Lesson 6 ◆ 6.14 Worked Example -- Dose Calculation for Decommissioning

Problem:

During decommissioning of a Magnox reactor, a section of the reactor’s mild steel thermal shield is found to contain Fe-55 with a total activity of 8 × 10¹⁰ Bq. Fe-55 decays by electron capture, emitting Mn K-shell X-rays with an average energy of approximately 5.9 keV and a very low specific gamma ray constant of Γ ≈ 3.5 × 10⁻¹⁶ Sv·m²·Bq⁻¹·h⁻¹. Calculate the dose rate at 1 m from this source.

Solution:

Step 1: Apply the point source formula.

D˙=A×Γr2=8×1010×3.5×10−1612\dot{D} = \frac{A \times \Gamma}{r^2} = \frac{8 \times 10^{10} \times 3.5 \times 10^{-16}}{1^2}

D˙=2.8×10−5 Sv/h=0.028 mSv/h=28 μSv/h\dot{D} = 2.8 \times 10^{-5} \text{ Sv/h} = 0.028 \text{ mSv/h} = 28 \text{ } \mu\text{Sv/h}

Step 2: Interpret the result.

At 28 μSv/h, a worker could remain at 1 m for approximately:

t=20 mSv0.028 mSv/h≈714 hourst = \frac{20 \text{ mSv}}{0.028 \text{ mSv/h}} \approx 714 \text{ hours}

before reaching the annual dose limit of 20 mSv. This is a manageable dose rate that permits hands-on work with appropriate monitoring, though the ALARP principle still applies.

Key insight: Fe-55 is an important activation product in reactor steel components, but its very low gamma energy (5.9 keV X-rays) means the external dose hazard is much lower than from Co-60 (1.17 and 1.33 MeV gammas). The primary concern with Fe-55 during decommissioning is contamination control during cutting operations, as inhaled or ingested Fe-55 contributes to internal dose.