During the nuclear explosion, one of the products is Sr with a half-life of 6.93 years. If 1 µg of S — Chemical Kinetics Chemistry Question
Question
During the nuclear explosion, one of the products is Sr with a half-life of 6.93 years. If 1 µg of Sr was absorbed in the bones of a newly born baby in place of Ca, how much time, in years, is required to reduce it by 90% if it is not lost metabolically 90 90
💡 Solution & Explanation
# Solution: Radioactive Decay of Sr-90 **Step 1: Identify the decay formula** Use the exponential decay equation: $$N_t = N_0 \left(\frac{1}{2}\right)^{t/t_{1/2}}$$ where N_t is remaining amount, N_0 is initial amount, t is time elapsed, and t₁/₂ is half-life. **Step 2: Set up the condition** If 90% is reduced, then 10% remains: $$N_t = 0.10 \times N_0$$ **Step 3: Substitute into the decay equation** $$0.10 \times N_0 = N_0 \left(\frac{1}{2}\right)^{t/6.93}$$ $$0.10 = \left(\frac{1}{2}\right)^{t/6.93}$$ **Step 4: Solve using logarithms** Taking log of both sides: $$\log(0.10) = \frac{t}{6.93} \times \log(0.5)$$ $$-1 = \frac{t}{6.93} \times (-0.301)$$ **Step 5: Calculate time** $$t = \frac{-1 \times 6.93}{-0.301} = \frac{6.93}{0.301} = 23.03 \text{ years}$$ Therefore, the answer is **23.03** years.