Question

If the intensity of the x-ray is inversely proportional to the square of the distance from the source, by how much does the intensity of the x-ray beam change when the distance from the source of radiation and a measurement point is quadrupled?

Answer 1

The intensity of an X-ray beam decreases to 1/16 of its original value when the distance from the source is quadrupled, as per the inverse square law.

Step-by-step explanation:

The question asks how the intensity of an X-ray beam changes when the distance from the radiation source is quadrupled. According to the inverse square law, the intensity of radiation is inversely proportional to the square of the distance from the source. If the distance is quadrupled, the new intensity is 1/4², or 1/16, of the original intensity.

If we consider an initial intensity at a certain distance, when that distance is increased by a factor of four, the area over which the radiation spreads is sixteen times larger, resulting in each unit area receiving only a sixteenth of the original intensity.