How many HVLs are required to reduce the intensity of a beam of monoenergetic photons to less than 15% of its original value?

To determine how many half-value layers (HVLs) are needed to reduce the intensity of a beam of monoenergetic photons to less than 15% of its original value, it's important to understand how HVLs function. Each HVL represents a thickness of material that reduces the intensity of the radiation beam by half.

Starting with 100% intensity:

1. After one HVL, the intensity is reduced to 50% (100%/2).

2. After two HVLs, the intensity decreases to 25% (50%/2).

3. After three HVLs, the intensity is reduced to 12.5% (25%/2).

At three HVLs, the intensity falls below 15%, reaching 12.5%. This demonstrates that three HVLs are required to achieve an intensity of less than 15%. In contrast, two HVLs would leave the intensity at 25%, which is above the 15% threshold, and four HVLs would reduce the intensity even further, but the requirement is to drop below 15%, which is achieved at three. Thus, the correct answer indicates the minimum number of HVLs necessary to accomplish the specified reduction in intensity.