Final answer:
To reduce gamma radiation to 0.100%, multiple layers of lead shielding are required, each absorbing a fraction of the remaining gamma rays not blocked by the previous layer.
Step-by-step explanation:
The question concerns the amount of lead shielding required to reduce gamma radiation from a radium 226 source by a certain amount. Gamma rays, unlike alpha and beta particles, have a much greater range and can penetrate our bodies and many meters of air, but can be effectively shielded by lead. The principle to understand here is that if a specific thickness of lead absorbs a certain percentage of gamma rays, an additional layer of the same thickness will absorb the same percentage of the remaining unabsorbed rays, not the initial amount. Therefore, when a 1.50-cm-thick lead absorbs 90% of gamma rays, another 1.50-cm thickness will absorb 90% of the 10% that penetrated the first layer, and this continues with each additional layer. To reduce the radiation level to 0.100%, we use a logarithmic calculation based on the half-value layer principle.