A small quantity of solution containing of $$11Na$$ $$24$$ radionuclide $$t1/2=15hrs$$ of activity $$1.0$$μCi is injected in to the blood of a person. A sample of the blood of volume $$1cm3$$ taken after $$5hour$$ shows an activity of $$296$$ dpm. Determine the total volume of the blood in the body of the person. Assume the radioactive solution mixes uniformly in the blood of the person $$1.0Ci=3.7$$×$$1010dps(antilog$$ of $$0.1$$≃$$1.26)$$

Question

A small quantity of solution containing of  $$11Na$$ $$24$$ radionuclide $$t1/2=15hrs$$ of activity $$1.0$$μCi is injected in to the blood of a person. A sample of the blood of volume $$1cm3$$ taken after $$5hour$$ shows an activity of $$296$$ dpm. Determine the total volume of the blood in the body of the person. Assume the radioactive solution mixes uniformly in the blood of the person $$1.0Ci=3.7$$×$$1010dps(antilog$$ of $$0.1$$≃$$1.26)$$

Infinity Learn · Accepted Answer

$$t=2.303$$λ$$log10R0R$$,λ$$=0.69315t=2.3030.693/15log10R0296log10R0296=5$$×$$0.6932.303$$×$$15$$,$$R0296=1.26R0=373dpm=37360dps$$ If activity $$37360$$ , volume of blood $$1$$ $$cm3$$ . $$5951.7$$ $$cm3=5.951$$≈$$6lts$$

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