A sample contains 60 grams of carbon $\left( { } ^ { 14 } C \right) . { } ^ { 14 } C$ has a half-life of 5715 years. How much ${ } ^ { 14 } C$ remains after 1900 years? Round your answer to three decimal places.
A) $40.052$ grams
B) $47.651$ grams
C) $33.913$ grams
D) $19.948$ grams
E) $32.913$ grams

Question

Quizplus · Accepted Answer

To find the remaining amount of ${ } ^ { 14 } C$ after 1900 years, we use the formula for exponential decay: $N = N_0 \times \left( \frac{1}{2} \right)^{\frac{t}{T}}$, where $N$ is the final amount, $N_0$ is the initial amount, $t$ is the time elapsed, and $T$ is the half-life. Plugging in the values: $60 \times \left( \frac{1}{2} \right)^{\frac{1900}{5715}}$, we get approximately $47.651$ grams.

A Sample Contains 60 Grams of Carbon (14C).14C\left( { } ^ { 14 } C \right) . { } ^ { 14 } C(14C).14C

A Sample Contains 60 Grams of Carbon $\left( { } ^ { 14 } C \right) . { } ^ { 14 } C$