Nuclear Fuel Cycle

The inverse square law states that the dose rate at a distance r from a point source is inversely proportional to the square of the distance:

$\dot{D}(r) = \dot{D}_0 \times \left(\frac{r_0}{r}\right)^2$

where:

• D-dot(r) = dose rate at distance r
• D-dot_0 = known dose rate at reference distance r_0
• r_0 = reference distance = 1 m
• r = actual distance = 1.5 m

Step 1: Identify the known values

• D-dot_0 = 50 microSv/h (dose rate at 1 m)
• r_0 = 1 m
• r = 1.5 m
• t = 2 hours (time spent by the worker)

Step 2: Calculate the dose rate at 1.5 m

D-dot(1.5) = 50 x (1 / 1.5)^2

D-dot(1.5) = 50 x (0.6667)^2

D-dot(1.5) = 50 x 0.4444

D-dot(1.5) = 22.2 microSv/h

Step 3: Calculate the total dose received

D = D-dot x t

D = 22.2 microSv/h x 2 h

D = 44.4 microSv