What mass of ¹⁴C, with a half-life of 5730 y, do you need to provide a decay rate of $280.0 \mathrm {~Bq} ?$ The mass of ¹⁴C is 14.00 u, and 1 u = 1.6605 × 10^-27 kg.

Question

Quizplus · Accepted Answer

The decay rate (activity) is given by $ A = \lambda N $, where $ \lambda $ is the decay constant and $ N $ is the number of atoms. The decay constant $ \lambda $ is related to the half-life $ T_{1/2} $ by $ \lambda = \frac{\ln(2)}{T_{1/2}} $. Using the given half-life, calculate $ \lambda $, then find $ N $ using $ N = \frac{A}{\lambda} $. Convert $ N $ to mass using the atomic mass and Avogadro's number. The correct mass is 1.70 × 10^-12 kg.

What Mass of 14C, with a Half-Life of 5730 Y 280.0 Bq?280.0 \mathrm {~Bq} ?280.0 Bq?

What Mass of ¹⁴C, with a Half-Life of 5730 Y $280.0 \mathrm {~Bq} ?$