A research laboratory stores a mixed radioactive sample that emits α, β−, and γ radiation of equal initial intensities. The laboratory manager must design a single shield that reduces the external intensity of each radiation type to less than 1 percent of its original value before it reaches a distance of 0.5 m from the source. The manager may use any combination of ordinary paper (density comparable to wood fiber), acrylic plastic (density ≈1.2gcm−3), and lead (density ≈11.3gcm−3). Empirical tests provide the following information.
• A sheet of paper 0.1 mm thick stops more than 99 percent of 5 MeV α particles.
• A 10 mm thickness of acrylic stops more than 99 percent of 1 MeV β− particles.
• A 50 mm thickness of lead attenuates 1 MeV γ rays to 1 percent of their original intensity.
(1) Design a composite shield using only the three listed materials that meets the manager’s requirement. State the material(s) chosen, their order relative to the source, and the minimum thickness of each layer.
(2) Explain for each layer in your design why that particular material and thickness are appropriate for stopping the corresponding radiation.
(3) Suppose the order of the layers were reversed so that the lead were nearest the source and the paper were outermost. Predict qualitatively how the overall effectiveness of the shield would change for each radiation type, and justify your predictions.