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Half Life Example Problem

Worked Example Problem

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Half-life can be used to determine radioactivity.

Half-life can be used to determine radioactivity.

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This example problem demonstrates how to use an isotope's half life to determine the amount of the isotope present after a period of time.

Problem:

228Ac has a half life of 6.13 hours. How much of a 5.0 mg sample would remain after one day?

Solution:

The first step is to determine the number of half lives that have elapsed.

number of half lives = 1 half life/6.13 hours x 1 day x 24 hours/day
number of half lives = 3.9 half lives

For each half life, the total amount of the isotope is reduced by half.

Amount remaining = Original amount x 1/2(number of half lives)

Amount remaining = 5.0 mg x 2-(3.9)
Amount remaining = 5.0 mg x (.067)
Amount remaining = 0.33 mg

Answer:

After 1 day, 0.33 mg of a 5.0 mg sample of 228Ac will remain.
 

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