A 4.50 mg sample of a newly discovered radioactive nucleus was analyzed and found to contain only 3.25 mg after a period of 32.1 h.What is the half-life of the nucleus?

Question

Quizplus · Accepted Answer

To find the half-life of the nucleus, we can use the following formula:

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

Where:
N0 = initial amount of the nucleus = 4.50 mg
N = final amount of the nucleus = 3.25 mg
t = time interval = 32.1 h
T = half-life

Substituting the given values, we get:

3.25 = 4.50 * (1/2)^(32.1/T)

Solving for T, we get:

T = 68.4 h

Therefore, the half-life of the nucleus is 68.4 h, which corresponds to choice B.

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