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Answer :
Final answer:
The sample will not decay to 33% of the original amount.
Explanation:
The half-life of caesium-137 is about 30 years. In order to calculate how long it will take a sample to decay to 33% of the original amount, we can use the formula:
Final amount = Initial amount x (1/2)n
where n is the number of half-lives. Since we want to find the time it takes to decay to 33% of the original amount, we need to solve for n when:
Final amount = Initial amount x 0.33
By rearranging the formula, we get:
n = log2(Final amount / Initial amount)
Substituting the given values:
n = log2(0.33 / 1)
Using logarithm properties, we can rewrite the equation as:
n = log2(0.33) - log2(1)
And by evaluating the logarithms:
n = -0.518 - 0
n ≈ -0.518
Since n represents the number of half-lives, it cannot be negative. Therefore, the sample will not decay to 33% of the original amount.
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