Fission practice questions.

A slow neutron is absorbed by a uranium-235 nucleus, causing induced fission. Which of the following is the typical set of products of this reaction?

• An alpha particle and a single daughter nucleus
• Two nuclei of roughly half the original mass, two or three neutrons and energy
• Two helium-4 nuclei and a gamma-ray photon
• A proton, an electron and a single daughter nucleus heavier than the original uranium

Answer: Two nuclei of roughly half the original mass, two or three neutrons and energy

Induced fission splits the heavy nucleus into two medium-mass fragments and releases two or three fast neutrons together with about 200 MeV of energy.

State the purpose of the moderator in a thermal nuclear fission reactor.

• It slows fast neutrons so that they are more likely to be absorbed by uranium-235 nuclei
• It absorbs the excess free neutrons so that the overall reaction rate stays roughly constant
• It transfers thermal energy from the core to the steam generator
• It reflects escaping neutrons back into the fuel rods

Answer: It slows fast neutrons so that they are more likely to be absorbed by uranium-235 nuclei

The probability of neutron capture by U-235 is much greater for slow (thermal) neutrons, so the moderator slows the fast fission neutrons through collisions.

A reactor operator pushes the control rods further into the core. What is the effect on the chain reaction, and why?

• The rate increases, because the control rods slow the fast neutrons down to thermal speeds
• The rate increases, because the rods reflect neutrons into the fuel
• The rate stays the same, because the rods only remove thermal energy
• The rate decreases, because the rods absorb neutrons that would otherwise cause fission

Answer: The rate decreases, because the rods absorb neutrons that would otherwise cause fission

Control rods contain neutron-absorbing material (e.g. boron or cadmium); inserting them removes neutrons from the chain reaction and lowers the fission rate.

A sample of fissile material smaller than the critical mass cannot sustain a chain reaction. Which statement best explains why?

• The nuclei are too far apart for any fission to occur
• The temperature of a small sample is too low for neutrons to be released
• Too large a fraction of the neutrons escapes through the surface before causing further fissions
• The neutrons produced in such a small sample move far too slowly to be able to split any other nuclei

Answer: Too large a fraction of the neutrons escapes through the surface before causing further fissions

In a small sample the surface-to-volume ratio is large, so most neutrons leave the material before being captured; on average fewer than one neutron per fission causes another fission.

Each fission of uranium-235 releases about 200 MeV ≈ 3.2 × 10⁻¹¹ J. Calculate the number of fissions per second needed to produce a thermal power of 3.2 GW.

• 1.0 × 10¹⁸ s⁻¹
• 1.0 × 10¹⁹ s⁻¹
• 1.0 × 10²⁰ s⁻¹
• 1.0 × 10²¹ s⁻¹

Answer: 1.0 × 10²⁰ s⁻¹

Rate = power ÷ energy per fission = (3.2 × 10⁹ J s⁻¹) ÷ (3.2 × 10⁻¹¹ J) = 1.0 × 10²⁰ fissions per second.

Fission fragments are almost always radioactive. Which statement explains why they typically decay by beta-minus emission?

• They have far too few neutrons compared with the stable nuclei of the same element, making them proton-rich
• The fragments inherit the high neutron-to-proton ratio of uranium, leaving them neutron-rich
• They are produced in an excited electronic state that emits electrons
• They absorb the free neutrons released in the fission and become unstable

Answer: The fragments inherit the high neutron-to-proton ratio of uranium, leaving them neutron-rich

Heavy nuclei need a high neutron-to-proton ratio for stability; the medium-mass fragments keep this ratio, which is too high for their size, so they convert neutrons to protons via β⁻ decay.