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The isotope 206po has a half-life of 8.8 days. if you have 5.68 x 1025 atoms of this isotope, how long will it take for the sample to decay to 8.88 x 1023 atoms?
Accepted Answer
Here's how to calculate the time it takes for the sample to decay:
1. Determine the number of half-lives:
Start with the initial number of atoms (5.68 x 10^25) and divide it by the final number of atoms (8.88 x 10^23) to find the fraction remaining: (8.88 x 10^23) / (5.68 x 10^25) = 0.0156
Since each half-life reduces the number of atoms by half, we need to figure out how many times we need to divide the initial amount by 2 to get to 0.0156. This can be done by taking the logarithm (base 2) of 0.0156: log2(0.0156) ≈ -6. This means the sample has gone through approximately 6 half-lives.
2. Calculate the total time:
Multiply the number of half-lives (6) by the half-life of 206Po (8.8 days): 6
8.8 days = 52.8 days.
Therefore, it will take approximately 52.8 days for the sample to decay to 8.88 x 10^23 atoms.
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