Bismuth-210 is a beta emitter with a half-life of 5.0 days. If a sample contains 1.2 g of Bi-210 (atomic mass = 209.984105 amu), how many beta emissions occur in 13.5 days? If a person’s body intercepts 5.5% of those emissions, what amount of radiation (in Ci) is the person exposed to?

Verified step by step guidance

1. Calculate the number of half-lives that have passed in 13.5 days by dividing the total time by the half-life of Bi-210.
2. Use the number of half-lives to determine the remaining mass of Bi-210 using the formula: \( \text{Remaining mass} = \text{Initial mass} \times \left( \frac{1}{2} \right)^{\text{number of half-lives}} \).
3. Calculate the decayed mass of Bi-210 by subtracting the remaining mass from the initial mass.
4. Convert the decayed mass of Bi-210 to moles using its atomic mass (209.984105 amu).
5. Calculate the total number of beta emissions by multiplying the moles of decayed Bi-210 by Avogadro's number (\(6.022 \times 10^{23}\) atoms/mol) and then by the percentage of emissions intercepted (5.5%).