decay of a radioactive substance\nhow many half lives has an isotope gone through if it has 12.5% of the…

Explanation:

Step1: Recall half-life decay formula

The remaining amount of a radioactive substance is given by: $$N(t) = N_0 \times \left(\frac{1}{2}\right)^n$$ where $N(t)$ is the remaining amount, $N_0$ is the initial amount, and $n$ is the number of half-lives.

Step2: Substitute given remaining percentage

We know $\frac{N(t)}{N_0} = 0.125$ (12.5% as a decimal). Substitute into the formula: $$0.125 = \left(\frac{1}{2}\right)^n$$

Step3: Solve for number of half-lives

Rewrite 0.125 as a fraction: $0.125 = \frac{1}{8} = \left(\frac{1}{2}\right)^3$. Equate exponents: $$n = 3$$

Answer:

3 (Option A)