A sample initially contains $2.0\times 10^4$ nuclei of a radioactive isotope whose half‑life is 8 days. How many nuclei remain after 24 days?

Step-by-step solution

1. Determine the number of half‑life periods in 24 days: $24\text{days}÷8\text{days}=3$ periods.
2. Use the decay law $N=N_0{\left(\frac{1}{2}\right)}^n$ where $n$ is the number of half‑lives.
3. Substitute $N_0=2.0\times 10^4$ and $n=3$: $N=2.0\times 10^4\times {\left(\frac{1}{2}\right)}^3=2.0\times 10^4\times \frac{1}{8}$.
4. Calculate: $2.0\times 10^4÷8=2.5\times 10^3$.
5. Thus, $2.5\times 10^3$ nuclei remain.

Concept tested: Radioactive decay law

Published 11 September 2026 · How this solution was prepared and checked