Rearranging the point-source dose-rate equation D = Gamma x A / d^2 for distance gives d = sqrt(Gamma x A / D_limit). This is the single most-used site radiation-safety calculation: it defines where the barrier rope, the flashing beacons and the warning signs go before the source ever leaves the projector.

The limit chosen sets the meaning of the boundary. In most regimes a controlled area boundary is drawn at 7.5 uSv/h, since a worker occupying it for a full 2000-hour year would reach 15 mSv and remain below the 20 mSv annual dose limit. A supervised area boundary is commonly 2.5 uSv/h, and boundaries protecting members of the public are set far lower, often 0.5 uSv/h, to satisfy a 1 mSv annual public constraint. Confirm the figure against your own national regulations and the site radiation protection adviser before roping off.

Because the distance goes as the square root of the activity, the barrier does not grow as fast as intuition suggests: quadrupling the activity only doubles the radius. But it also means halving the limit multiplies the radius by 1.41, and moving from an iridium source to a cobalt source of the same activity pushes the barrier out by a factor of 1.68 on the gamma constant alone.

This result is for a bare, uncollimated source in free air. A directional collimator can cut the barrier radius dramatically in the shielded directions, and site structures give real attenuation. Neither can be assumed – the barrier position must be confirmed by survey once the source is exposed.

Worked example

Isotope	ir192
Present activity	50 Ci
Boundary dose-rate limit	7.5 uSv/h
Collimator attenuation factor (1 = bare source)	1
Override gamma constant (0 = use table)	0
Gamma constant used	0.48
Barrier distance	167.43 m
Barrier distance	549.3 ft
Barrier distance in the collimated directions	167.43 m

The 7.5 uSv/h limit is 7.5/8760 = 8.5616e-4 R/h. d = sqrt(0.48 x 50 / 8.5616e-4) = sqrt(24 x 8760 / 7.5) = sqrt(28 032) = 167.43 m, which is 167.43 x 3.28084 = 549.30 ft.

Use at your own risk — verify before you act

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