2.7 Radiation Exposure, Dose, and Distance

Time, Distance, Shielding, and Units

The ASP11 blueprint includes radiation exposure in Domain 1. Radiation math on a safety exam is practical: it asks how exposure changes with time, distance, shielding, or dose rate. The three protective principles are time, distance, and shielding -- minimize time near the source, maximize distance, and interpose appropriate shielding.

Dose Equals Rate Times Time

If the dose rate is constant, dose = dose rate x time. A worker exposed to 2 millirem per hour (mrem/hr) for 3 hours receives 6 mrem. This simple relationship fails only when the rate changes, units are inconsistent, or the question includes a distance or shielding change that must be applied first. The reverse form, time = dose limit / rate, answers how long a worker may stay: at 5 mrem/hr, a 30 mrem administrative limit allows 6 hours.

A reasonableness anchor: the OSHA / NRC occupational whole-body limit is 5 rem (5,000 mrem) per year. If a single short task computes to thousands of mrem, recheck the setup or the unit.

The Inverse-Square Law

Distance is powerful. For a point source, intensity follows the inverse-square law: I2 = I1 x (D1^2 / D2^2). Doubling distance reduces intensity to one-fourth; tripling distance reduces it to one-ninth. This is the cheapest control available because moving back a few feet can cut dose rate dramatically.

Worked example: a source reads 8 mrem/hr at 2 ft. At 4 ft, I2 = 8 x (2^2 / 4^2) = 8 x (4 / 16) = 2 mrem/hr. If a worker then stays at 4 ft for 30 minutes, the dose is 2 mrem/hr x 0.5 hr = 1 mrem. The distance adjustment must come before the time calculation, and the time must be in hours to match a per-hour rate.

Shielding and Half-Value Layers

Shielding reduces the rate by a transmission factor. If a shield transmits 25% of the radiation, multiply the unshielded rate by 0.25. A shield that reduces exposure by 75% leaves 25% remaining -- reduction and transmission are complementary, and confusing them is a frequent trap. Shielding is sometimes expressed in half-value layers (HVL), the thickness that cuts intensity in half: after n half-value layers, the fraction remaining is (1/2)^n. Three HVL leave (1/2)^3 = 1/8, or 12.5%, of the original rate.

Units and Reasonableness

Radiation unit conversions require care: a question may use rem, millirem, sievert, or microsievert. Recall 1 rem = 1,000 mrem and 1 sievert (Sv) = 100 rem. Do not compare 0.005 rem with 5 mrem until both are in the same unit; here they are equal (0.005 rem = 5 mrem). Convert before comparing.

Reasonableness checks are straightforward: more time increases dose, more distance from a point source decreases dose, and appropriate shielding reduces the dose rate. If your arithmetic violates those patterns, revisit the setup. Beyond the math, scenario questions may test planning, access control, posting and signs, dosimetry monitoring, and training as administrative complements to time-distance-shielding.

When a question mixes dose rate, time, and distance, solve in steps: first adjust the rate for distance or shielding, then multiply by time, then convert units and compare with the requested answer. Solving in order prevents applying a time multiplier to an uncorrected rate.

Combining Time, Distance, and Shielding in One Problem

The richest radiation items stack all three controls. Suppose a source reads 40 mrem/hr at 1 ft with no shield. A worker must perform a 15-minute task. (1) Distance: at 5 ft, intensity = 40 x (1^2 / 5^2) = 40 / 25 = 1.6 mrem/hr. (2) Shielding: a barrier transmitting 50% drops the rate to 0.8 mrem/hr. (3) Time: 0.8 mrem/hr x 0.25 hr = 0.2 mrem dose. Compare against a 5,000 mrem annual limit and the task is trivially within bounds, illustrating how stepping back and adding even modest shielding compounds protection.

Reversing the order -- multiplying the unshielded 40 mrem/hr by time first -- produces a wildly overstated dose and a wrong answer.

Tenth-Value Layers and Activity Decay

Alongside the half-value layer (HVL), shielding is sometimes given as tenth-value layers (TVL), the thickness that cuts intensity to one-tenth. After n TVL the fraction remaining is (1/10)^n, so two TVL leave 1%. One TVL is approximately 3.32 HVL. Radioactive decay may also appear: activity halves every half-life, so after n half-lives the remaining fraction is (1/2)^n. A source with a 6-hour half-life retains 1/8 of its activity after 18 hours (three half-lives).

Do not confuse the half-life of the source activity with the half-value layer of a shield; they use the same one-half-per-step math but describe different physical quantities.

Keeping the Safety Frame

Ultimately the arithmetic serves ALARA -- keeping exposure As Low As Reasonably Achievable. A correct dose number that ignores an obvious distance or shielding control is not the safest answer the exam is looking for. When a scenario offers a choice between accepting a computed dose and reducing it through more distance, brief shielding, or shorter stay time, the defensible response applies the control. Always confirm units (rem, mrem, sievert) match before any comparison, and let more time, less distance, or weaker shielding move the dose in the directions physics requires.