Question

Cs-137 is used in medical treatments. It has a half-life of 30.0 years.

How many years must pass in order for a 40.0 mg sample to decay to 20.0 mg sample? Show your work.

Answer 1

half life t1/2 = 30 yrs

decay constant k = ( ln2) / t1/2   = ( 0.693 / 30 yrs) = 0.0231 yr-1

we use 1st order kinectics , to solve this since decay follows 1st order

t = ( 1/k) ln ( a/a-x)

where a= initial amount = 40 mg , a-x = final amount = 20 mg , k = decay constant = 0.0231 yr-1

t = ( 1/0.0231 yr-1) ln ( 40/20)

= 30 yrs

we can do in other direct way since 40 mg decayed to 20 mg it means half amount decayed. Hence it takes one half life i.e 30 yrs