Which statement best describes the relationship between radiation dose and distance according to the inverse square law?

Which statement best describes the relationship between radiation dose and distance according to the inverse square law?

• A. Dose is independent of distance
• B. Dose increases with distance
• C. Dose decreases with distance according to the inverse square law
• D. Dose varies randomly with distance

Answer: (C)

The relationship being tested is how radiation dose changes with distance, and it follows the inverse square law: dose decreases as distance increases, with dose proportional to 1 over the distance squared. Because the radiation spreads over a spherical surface, doubling the distance makes that surface four times larger, so the dose drops to one quarter of its original value. If you triple the distance, the dose becomes one ninth of the original, and so on. This means the dose must decrease with distance according to 1/r^2, which is why the statement that dose decreases with distance according to the inverse square law is the best description. The other ideas—dose being independent of distance, increasing with distance, or varying randomly—do not fit this predictable, distance-dependent relationship.

The relationship being tested is how radiation dose changes with distance, and it follows the inverse square law: dose decreases as distance increases, with dose proportional to 1 over the distance squared. Because the radiation spreads over a spherical surface, doubling the distance makes that surface four times larger, so the dose drops to one quarter of its original value. If you triple the distance, the dose becomes one ninth of the original, and so on. This means the dose must decrease with distance according to 1/r^2, which is why the statement that dose decreases with distance according to the inverse square law is the best description. The other ideas—dose being independent of distance, increasing with distance, or varying randomly—do not fit this predictable, distance-dependent relationship.