The half-life of the radium isotope Ra-226 is approximately 1,599 years. If the initial quantity of the isotope is 38 g, what is the amount left after 1,000 years? Round your answer to two decimal places.
A) 24.63 g
B) 30.60 g
C) 25.13 g
D) 11.88 g
E) 12.32 g

Question

Quizplus · Accepted Answer

The amount of a radioactive isotope left 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 left, $A_0$ is the initial amount, $t$ is the time elapsed, and $T$ is the half-life of the substance. Plugging in the given values: $A = 38 \left(\frac{1}{2}\right)^{\frac{1000}{1599}}$, we get approximately 24.63 g.

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