Answer :

The given question is based on half-life. The relationship between the decay rate, the half-life, and the initial quantity of radioactive atoms of the material is given by the radioactive decay law.

According to the radioactive decay law, the decay of radioactive atoms is governed by the following equation: `N = N₀(1/2)^(t/h)` where N is the final quantity of radioactive atoms remaining after a certain time t, N₀ is the initial quantity of radioactive atoms, and h is the half-life of the material. Given: Initial quantity N₀ = 100 g, Final quantity N = 6.25 g, Time taken to decay t = 10.8 days. Now, we can use the formula to calculate the half-life of Au-198. First, we need to find the decay constant k. We know that, at the end of 10.8 days, the amount of Au-198 remaining is 6.25 g.

Using this value, we can write:`N = N₀e^(-kt)`6.25 = 100e^(-k * 10.8). Simplifying: 0.0625 = e^(-10.8k). Taking the natural logarithm of both sides:` ln (0.0625) = -10.8k`k = -0.0641 (rounded to 4 significant figures)

Now we can calculate the half-life h of Au-198:`1/2 = e^(-k * h)`0.5 = e^(0.0641h). Taking the natural logarithm of both sides:`ln(0.5) = 0.0641h`h = 10.8 days (rounded to 3 significant figures)

Therefore, the half-life of Au-198 is 10.8 days.

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