If \( N_0 \) is the original mass of the substance of half life \( t_{1/2} = 4 \) years, then the amount of substance left after 12 years is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( N_0/8 \)
In every half-life the amount of a radioactive substance falls to half. After \( n \) half-lives the amount left is
\( \displaystyle N = \frac{N_0}{2^{n}} \)
The number of half-lives in 12 years is
\( \displaystyle n = \frac{t}{t_{1/2}} = \frac{12\,\mathrm{years}}{4\,\mathrm{years}} = 3 \)
\( \displaystyle N = \frac{N_0}{2^{3}} = \frac{N_0}{8} \)