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

Question

Quizplus · Accepted Answer

The amount of radium left after 1,000 years can be calculated using the formula for exponential decay: $A = P(1/2)^{t/T}$, where $A$ is the amount remaining, $P$ is the initial amount, $t$ is the time elapsed, and $T$ is the half-life. Substituting the given values: $A = 38(1/2)^{1000/1599}$, which approximately equals $24.63 \mathrm{~g}$.

The half-life of the radium isotope Ra-226 is approximately 1,599 years. If the initial \text { The half-life of the radium isotope Ra-226 is approximately } 1,599 \text { years. If the initial } The half-life of the radium isotope Ra-226 is approximately 1,599 years. If the initial

$\text { The half-life of the radium isotope Ra-226 is approximately } 1,599 \text { years. If the initial }$