Question 3 of 7: Detection of Radiation, Radiation Instrumentation, Radiation Protection

Question 3: Detection of Radiation, Radiation Instrumentation, Radiation Protection (19 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. Thermal-neutron-induced fission of ${}^{235}$U producing ${}^{92}$Kr, ${}^{142}$Ba, two prompt neutrons, and a prompt gamma; total fission energy release is the well-known $\approx 200$ MeV per fission.

Find. The incident-neutron energy for peak fission probability, suitable detectors for the incident and produced neutrons, the fission-neutron spectrum shape, a shielding arrangement, the reaction's energy budget, and why/how the fragments decay.

Approach. Work through each sub-part with the standard reactor-physics and health-physics facts for thermal-neutron ${}^{235}$U fission: the huge thermal fission cross-section, standard neutron detectors, the Watt/Maxwellian prompt-neutron spectrum, shielding by moderation + absorption + gamma attenuation, the textbook fission energy budget, and the neutron-excess argument for fragment instability.

1. Part (a) — most probable fission-inducing neutron energy. ${}^{235}$U's fission cross-section follows a $1/v$ law at low energy and is largest for thermal neutrons, peaking around $$\boxed{E_n \approx 0.025\text{ eV (thermal)}}$$ where the microscopic fission cross-section is roughly 580 barns — orders of magnitude above the fast-neutron cross-section, which is why thermal (moderated) reactors use a moderator to slow fission neutrons down before they induce the next fission.
2. Part (b) — detectors for the incident (thermal) neutrons. Two standard high-efficiency thermal-neutron detectors: a BF₃ (boron trifluoride) proportional counter (relies on ${}^{10}\text{B}(n,\alpha)^7\text{Li}$) and a $^3$He proportional counter (relies on $^3\text{He}(n,p)^3\text{H}$); a ${}^{235}$U-lined fission chamber is a third common choice.
3. Part (c) — prompt fission-neutron spectrum. Prompt fission neutrons follow a Watt (near-Maxwellian) spectrum: essentially zero yield at $E=0$, rising to a peak at low-to-moderate energy, then a long tail extending to several MeV, with a mean energy near 2 MeV but a most probable energy well below the mean. $$\boxed{E_{p} \approx 0.7\text{ MeV (most probable)}}$$
   Figure 2 — Watt (near-Maxwellian) prompt fission-neutron spectrum; most probable energy marked, mean energy (≈2 MeV) sits further out under the long tail.
4. Part (d) — measuring the neutron spectrum. A proton-recoil scintillation spectrometer (e.g. an organic liquid scintillator such as NE-213 with pulse-shape discrimination against gammas): fast neutrons elastically scatter from hydrogen nuclei in the scintillator, and each recoil proton deposits a light pulse proportional to its kinetic energy; unfolding the measured recoil-proton pulse-height distribution (using the known scattering kinematics and cross-section) reconstructs the incident neutron energy spectrum.
5. Part (e) — measuring neutron dose. Neutron dose equivalent is measured with instruments whose response is weighted to track the neutron quality factor across energy — a moderating "rem meter" (a thermal-neutron detector, e.g. BF₃ or $^3$He, embedded in a polyethylene sphere, the classic Bonner-sphere/"long counter" design) for area monitoring, or personal neutron dosimeters (track-etch CR-39, albedo TLD, or bubble detectors) for individual dose equivalent.
6. Part (f) — shielding arrangement. Fission neutrons (fast, mean ≈ 2 MeV) and prompt gammas need different shielding physics, so an effective barrier layers both: a hydrogenous moderator (water, polyethylene, or ordinary concrete, ≈30–40 cm) to slow fast neutrons by elastic scattering, optionally with a thin boron or boron-loaded layer (a few mm, e.g. borated polyethylene) to capture the resulting thermal neutrons without the higher-energy capture gammas that iron or hydrogen capture would produce, followed by a high-Z gamma shield (lead, ≈5–10 cm, or the equivalent thickness of dense concrete) to attenuate the prompt and capture gamma rays. A single ≈1 m slab of ordinary concrete is a common practical equivalent, combining moderation and gamma attenuation in one bulk material.
7. Part (g) — energy distribution among the products. Of the ≈200 MeV released per fission: the two heavy fragments (Kr, Ba here) carry the large majority as kinetic energy from Coulomb repulsion, roughly 84%; the prompt neutrons carry roughly 2.5%; prompt gamma rays carry roughly 3.5%; the remaining roughly 10% is released later as the neutron-rich fragments beta-decay down their chains (beta particles, antineutrinos, and delayed gamma rays) — energy that is nominally "theirs" (Kr's and Ba's) but is emitted well after the prompt fission event.
8. Part (h) — why the fragments are unstable. ${}^{235}$U has a neutron-to-proton ratio ($N/Z \approx 1.55$) far higher than the stable nuclei sitting at $Z=36$ (Kr) or $Z=56$ (Ba); when the nucleus splits, each fragment inherits roughly the parent's high $N/Z$ ratio, leaving both ${}^{92}$Kr and ${}^{142}$Ba well above the valley of stability — i.e. carrying far more neutrons than a stable nucleus of that same $Z$ would have.
9. Part (i) — decay mode. Both are neutron-rich, so both decay by $\beta^-$ emission (converting a neutron to a proton, moving each isobaric chain toward the valley of stability); each undergoes a chain of successive beta decays before reaching a stable isobar.