Radioactive tracers are used to study ion transport across cell membranes. The b

Question

Radioactive tracers are used to study ion transport across cell membranes. The beta-minus emitting isotope 42K (t1/2 = 12.4 h) has been particularly important for measuring the movement of potassium ions. A saline solution that contains the isotope bathes cells in a test tube, and the amount of 42K that has accumulated inside the cells is measured after a short time. A sample of liquid extracted from the cells must have an activity of at least 50 Bq for an accurate measurement to be made. The activity of a sample just after extraction is 725,000 Bq. If a scientist wishes to confirm the result by measuring the sample a week later, how much activity will remain? Bq

Explanation / Answer

The isotope decays according to the law:

N(t) = N0*e^(-kt) ..........................(1)

where N0 = activity at time t = 0 and k = decay constant

decay constant K=Log(2)/T....................(2)
equation 2 is substituting in equation 1
So now you have N(t) = N0*e^(-ln(2)*t/T)

Set T = 12.4 hrs and t = 1 week = 7 days = 24*7 hrs = 168 hrs

Then e^(-ln(2) t/T) = 8.35x10^-5 so N(t) = 725,000 Bq*8.35x10^-5 = 60.54 Bq

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