2.7 Radiation Exposure, Dose, and Distance

Time, Distance, Shielding, and Units

The ASP11 blueprint includes radiation exposure in Mathematical Calculations. Radiation math on a safety exam is usually practical. It asks how exposure changes with time, distance, shielding, or dose rate. The safety goal is to recognize and control exposure, not to perform advanced physics derivations.

If the dose rate is constant, dose equals dose rate times time. If a worker is exposed to 2 millirem per hour for 3 hours, the dose is 6 millirem. This simple relationship fails only when the rate changes, units are inconsistent, or the question includes shielding or distance changes that must be applied first.

Distance can be powerful. For a point source, the inverse-square relationship says intensity at a new distance equals intensity at the old distance times old distance squared divided by new distance squared. Doubling distance reduces intensity to one-fourth. Tripling distance reduces it to one-ninth.

Suppose a source produces 8 mrem/hr at 2 ft. At 4 ft, the rate is 8 x 2^2 / 4^2 = 8 x 4 / 16 = 2 mrem/hr. If a worker stays at 4 ft for 30 minutes, the dose is 2 mrem/hr x 0.5 hr = 1 mrem. The distance change must be calculated before the time dose.

If shielding transmits 25% of the radiation, multiply the unshielded rate by 0.25. A shield that reduces exposure by 75% leaves 25% remaining. That wording is a common trap. Reduction and transmission are not the same number unless the problem clearly defines them.

Radiation unit conversions require care. A question may use rem, millirem, sievert, or microsievert depending on context. Convert before comparing values. Do not compare 0.005 rem with 5 mrem until both are in the same unit.

The safety controls remain time, distance, and shielding. Reduce time near the source, increase distance when feasible, and use appropriate shielding. Planning, access control, signs, monitoring, and training may also appear in scenario questions.

Reasonableness checks are straightforward. More time increases dose. More distance from a point source decreases dose. More shielding should reduce the dose rate if the shield is appropriate for the radiation type. If your arithmetic violates those patterns, revisit the setup.

When a question mixes dose rate, time, and distance, solve in steps. First adjust the rate for distance or shielding. Then multiply by time. Finally convert units and compare with the requested answer.