Question

the % of the parent isotope remaining after 2 half lives.

Explanation:

Step1: Understand half - life concept

The amount of a parent isotope remaining after \(n\) half - lives is given by the formula \(N = N_0\times(\frac{1}{2})^n\), where \(N_0\) is the initial amount of the parent isotope and \(n\) is the number of half - lives. Here, we want to find the percentage, so we can assume \(N_0 = 100\%\) (or \(N_0=1\) in decimal form and then convert to percentage at the end).

Step2: Substitute \(n = 2\) into the formula

When \(n = 2\), we have \(N=100\%\times(\frac{1}{2})^2\). Using the exponent rule \((\frac{1}{2})^2=\frac{1\times1}{2\times2}=\frac{1}{4}\). Then \(N = 100\%\times\frac{1}{4}\).

Step3: Calculate the value

\(100\%\times\frac{1}{4}=25\%\)

Answer:

\(25\%\)