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Answer :
The time since the rock reached its closure temperature is approximately 579.8 years. When the rock was discovered, it had 4.375 grams of europium-151.
To find the time since the rock reached its closure temperature, we can use the following formula
t = t(1/2) * log(N0/Nt)
where t is the time elapsed, t(1/2) is the half-life, N0 is the initial amount of the isotope, and Nt is the amount of the isotope at the time it was discovered.
Substituting the given values, we get
t = 96.6 * log(5/0.625) ≈ 579.8 years
Therefore, the time since the rock reached its closure temperature is approximately 579.8 years.
To find the amount of europium-151 in the rock when it was discovered, we can use the fact that the total amount of samarium-151 and europium-151 in the rock is constant.
Since the rock originally contained 5 grams of samarium-151, it must have contained 5 - 0.625 = 4.375 grams of europium-151 when it was discovered.
Therefore, the rock had 4.375 grams of europium-151 when it was discovered.
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