Answer :
The polonium-218 half-life is 3 minutes.
We may use the following formula to determine how long it will take the sample to reduce to 625 atoms:
N = N0 * (1/2) ^(t/T)
where N0 is the starting atom count (2500).
N is the final atom count (625).
T is the passing of time
T is the polonium-218 half-life (3.05 minutes).625 = 2500 * (1/2) ^(t/3.05) (625/2500) = (1/2) (t/3) log (625-2500) = (t/3) log (1/2) log (625-2500) = (t/3) * log (1/2) = t/3.05 log (625/2500) / log (1/2) = t = 3.05 * log (1/2) = t/3.05
Time is 9.15 minutes.
The sample will thus reach its final state of 625 atoms after 9.15 minutes.
The chemical element polonium has the atomic number 84 and the symbol Po. Although it is a chalcogen and chemically related to selenium and tellurium, polonium is a rare, extremely radioactive metal with no stable isotopes. Its metallic properties are analogous to those of thallium, lead, and bismuth, which are its horizontal Neighbours on the periodic table.
As polonium-210, the ephemeral isotope with a half-life of 138 days, is the last daughter of naturally occurring uranium-238, its natural occurrence is restricted to minute amounts in uranium ores due to the short half-lives of all its isotopes. Even while they do exist, longer-living isotopes are far more challenging to create.
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