Final answer:
To find the mass of 40K responsible for a decay rate of 4140 Bq, one must use the decay constant derived from the half-life. The mass is then obtained by converting nuclei to moles and grams. For the fraction of 40K in natural potassium, one uses the natural abundance and decay rate per mole to calculate the moles of 40K in the given amount of potassium in the body.
Step-by-step explanation:
To calculate the mass of 40K in a person that would result in a decay rate of 4140 Bq, we must use the formula that relates activity (A) to the number of radioactive nuclei (N) and the decay constant (λ), which is A = λN. The decay constant can be found from the half-life (T1/2) using the formula λ = ln(2) / T1/2. The mass of 40K can then be determined by converting the number of nuclei to moles and then to grams, keeping in mind the molar mass of 40K.
To find the fraction of 40K in natural potassium when a person has 140 g of potassium in their body, we must use the natural abundance of 40K and the total amount of potassium present. Factoring in that the decay rate of 1 mol of 40K is 1.05 × 107 decays/second, we can calculate the number of moles of 40K. This fraction can be further used to find the total mass of 40K in the body and relate it to the given 140 g of potassium.