The half-life of the radium isotope Ra-226 is approximately 1,599 years.What percent of a given amount remains after 100 years? Round your answer to two decimal places.
A)95.76 %
B)5.96 %
C)97.76 %
D)3.13 %
E)0.96 %

Question

The half-life of the radium isotope Ra-226 is approximately 1,599 years.What percent of a given amount remains after 100 years? Round your answer to two decimal places. ​
A)95.76 %
B)5.96 %
C)97.76 %
D)3.13 %
E)0.96 %

Quizplus · Accepted Answer

To find the remaining percent of Ra-226 after 100 years, use the formula for exponential decay: $N = N_0 \times (1/2)^{\frac{t}{T}}$, 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: $N = N_0 \times (1/2)^{\frac{100}{1599}}$. This calculation gives a value of approximately 0.9576 or 95.76% remaining.

The Half-Life of the Radium Isotope Ra-226 Is Approximately 1,599