Question

Question 5: 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

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