Question

how much of a radioactive kind of cadmium will be left after 28 years if you start with 982,168 grams and the half - life is 14 years? grams

Explanation:

Step1: Determine the number of half - lives

The half - life of cadmium is 14 years, and the time elapsed is 28 years. To find the number of half - lives \(n\), we use the formula \(n=\frac{t}{T}\), where \(t = 28\) years and \(T=14\) years.
\(n=\frac{28}{14}=2\)

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 remaining amount.
We know that \(N_0 = 982168\) grams and \(n = 2\). Substitute these values into the formula:
\(N=982168\times(\frac{1}{2})^2\)
First, calculate \((\frac{1}{2})^2=\frac{1}{4}\)
Then, \(N = 982168\times\frac{1}{4}\)
\(N=\frac{982168}{4}=245542\)

Answer:

245542