Answer :
The estimated half-life of Po-218 is approximately 3.03 minutes.
To estimate the half-life of polonium-218 (Po-218), we can use the concept of half-life, which is the time it takes for half of the radioactive substance to decay.
Given that 62.0% of the sample remains after 2.14 minutes, it means that 38.0% of the sample has decayed. Since half of the sample decays in one half-life, we can set up the following equation:
0.380 = (1/2)^n
Where n is the number of half-lives. We can solve for n by taking the logarithm of both sides:
log(0.380) = n * log(1/2)
n ≈ log(0.380) / log(1/2)
n ≈ 1.415
Since n represents the number of half-lives, we can estimate the half-life of Po-218 by multiplying the time interval by the number of half-lives:
half-life ≈ 2.14 minutes * 1.415 ≈ 3.03 minutes
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