Final answer:
The exposure rate at 2 meters can be found using the inverse square law of radiation, resulting in 468.75 mR/hr, which rounds to the closest answer choice, 469 mR/hr.
Step-by-step explanation:
The question is related to the inverse square law in radiation physics, which states that the intensity of radiation at a certain distance from a point source is inversely proportional to the square of the distance. By calculating the dose rate at the new distance, we're assuming a point source for simplicity and that there is no attenuation or scattering.
The initial exposure rate at 5 meters is 75 mR/hr. To find the exposure rate at 2 meters, we apply the inverse square law:
(Organization ratio) = (distance1)^2 / (distance2)^2 = (5m)^2 / (2m)^2 = 25/4. Since the exposure rate is inversely proportional to the square of the distance,
(Exposure rate at 2m) = (Exposure rate at 5m) × (Organization ratio) = 75 mR/hr × (25/4) = 75 mR/hr × 6.25 = 468.75 mR/hr. Therefore, the closest answer choice to the calculated value is (d) 469 mR/hr.