High School

A sample of copper-64 was used in a procedure to study copper metabolism 39 hours ago, and now 3.50 mCi remain. What was the size of the original sample?

(Note: Copper-64 has a half-life of 13 hours.)

Answer :

Final answer:

The original sample of copper-64 used in the procedure to study copper metabolism was 28 mCi. The size was calculated using the formula for radioactive decay.

Explanation:

The problem involves radioactive decay of copper-64 which can be solved by the formula for exponential decay, N = N0 * (1/2)^(t/T), where N is the final amount, N0 is the initial amount, t is the time that has passed, and T is the half-life of the substance. Given that N is 3.50 mCi, the half-life T is 13 hours, and the time t is 39 hours, you can rearrange the equation to solve for N0 (the initial amount): N0 = N / (1/2)^(t/T) = 3.50 mCi / (1/2)^(39/13) = 3.50 mCi / (1/2)^3 = 3.50 mCi / 0.125 = 28 mCi. So, the original sample of copper-64 used in the procedure studying copper metabolism was 28 mCi.

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