How many curies of Ir-192 are indicated if the dose rate from the source is 320 mR/hr at 40 feet?

To determine the number of curies of Iridium-192 (Ir-192) based on a given dose rate, the calculation follows the inverse square law, which states that the intensity of radiation decreases with the square of the distance from the source.

The dose rate is measured in millirems per hour (mR/hr), and the relationship between the dose rate at a certain distance and the activity of the radioactive source (in curies) is derived from calibration data. For Ir-192 specifically, there is a known dose rate of approximately 1.1 mR/hr per curie of activity at 1 meter.

In this scenario, the stated dose rate is 320 mR/hr at a distance of 40 feet. To utilize the inverse square law, it’s essential to convert feet to meters for consistency, knowing that 40 feet is approximately 12.19 meters.

Using the formula:

[ \text{Dose Rate} = \frac{A}{d^2} ]

where (A) is the activity in Curies and (d) is the distance in meters, we can rearrange it to:

[ A = \text{Dose Rate} \times d^2 ]