1 Multiple Choice 1 point Sodium- 24 has a half-life of 15 hours. After 15 days, how much is left of a 500-gram sample? 1.39 g 20.83 g \( 2.99 \times 10^{-5} \mathrm{~g} \) \( 1.5 \times 10^{-5} \mathrm{~g} \) 2.99 g

To determine how much of the **500-gram** sodium-24 sample remains after **15 days**, we'll follow these steps: 1. **Calculate the Total Time in Hours:** - **15 days** × **24 hours/day** = **360 hours** 2. **Determine the Number of Half-Lives:** - **Half-life of Sodium-24** = **15 hours** - Number of half-lives = **360 hours / 15 hours/half-life** = **24 half-lives** 3. **Calculate the Remaining Amount:** - After each half-life, the amount of the substance reduces by half. - Remaining amount = Initial amount × \( \left(\frac{1}{2}\right)^{\text{number of half-lives}} \) - Remaining amount = **500 g** × \( \left(\frac{1}{2}\right)^{24} \) 4. **Compute the Exponential Decay:** - \( 2^{24} = 16,777,216 \) - So, \( \left(\frac{1}{2}\right)^{24} = \frac{1}{16,777,216} \approx 5.96 \times 10^{-8} \) 5. **Final Remaining Amount:** - **500 g** × \( 5.96 \times 10^{-8} \) ≈ **2.98 × 10⁻⁵ g** **Therefore, the remaining amount after 15 days is approximately \( 2.99 \times 10^{-5} \) grams.** **Answer:** \( 2.99 \times 10^{-5} \mathrm{~g} \)