Question

How long will it take for 2 g of a sample of iodine-131, which has a half-life of about 8 days, to decay to 0.04 g?

Answer 1

We know that

This problem can be represented through the following equation

A = A₀(1/2)^t/h
where
A----------->  is the amount of substance left after time t
A₀ ----------> is the original amount---------> 2 g
h------------->  is the half-life-----------> 8 days

for A=0.04 g
t=?
0.04 = 2(1/2)^t/8
0.02 = (1/2)^t/8
Take ln on both sides:
ln(0.02) = ln [(1/2)^t/8]
ln(0.02) = (t/8)(ln 1/2)
t = 8*ln(0.02)/ln(1/2)
t = 45.15 days

the answer is 45.15 days