Question

The half-life of a certain element is 4 years. Find out the fraction of a sample of that isotope remain after 8 years?

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{4}$
• D. $\frac{1}{8}$
• E. $\frac{1}{12}$

Answer 1

Answer: (C)

$\frac{1}{4}$

Given : $T_{1/2}=4$ years $t=8$ years

Let the initial amount the sample be $R_o$.

Thus remaining amount, $R=\frac{R_o}{2^n}$ where $n=\frac{t}{T_{1/2}}$

$\therefore$ $n=\frac{8}{4}=2$

$⟹$ Fraction of remaining amount, $\frac{R}{R_o}=\frac{1}{2^2}=\frac{1}{4}$

Thus, one-fourth (1/4) of the original amount is left after 8 years.