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}.

Key Concepts

Half-life

Half-life is the time required for half of the radioactive nuclei in a sample to decay. For Polonium-218, with a half-life of 3.0 minutes, this means that after 3.0 minutes, half of the original amount will have decayed. Understanding half-life is crucial for calculating the remaining quantity of a radioactive substance over time and determining the number of decay events that occur within a specified period.

Alpha decay

Alpha decay is a type of radioactive decay in which an unstable nucleus emits an alpha particle, consisting of two protons and two neutrons. This process reduces the atomic number of the element by two, transforming it into a different element. In the context of Polonium-218, each decay event results in the emission of an alpha particle, which is essential for calculating the total number of emissions over a given time frame.

Curie (Ci)

The Curie (Ci) is a unit of radioactivity that quantifies the rate of decay of radioactive materials. One Curie is defined as 3.7 x 10^10 disintegrations per second, which provides a measure of the intensity of radiation emitted by a radioactive source. When assessing the exposure to radiation from ingested Polonium-218, converting the decay events into Curie units helps quantify the potential health risks associated with the radiation exposure.