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

8.04625882 days

Step-by-step 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

Answer 2

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