Describe the inverse square law for external exposure and when it applies.

• A. I ∝ r^2; applies for any distance.
• B. I ∝ 1/r; applies for distant sources.
• C. I ∝ 1/r^2; applies when distance is small relative to source size.
• D. I ∝ 1/r^2; applies for a point isotropic source in free space and when distance is large relative to source dimensions.

Answer: (D)

The main idea is that the exposure rate from a radiating source that emits equally in all directions decreases with the square of the distance. This happens because the energy spreads out over the surface of a sphere as you move away; the sphere’s area grows as 4πr^2, so the energy per unit area falls as 1/r^2. This rule applies when the source can be treated as a point that radiates isotropically and you’re in free space with no significant attenuation or obstructions. In that regime, doubling the distance makes the exposure roughly four times smaller.

Keep in mind that if the distance is small compared to the source’s size, the source is extended, and different parts are at different distances, so the simple 1/r^2 relationship no longer holds. Likewise, any shielding, air attenuation, or scattering will also modify the exposure beyond the pure geometric falloff.