Question

1. carbon - 14 has a half - life of 5730 years. how much of a 144 g sample of carbon - 14 will remain after 17,190 years?

Explanation:

Step1: Calculate the number of half - lives

The formula for the number of half - lives \(n=\frac{t}{T}\), where \(t = 17190\) years (time elapsed) and \(T=5730\) years (half - life).
\(n=\frac{17190}{5730}=3\)

Step2: Use the radioactive decay formula

The formula for the remaining amount of a radioactive substance is \(N = N_0\times(\frac{1}{2})^n\), where \(N_0 = 144\) g (initial amount) and \(n = 3\) (number of half - lives).
\(N=144\times(\frac{1}{2})^3\)
First, calculate \((\frac{1}{2})^3=\frac{1}{8}\)
Then, \(N = 144\times\frac{1}{8}=18\) g

Answer:

\(18\) g