $N/Z \approx 1.55$ for uranium); mid-mass stable nuclei need less ( $\approx 1.3$ ). Fission fragments inherit uranium's ratio and are therefore neutron-rich for their size, decaying by $\beta^-$ emission (often in chains) towards stability.

B3: Challenges: some products remain hazardous for thousands of years (long half-lives), and the waste generates heat requiring active cooling initially; secure isolation from groundwater and society is needed throughout. Strategy: interim cooling ponds followed by vitrification and deep geological repositories in stable rock formations (also acceptable: reprocessing to recover usable fuel).