radioactive decay

Question

The half-life of a radioactive substance is 10 days. What fraction of the original amount will remain after 30 days?

RankGuru · Accepted Answer

1. **Identify Timing**: Life of substance $T = 30$ days. Half-life $T_{1/2} = 10$ days.
2. **Calculate Number of Half-lives ($n$)**:
   - $n = \frac{T}{T_{1/2}} = \frac{30}{10} = 3$ cycles passed.
3. **Determine Fraction Remaining**: The amount remaining is $N = N_0 \left( \frac{1}{2} ight)^n$.
4. **Substitution**:
   - Fraction $= \left( \frac{1}{2} ight)^3 = \frac{1}{2 	imes 2 	imes 2} = \frac{1}{8}$.
5. **Result**: $\frac{1}{8}$ of the original quantity remains.

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