Final answer:
To find the mass of a radioactive sample of Pb-214, we connect its activity with the decay constant and number of nuclei, then derive the mass from the quantity of nuclei present.
Step-by-step explanation:
To calculate the mass of a radioactive sample of Pb-214 with an activity of 3.17 x 10⁴ decay/s and a half-life of 26.8 minutes, we use the decay law formula, which relates the activity (A) of a radioactive substance to the number of radioactive nuclei (N) and the decay constant (λ).
The decay constant can be calculated using the half-life formula λ = ln(2) / t₁, where t₁ is the half-life. Once λ is known, the number of nuclei N can be found using A = λN. Finally, to obtain the mass m, we use m = N × (mass of one atom of Pb-214), taking into account Avogadro's number for conversion.
Using these equations, we can perform a step-by-step calculation to find the mass of the Pb-214 sample. However, it is critical to keep units consistent, convert the half-life into seconds, and use the atomic mass of Pb-214 in accordance with the periodic table.