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P32 is a radioactive isotope with a half-life of 14.3 days. If

you currently have 62.7 g of P32, how much P32 was present 3.00
days ago?
Please show all work :)

1 Answer

4 votes

Final answer:

About 69.7 g of P32 was present 3.00 days ago before decaying to the current 62.7 g, calculated using the radioactive decay formula with a half-life of 14.3 days.

Step-by-step explanation:

To find out how much P32 was present 3.00 days ago, we can use the half-life formula for radioactive decay. The half-life of P32 is 14.3 days. The amount of radioactive isotope remaining can be calculated by the following equation:

N = N0 * (1/2)^(t/T)

Where:

t is the elapsed time,

Given that t = 3.00 days and T = 14.3 days and currently, there is 62.7 g of P32, we want to find out N0. Rearranging the formula to solve for N0, we get:

N0 = N / (1/2)^(t/T)

Replacing the known values:

N0 = 62.7 g / (1/2)^(3/14.3)

Now, using a calculator to find the results:

N0 = 62.7 g / (1/2)^(0.20979)

N0 = 62.7 g / 0.8992

N0 ≈ 69.7 g (rounded to two decimal places)

Therefore, about 69.7 g of P32 was present 3.00 days ago.

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