Question

the half - life of radium - 226 is 1,600 years. what fraction of a radium - 226 sample will remain after 4,800 years?
a. $\frac{1}{2}$
b. $\frac{1}{4}$
c. $\frac{1}{8}$
d. $\frac{1}{16}$

Explanation:

Step1: Calculate number of half - lives

The number of half - lives $n=\frac{4800}{1600}=3$.

Step2: Use decay formula

The fraction of the sample remaining $N = (\frac{1}{2})^n$. Substituting $n = 3$ into the formula, we get $N=(\frac{1}{2})^3=\frac{1}{8}$.

Answer:

C. $\frac{1}{8}$