Question

how much of a radioactive kind of rhodium will be left after 168 minutes if you start with 878,832 grams and the half - life is 56 minutes? 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 and \(T\) is the half - life.
Given \(t = 168\) minutes and \(T=56\) minutes.
So \(n=\frac{168}{56}=3\)

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 \(N_0 = 878832\) grams and \(n = 3\).
Substitute the values into the formula: \(N=878832\times(\frac{1}{2})^3\)
First, calculate \((\frac{1}{2})^3=\frac{1}{8}\)
Then, \(N = 878832\times\frac{1}{8}\)
\(878832\div8 = 109854\)

Answer:

109854