An x-ray exposure at 40 inches (102 cm) results in 200 uGy. What is the new intensity at 50 inches (127 cm)?

To determine the new intensity of an x-ray exposure when changing the distance, you can use the inverse square law. The inverse square law states that the intensity of radiation is inversely proportional to the square of the distance from the source. It can be mathematically described as:

[ I_1 / I_2 = (D_2^2) / (D_1^2) ]

In this scenario, the initial intensity ((I_1)) is 200 µGy at a distance of 40 inches ((D_1)), and we want to find the new intensity ((I_2)) at a distance of 50 inches ((D_2)).

By substituting the values:

• (I_1 = 200) µGy

• (D_1 = 40) inches

• (D_2 = 50) inches

Using the formula:

[ 200 / I_2 = (50^2) / (40^2) ]

Calculating the square of the distances:

• (50^2 = 2500)

• (40^2 = 1600)

Substituting these values into the equation