# Calculating a radioactive sample's mass from its activity [closed]

The question reads as such: "What is the mass of a 1.05 µCi carbon-14 source?"

First I convert to decays/s: $R = 1.05 µCi=3.885 \times 10^4 decays/s$.

The half-life for carbon-14 that we've been using is 5730 years or $T_{1/2}=1.808 \times 10^{11} s$, so $\lambda=\frac{ln(2)}{T_{1/2}}=3.834 \times 10^{-12}s^{-1}$

$R=\lambda N$, so $N=\frac{R}{\lambda}=1.0133 \times 10^{16}nuclei$

Now just to convert to grams: $1.0133 \times 10^{16}nuclei \times \frac{1mol}{N_A} \times \frac{12.011g}{1mol}=2.02 \times 10^{-7}g$. Which unfortunately is the wrong answer. Maybe someone sees a conversion error I made somewhere?

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## closed as off-topic by Brandon Enright, jinawee, Kyle Kanos, BMS, Qmechanic♦Apr 11 '14 at 10:24

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