What will be the new intensity for an x-ray exposure at 72 inches (183 cm) if the intensity at 60 inches (152 cm) is 100 microgray (uGy)?

To determine the new intensity of an x-ray exposure at a different distance, the inverse square law is applied. This law states that the intensity of radiation is inversely proportional to the square of the distance from the source. The formula for this is:

I1 / I2 = (d2^2) / (d1^2)

In this scenario, the known intensity at 60 inches is 100 microgray, and we want to find the intensity at 72 inches.

1. First, we identify our distances: d1 = 60 inches and d2 = 72 inches.

2. We can set up our equation:

I1 / I2 = (72^2) / (60^2)

3. Rearranging the equation to solve for I2 (the intensity at 72 inches):

I2 = I1 * (60^2 / 72^2)

4. Now, substituting the known values:

I2 = 100 μGy * (60^2 / 72^2)

This calculates to:

I2 = 100 μGy * (3600 / 5184)

I2 = 100 μGy * (0.694