Chromium-51 is used in imaging red blood cells and has an effective half-life of 27 days. if a dose with an activity of 32 μci is given to a patient, how long will it take for the patient to have less than 8 μci present?

54 days

Explanation:

The half-life is the time need for the mass decrease by half. Thus, if the initial mass is m, after one half-live it will be m/2. Then, if another half-live pass, the m/2 mass will decrease by half, being m/4, and then successfully. After n half-lives, the final mass (M) is:

M = m/2ⁿ

So, if the final mass is 8μCi, and the initial is 32:

8 = 32/2ⁿ

2ⁿ = 32/8

2ⁿ = 4

n = 2

So, it's necessary to pass 2 half-lives, or 54 days to the mass decrease to 8μCi, thus after 54 days it will be less than 8μCi.

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