a sample contains 6.25 percent parent isotope and 93.75 percent daughter isotopes. if the half - life of the…

a sample contains 6.25 percent parent isotope and 93.75 percent daughter isotopes. if the half - life of the parent isotope is 58 years, how old is the sample? years done

a sample contains 6.25 percent parent isotope and 93.75 percent daughter isotopes. if the half - life of the parent isotope is 58 years, how old is the sample? years done

Answer

Explanation:

Step1: Determine number of half - lives

The fraction of parent isotope remaining is $0.0625$. We know that the amount of parent isotope $N$ after $n$ half - lives is given by $N = N_0(\frac{1}{2})^n$. If we assume the initial amount of parent isotope $N_0 = 1$, then $0.0625=(\frac{1}{2})^n$. Since $0.0625=\frac{1}{16}=(\frac{1}{2})^4$, $n = 4$.

Step2: Calculate age of sample

The age of the sample $t$ is given by $t=n\times t_{1/2}$, where $t_{1/2}$ is the half - life. Given $t_{1/2}=58$ years and $n = 4$. So $t=4\times58$. $t = 232$

Answer:

232