the half-life of a radioactive kind of americium is 432 years. if you start with 814,816 grams of it, how…

Explanation:

Step1: Calculate number of half-lives

$\text{Number of half-lives} = \frac{2160}{432} = 5$

Step2: Apply half-life decay formula

The remaining mass formula is $M = M_0 \times \left(\frac{1}{2}\right)^n$, where $M_0=814816$ and $n=5$. $M = 814816 \times \left(\frac{1}{2}\right)^5 = 814816 \times \frac{1}{32}$

Step3: Compute final remaining mass

$M = \frac{814816}{32} = 25463$

Answer:

25463 grams