Is a small or large decay constant best for protection against gamma radiation? Hint: Calculate half thickness.
Example: Decay constants for Pb, Al, water, and Fe are 0.77, 0.16, 107, and 0.44. Which is better for radiation shielding?
The larger the decay constant, the fewer penetrations of the material.
To determine whether a small or large decay constant is best for protection against gamma radiation, we can calculate the half thickness of various materials.
The half thickness, which is denoted as "H," represents the thickness of a material required to reduce the gamma radiation intensity by half. It is inversely proportional to the decay constant.
The formula to calculate the half thickness is given by:
H = (ln 2) / μ,
where μ is the decay constant of the material.
To calculate the half thickness for each material, we can use the provided decay constants:
For Lead (Pb):
H(Pb) = (ln 2) / 0.77
For Aluminum (Al):
H(Al) = (ln 2) / 0.16
For Water:
H(Water) = (ln 2) / 107
For Iron (Fe):
H(Fe) = (ln 2) / 0.44
By calculating these values, we can determine the best material for radiation shielding based on the smaller half thickness.
After performing the calculations, we find:
H(Pb) ≈ 0.899 cm
H(Al) ≈ 4.324 cm
H(Water) ≈ 0.006 cm
H(Fe) ≈ 1.579 cm
Comparing the half thicknesses, we can see that water has the smallest value, indicating that it requires the least thickness to reduce the gamma radiation intensity by half. Thus, it is the best material for radiation shielding among the given options.
Therefore, a large decay constant is more suitable for protection against gamma radiation as it results in a smaller half thickness, indicating a more efficient shielding material.