Question

A substance has a half-life of 5 years, Find out how much of the initial sample remains after 10 years?

• A. one-fourth (1/4)
• B. one-sixteenth (1/16)
• C. one-half (1/2)
• D. one-fifth (1/5)
• E. one-eighth (1/8)

Answer 1

The correct option is A one-fourth (1/4)

Given : $T_{1/2}=5$ years $t=10$ years

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

$\therefore$ $n=\frac{10}{5}=2$

Thus remaining amount, $R=\frac{R_o}{2^2}=\frac{R_o}{4}$

Hence one-fourth (1/4) of the original amount remains after $10$ years.