Mixed-Field Equivalent Dose from Neutron and Gamma Exposure: 17-Phys-B1 Radiation Physics, May 2016, Q2

Question 2: Mixed-Field Equivalent Dose from Neutron and Gamma Exposure (5 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. Absorbed doses from three field components over a 3-month period, in the source's own units.

Given data
Field component	Absorbed dose $D$	Radiation weighting factor $w_R$
Thermal neutrons	50 (source units)	5 (ICRP-60, $E<10$ keV)
Fast neutrons ($<2$ MeV)	20	20 (ICRP-60, 100 keV–2 MeV peak)
Gamma rays	100	1

Find. (a) the total biological (equivalent) dose $H=\sum w_R D_R$; (b) which component dominates the equivalent dose and is therefore the best target for dose reduction.

Approach. Apply the ICRP radiation weighting factor $w_R$ appropriate to each field's energy (thermal neutrons sit in the lowest-$w_R$ neutron bracket; fast neutrons below 2 MeV sit in the highest, $w_R=20$, bracket; photons always carry $w_R=1$), sum the per-component equivalent doses, then compare their individual shares of the total.

Part (a) — equivalent dose from each component. $$H_R = w_R \times D_R$$ $$\boxed{H_{\text{thermal}} = 5\times50 = 250,\quad H_{\text{fast}} = 20\times20 = 400,\quad H_{\gamma} = 1\times100 = 100 \ \ (\text{source-unit equivalent dose})}$$ $$\boxed{H_{\text{total}} = 250+400+100 = 750\ (\text{source-unit equivalent dose})}$$
Part (b) — which component to target. Despite having the smallest absorbed dose of the three (20 vs. 50 and 100), the fast-neutron component carries the largest equivalent dose (400 of 750, or 53%) because its weighting factor ($w_R=20$) is four times the thermal-neutron value and twenty times the gamma value — fast neutrons in the 100 keV–2 MeV range are the most biologically damaging radiation per unit absorbed energy of any of the three. Reducing the fast-neutron field (e.g. additional hydrogenous moderation/shielding near the source) therefore yields the largest reduction in total equivalent dose per unit of absorbed-dose reduction achieved — more effective than an equal effort spent on the gamma or thermal-neutron components.

Check: the source prints the absorbed doses in "pGy" (picogray); at that magnitude ($10^{-12}$ Gy) none of these exposures would be measurable over a 3-month monitoring period, so the intended unit is almost certainly "mGy" or "μGy" (both plausible occupational-monitoring scales). The comparison in part (b) is a ratio of $w_R D_R$ products and is therefore unaffected by which absolute unit is intended; the numbers are used literally as printed, per the exam's own invitation to state assumptions.

Question 2 — results
Quantity	Value
(a) $H_{\text{thermal}}$	250 (source-unit equiv. dose)
(a) $H_{\text{fast}}$	400
(a) $H_{\gamma}$	100
(a) $H_{\text{total}}$	750
(b) Target for reduction	fast neutrons (53% of total equivalent dose)

Topic. Radiation weighting factors and equivalent dose for a mixed neutron/photon field.

Key relations. $H=\sum_R w_R D_R$; ICRP-60 neutron weighting steps: $w_R=5$ ($E<10$ keV), $10$ ($10$–$100$ keV), $20$ ($100$ keV–$2$ MeV), $10$ ($2$–$20$ MeV), $5$ ($>20$ MeV); $w_R=1$ for photons/electrons.

Why this works. $w_R$ encodes relative biological effectiveness, which for neutrons peaks sharply near 1 MeV (dense, short-range proton recoils from elastic scattering) and falls off at both lower (thermal, mostly capture-gamma dominated) and higher energy.

Common pitfall. Ranking components by absorbed dose alone; the component with the smallest $D_R$ can still dominate $H$ if its $w_R$ is large enough, exactly as here.

Source. J. R. Cember and T. E. Johnson, Introduction to Health Physics, 5th ed., Ch. 3 (dose quantities and weighting factors).

Question 2 of 7: Mixed-Field Equivalent Dose from Neutron and Gamma Exposure

Question 2: Mixed-Field Equivalent Dose from Neutron and Gamma Exposure (5 marks)