Question

you have 0,560 grams of a radioactive kind of rubidium. if its half - life is 15 minutes, how much will be left after 45 minutes? grams

Explanation:

Step1: Determine the number of half - lives

The half - life of rubidium is 15 minutes, and the total time elapsed is 45 minutes. To find the number of half - lives \(n\), we use the formula \(n=\frac{\text{Total time}}{\text{Half - life}}\).
Substituting the values, we get \(n = \frac{45}{15}=3\).

Step2: Calculate the remaining amount

The formula for the remaining amount \(A\) of a radioactive substance after \(n\) half - lives is \(A = A_0\times(\frac{1}{2})^n\), where \(A_0\) is the initial amount.
We know that \(A_0 = 6560\) grams and \(n = 3\). So we substitute these values into the formula:
\(A=6560\times(\frac{1}{2})^3\)
First, calculate \((\frac{1}{2})^3=\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{8}\)
Then, \(A = 6560\times\frac{1}{8}\)
\(6560\div8 = 820\)

Answer:

820