Radioactive carbon, ${ } ^ { 14 } \mathrm { C }$ , has a has a half-life of 5730 years. After 1000 years, 3.7 grams remain. What was the initial quantity of ${ } ^ { 14 } \mathrm { C }$ ? Round your answer to two decimal places.
A)4.18 grams
B)3.90 grams
C)4.35 grams
D)6.98 grams
E)3.94 grams

Question

Quizplus · Accepted Answer

The amount of radioactive carbon remaining after a certain period can be calculated using the formula $A = A_0 \left(\frac{1}{2}\right)^{\frac{t}{T}}$, where $A$ is the amount remaining, $A_0$ is the initial amount, $t$ is the time elapsed, and $T$ is the half-life. Rearranging to solve for $A_0$, we get $A_0 = A \left(\frac{1}{2}\right)^{-\frac{t}{T}}$. Substituting $A = 3.7$ grams, $t = 1000$ years, and $T = 5730$ years, we find $A_0 \approx 4.18$ grams.

Radioactive Carbon 14C{ } ^ { 14 } \mathrm { C }14C

Radioactive Carbon ${ } ^ { 14 } \mathrm { C }$