Iodine131 is a radioactive isotope After 700 days 547 of a s

Iodine-131 is a radioactive isotope. After 7.00 days, 54.7% of a sample of 131I remains. What is the half-life of 131I?

The concentration-time equation for radioactive decay is

ln (Nt/No) = -kt . . .where Nt/No is the fraction of sample remaining at time t.

54.7%, or 0.547 expressed in decimals.

ln (0.547) = -(k)(7.00 d)

-0.603 = -7.00k

k = 0.0862 d^-1

The half life for radioactive decay is

t1/2 = 0.693 / k = 0.693 / 0.0862 d^-1 = 8.039 days