Question

Iodine-131 is a radioactive isotope. after 8.00 days, 50.2% of a sample of 131i remains. what is the half-life of 131i?

Answer 1

 The half life  of 131 i  is  8.06  days

   calculation

by  use  of concentration  time   equation  for  radioactive  decay

In Nt/No = -Kt

where  Nt/No  is the  fraction  of the sample   remaining  at  time T

convert 50.2%  in  decimal  = 50.2/100 = 0.502

therefore = In  0.502 = -  K 8.0 t
                     - 0.689 =-8.0 k
divide both side by 8.0

                       K =  0.860

t1/2  =  0.693/K

t1/2 = 0.693/0.860 =  8.06   days

Answer 2

Answer:

8.04625882 days

Explanation:

50.2% of a sample remains after 8 days, which means 49.8% has decayed. So:

50%^x=49.8%

log .5^x=log .498

x log .5=log .498

x=1.005782352594

Then:

1.005782352594 x 8=8.04625882 days as the half-life of Iodine-131