Question

a sample contains 100 g of a radioactive isotope. how much radioactive isotope will remain in the sample after 3 half - lives?

a. 12.5 g
b. 50 g
c. 25 g
d. 100 g

Explanation:

Step1: Recall half - life formula

The formula for the amount of a radioactive substance remaining after \(n\) half - lives is \(N = N_0\times(\frac{1}{2})^n\), where \(N_0\) is the initial amount and \(n\) is the number of half - lives.

Step2: Identify values

Here, \(N_0 = 100\ g\) and \(n = 3\).

Step3: Calculate remaining amount

Substitute the values into the formula: \(N=100\times(\frac{1}{2})^3=100\times\frac{1}{8} = 12.5\ g\).

Answer:

A. 12.5 g