activity of radioactive sample

Question

The decay constant of a radioactive substance is 0.693 per day. What is its half-life?

RankGuru · Accepted Answer

1. **Fundamental Relationship**: The half-life $T_{1/2}$ and decay constant $\lambda$ are related by:
   - $T_{1/2} = \frac{\ln 2}{\lambda}$.
2. **Substitute Values**: Given $\lambda = 0.693$ day$^{-1}$. Use the approximation $\ln 2 \approx 0.693$.
3. **Calculation**:
   - $T_{1/2} = \frac{0.693}{0.693} = 1$ day.
4. **Conclusion**: The substance takes one day to decay to half its size.

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activity of radioactive sample

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