A sample contains 75 grams of carbon $\left( { } ^ { 14 } C \right) . { } ^ { 14 } C$ has a half-life of 5715 years. How much ${ } ^ { 14 } C$ remains after 100 years? Round your answer to three decimal places.
A) 73.688 grams
B) 74.096 grams
C) 49.524 grams
D) 1.312 grams
E) 37.524 grams

Question

Quizplus · Accepted Answer

The decay of ${ } ^ { 14 } C$ can be calculated using the formula $ N(t) = N_0 \times (1/2)^{t/T} $, where $ N_0 $ is the initial amount, $ t $ is the time elapsed, and $ T $ is the half-life. Substituting the given values, $ N(100) = 75 \times (1/2)^{100/5715} \approx 74.096 $ grams.

A Sample Contains 75 Grams of Carbon (14C).14C\left( { } ^ { 14 } C \right) . { } ^ { 14 } C(14C).14C

A Sample Contains 75 Grams of Carbon $\left( { } ^ { 14 } C \right) . { } ^ { 14 } C$