Question

The radioactive decay of I-131 is first order with a half life of 8.02 days. How long will it take for 80% of a sample to decay? The answer is 19 days. I need help working it out to get that answer. Thank you in advance.

Answer #1

**Answer** – we are given, Half-life t ½ = 8.02
days, t = ?

I_{o} = 100 % , I_{t} = 100 -80 = 20 %

First we need to calculate the decay constant from the given half-life

We know formula for first order half life ,

t ½ = 0.693 /k

k = 0.693 / t ½

= 0.693 / 8.02 days

= 0.0864 day^{-1}

Now we need to use the integrated formula for first order

ln I_{t} /I_{o} = -k * t

ln 20 /100 = - 0.0864 day^{-1} * t

-1.609 = - 0.0864 day^{-1} * t

So, t = 1.609/0.0864 day^{-1}

= 18.6 days

= 19 days

So **19 days** will it take for 80% of a sample to
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