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# Radioisotope Medicinal Use and Half-life

CHEM-Y6NQIZ

Cancer cells have a tendency to accumulate phosphate compared to normal cells. Phosphorus-32 is used in the identification of malignant tumors in the body.

$_{ }^{ 32 }{ P }$ is a therapeutic radionuclide that has a half-life of 14.3 days.

If a patient is given this radionuclide containing 10 $\mu g$ $_{ }^{ 32 }{ P }$, how long will it take for the amount of $_{ }^{ 32 }{ P }$ to decrease to one-hundredth of the original amount?

Use the following formulas to answer the question:

$${ t }_{ 1/2 }=\cfrac { ln \ 2 }{ k } =\cfrac { 0.693 }{ k }$$

and

$$ln\cfrac { A_o }{ A } =kt$$

A

14.30 days

B

95.02 days

C

47.48 days

D

142.40 days