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?

Ava-May Nelson 2021-03-07 Answered
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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Expert Answer

Tuthornt
Answered 2021-03-08 Author has 107 answers

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 't' = ?
Solution
The decay of an radioactive substance is exponential.
And the amount of substance (P) left fter 't' days is given by,
P=P0eλ t
Where lambda is decay constant.
Given t1/2=8 days
That is by 8 days, amount left will become half.
 (P0/2)=P0eλ(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)

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