A lab animal was injected with a solution of radioactive 24 NaCl (t 1/2 for 24 N

Question

A lab animal was injected with a solution of radioactive 24NaCl (t1/2 for 24Na = 14.8 hr). Blood samples were withdrawn at different times after injection and the activity counted with the following results:

Time (hours) 2 4 8 12

Activity (disintegrations min-1 ml-1) 3248 2638 1740 1148

Calculate the effective half-life of the radioactivity in the bloodstream and use your result to obtain the "biological half-life" of Na+ ions due to their removal from the bloodstream by a first order  process of transport to tissue and various other excretion pathways.

Explanation / Answer

Since radioactive decay is the first order reaction, time versus activity (Concentration) gives a striaght line.

The slope of the curve is equal to rate constant -k.

Half-life (t1/2) = (0.693/k).

From the graph, the slope is -3.4709

k = 3.4709 min-1

t1/2 = 0.693 / (3.4709 min-1) = 0.200 min

Half-life is 0.200 min

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