An x-ray exposure measured at 38 inches results in a beam intensity of 90 microgray. What is the new intensity for an x-ray exposure at 48 inches?

To determine the new intensity of the x-ray beam at 48 inches using the inverse square law, it's essential to understand the relationship between the distance from the x-ray source and the intensity of the x-ray beam. The inverse square law states that the intensity of radiation is inversely proportional to the square of the distance from the source.

In mathematical terms, this is expressed as:

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

where ( I_1 ) and ( I_2 ) are the intensities at distances ( D_1 ) and ( D_2 ), respectively.

In this case, the initial distance ( D_1 ) is 38 inches and the measured intensity ( I_1 ) is 90 microgray. We want to find ( I_2 ) at a new distance ( D_2 ) of 48 inches.

Plugging in the values:

• ( D_1 = 38 )

• ( I_1 = 90 )

• ( D_2 = 48 )

Using the inverse square law formula:

[ 90 / I_2 = (48