Lodine - 131, a radioactive substance that is effective in localing brain tumors, a half-life of only eight days. A hospital purchased 22 grams of the substance but had to wail five days before it could be used. How much of the substance was left after five days?

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Data analysis Given data, Initial amount of substance (P0)=22gms Half-life (t1/2)=8 days Time period (t)=5 days Amount of substance left after &#039;t&#039; = ? Solution The decay of an radioactive substance is exponential. And the amount of substance (P) left fter &#039;t&#039; days is given by, P=P0e−λ t Where lambda is decay constant. Given t1/2=8 days That is by 8 days, amount left will become half. ⇒ (P0/2)=P0e−λ(8) ⇒ 8λ=ln⁡(2) ⇒ λ=(1/8)ln⁡(2) ⇒ λ=0.0866434 (rounded to 7 decimals) Now after 5 days, amount left, ⇒ P=22(e0.0866434(5)) =22(0.6484198) ⇒ P=14.2652356    Hence amount left after 5 days is 14.265 grams (rounded to 3 decimals)

Lodine - 131, a radioactive substance that is effective in localing brain tumors, a half-life of only eight days. A hospital purchased 22 grams of the substance but had to wail five days before it could be used. How much of the substance was left after five days?

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