the half - life of carbon - 14 is 5730 years. how long will it take for 7/8 of a sample of carbon - 14 to…

Explanation:

Step1: Determine remaining fraction

If 7/8 of the sample decays, the remaining fraction $N$ of carbon - 14 is $1-\frac{7}{8}=\frac{1}{8}$.

Step2: Use half - life formula

The formula for radioactive decay in terms of half - life $T_{1/2}$ is $N = (\frac{1}{2})^n$, where $n$ is the number of half - lives. We set $\frac{1}{8}=(\frac{1}{2})^n$. Since $\frac{1}{8}=\frac{1}{2^3}$, then $n = 3$.

Step3: Calculate time passed

Given that the half - life $T_{1/2}=5730$ years, and the number of half - lives $n = 3$. The time $t$ passed is $t=n\times T_{1/2}$. So $t = 3\times5730=17190$ years.

Answer:

17,190 years