= 7.55 days
Half life is the time taken by a radioactive isotope to decay by half its original amount.
To calculate the new mass or amount;
New mass = Original mass × (1/2)^n ; where n is the number of half lives.
New mass = 18%, while the original mass = 100 %, half life = 3.05 days
18 = 100 × (1/2)^n
(1/2)^n = 0.18
introducing logarithms;
n log 0.5 = log 0.18
n = log 0.18/ log 0.5
= 2.474
But 1 half life is 3.05 days
Hence; time taken will be;
= 3.05 × 2.474
= 7.55 days
