Question

study of matter - nuclear reactions
what fraction of carbon - 14 will remain after 3 half - lives?
a 1/16
b 1/4
c 1/8
d 1/2

Explanation:

Step1: Understand the 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 final amount.

Step2: Substitute \(n = 3\) into the formula

When \(n = 3\), we have \(N=N_0\times(\frac{1}{2})^3\).
Using the exponent rule \((\frac{1}{2})^3=\frac{1\times1\times1}{2\times2\times2}=\frac{1}{8}\).

Answer:

C. \(1/8\)