Polonium-218 is an alpha emitter with a half-life of 3.0 minutes. If a sample contains 55 mg of Po-218 (atomic mass = 218.008965 amu), how many alpha emissions occur in 25.0 minutes? If the polonium is ingested by a person, to what amount of radiation (in Ci) is the person exposed?

Verified step by step guidance

1. <insert step 1> Determine the number of half-lives that occur in 25.0 minutes by dividing the total time by the half-life of Po-218.>
2. <insert step 2> Calculate the remaining mass of Po-218 after 25.0 minutes using the formula: \( \text{Remaining mass} = \text{Initial mass} \times \left( \frac{1}{2} \right)^n \), where \( n \) is the number of half-lives.>
3. <insert step 3> Find the mass of Po-218 that has decayed by subtracting the remaining mass from the initial mass.>
4. <insert step 4> Convert the decayed mass of Po-218 to moles using its atomic mass (218.008965 amu) and Avogadro's number (\(6.022 \times 10^{23}\) atoms/mol).>
5. <insert step 5> Calculate the total number of alpha emissions by multiplying the moles of decayed Po-218 by Avogadro's number, and then convert the decayed mass to curies (Ci) using the conversion factor: 1 Ci = 3.7 \times 10^{10} \text{ disintegrations per second}.>