Half life of iodine-131, original amount, initial mass

Question

The radioisotope iodine-131 has a half-life of around 8 days.
How many days will it take to decay to 6.25% of its original amount?
If the initial mass is 1g what is the mass of radioactive material after this time?

Answer 1

A(t) = amount present as a function of time

 

A(0) = initial amount = 1g

 

t = days

 

A(t) = A(0) (1/2)^t/8

 

Solve for t in

 

0.0625 (1g) = (1g) (1/2)^t/8

 

log0.0625 = (t/8) log0.5

 

t = 8 (log0.0625 / log0.5) days = 32 days