Question

Iodine-131, a radioactive substance that is effective in locating brain​ tumors, has a​ half-life of only 8 days. A hospital purchased 24 grams of the substance but had to wait seven days before it could be used. How much of the substance was left after seven ​days?

Answer 1

The mass of substance left after 7 days is 13.09 g

The mass of substance left, N is given by

N = N₀exp(-λt) where λ = decay constant and N₀ = initial mass of substance present = 24 g and t = time

Also, λ = 0.693/t' where t' = half-life of iodine = 8 days

So, λ = 0.693/t'

λ = 0.693/8

λ = 0.086625/day

Since the mass of substance left is N = N₀exp(-λt) and we require the mass of substance after t = 7 days,

N = N₀exp(-λt)

N = 24 gexp(-0.086625/day × 7 days)

N = 24 gexp(-0.606375)

N = 24 g × 0.5453

N = 13.09 g

So, the mass of substance left after 7 days is 13.09 g

Learn more about radioactive decay here:

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