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A gamma-ray beam from a particular source has intensity I. After traversing 36 mm of lead, its intensity falls to one-eighth of the original value. What thickness of lead is needed to bring the intensity down to one-half of I?

1. 9 mm
2. 6 mm
3. 12 mm
4. 18 mm

Correct answer: 12 mm

Solution

The intensity of gamma rays decreases exponentially with thickness, and the relationship can be described using the half-value thickness. Since the intensity falls to one-eighth after 36 mm, this indicates that 36 mm corresponds to three half-value thicknesses. Therefore, to reduce the intensity to one-half, only one half-value thickness is needed, which is 12 mm.

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