The half life of the radium isotope Ra-226 is approximately 1,599 years.If the amount left after 1,000 years is 1.8 g, what is the amount after 2000 years? Round your answer to
Three decimal places.
A)1.167 g
B)0.939 g
C)1.800 g
D)0.490 g
E)2.334 g

Question

Quizplus · Accepted Answer

The half-life formula is used to calculate the remaining amount of a substance after a certain time. Given a half-life of 1,599 years and an initial amount of 1.8g after 1,000 years, we can calculate the amount after another 1,000 years (totaling 2,000 years) by recognizing that the substance will not have reached another half-life by 2,000 years but will have decayed further from the 1.8g. To find the exact amount, we use the formula: $A = P(1/2)^{t/T}$, where $A$ is the amount after time $t$, $P$ is the initial amount, $t$ is the elapsed time, and $T$ is the half-life period. Since the question asks for the amount after an additional 1,000 years from the 1.8g point, we calculate it as if 1.8g were the initial amount and 1,000 years have passed. However, the correct approach involves understanding the decay process over the total period, which leads to the realization that after another 1,000 years (making it 2,000 years in total), the amount will have decayed further but not halved again from the 1.8g. The exact calculation requires applying the decay formula correctly over the total period, but the provided options and the context suggest an approximation based on understanding the decay process, leading to the selection of 1.167g as the closest estimate given the options and the nature of radioactive decay, which is a continuous process described by the formula. This explanation corrects the initial guidance on calculation to clarify the conceptual understanding of radioactive decay over time.

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