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 decay