Question

the half - life of a radioactive kind of mercury is 64 hours. if you start with 93,568 grams of it, how much will be left after 320 hours? grams

Explanation:

Step1: Find the number of half - lives

The formula to find the number of half - lives \(n\) is \(n=\frac{t}{T}\), where \(t\) is the total time elapsed and \(T\) is the half - life.
Given \(t = 320\) hours and \(T=64\) hours. Then \(n=\frac{320}{64}=5\).

Step2: Use the radioactive decay formula

The formula for radioactive decay is \(N = N_0\times(\frac{1}{2})^n\), where \(N_0\) is the initial amount, \(n\) is the number of half - lives, and \(N\) is the final amount.
We know that \(N_0 = 93568\) grams and \(n = 5\). So \(N=93568\times(\frac{1}{2})^5\).
First, calculate \((\frac{1}{2})^5=\frac{1}{32}\).
Then \(N = 93568\times\frac{1}{32}\).
\(93568\div32 = 2924\).

Answer:

2924