Nuclear Fuel Cycle

Problem:

During decommissioning of a fuel handling facility, a concrete floor area measuring 4 m × 3 m is found to have uniform Cs-137 surface contamination with a total activity of 2 × 10⁹ Bq. Using the extended surface source formula, estimate the dose rate at a height of 1 m above the centre of the floor.

Data:

• Specific gamma ray constant for Cs-137: Γ = 8.46 × 10⁻¹⁴ Sv·m²·Bq⁻¹·h⁻¹
• Extended surface source formula: $\dot{D} = \Gamma \cdot C_A \cdot \ln\!\left[\frac{A \cdot W + h^2}{h^2}\right]$
• where $C_A$ = activity per unit area (Bq/m²), $A$ and $W$ are the dimensions of the rectangular area (m), and $h$ is the height above the surface (m).

Solution:

Step 1: Calculate the surface activity concentration.

$C_A = \frac{2 \times 10^9}{4 \times 3} = \frac{2 \times 10^9}{12} = 1.667 \times 10^8 \text{ Bq/m}^2$

Step 2: Substitute into the formula.

Using $A$ = 4 m, $W$ = 3 m, $h$ = 1 m:

$\dot{D} = 8.46 \times 10^{-14} \times 1.667 \times 10^8 \times \ln\!\left[\frac{4 \times 3 + 1}{1}\right]$

$\dot{D} = 1.41 \times 10^{-5} \times \ln(13)$

$\dot{D} = 1.41 \times 10^{-5} \times 2.565$

$\dot{D} = 3.62 \times 10^{-5} \text{ Sv/h} = 0.036 \text{ mSv/h} = 36 \text{ } \mu\text{Sv/h}$

Step 3: Interpret the result.

A dose rate of 36 μSv/h at 1 m above the floor means that a worker spending a full 8-hour shift in this area would receive approximately 0.29 mSv. Over a sustained decommissioning campaign, this would accumulate, so controls such as limiting time in the area, decontamination of the floor before extended work, and personal protective equipment would be appropriate.

Note: The extended surface source formula gives a more accurate result than treating the contamination as a point source, which would significantly underestimate the dose rate because the source is spread over a large area close to the worker. This formula is provided on the examination data sheet.