Final answer:
The half-value layer for lead with a linear attenuation coefficient of 4.5 cm^-1 for 300 keV γ-rays is calculated by dividing the natural logarithm of 2 by the linear attenuation coefficient, resulting in an HVL of 0.154 cm or 1.54 mm.
Step-by-step explanation:
The student's question pertains to the concept of the half-value layer in the context of gamma-ray attenuation by lead. The linear attenuation coefficient given is 4.5 cm-1 for 300 keV γ-rays, and we are asked to determine the half-value layer for this material, which is the thickness required to reduce the intensity of gamma radiation by half. The half-value layer (HVL) can be calculated using the formula HVL = ln(2)/μ, where μ is the linear attenuation coefficient.
To find the HVL, we take the natural logarithm of 2 (approx. 0.693) and divide it by the linear attenuation coefficient (4.5 cm-1). Thus, the half-value layer for lead with the given attenuation coefficient is calculated as follows:
HVL = 0.693 / 4.5 cm-1 = 0.154 cm or 1.54 mm. This represents the thickness of lead needed to reduce the intensity of 300 keV γ-rays by 50%.