A sample of a radioactive substance decayed to 96% of its original amount after a year. (Round your answers to two decimal places.) (a) What is the half-life of the substance? yr (b) How long would it take the sample to decay to 40% of its original amount? yr

a) The half life of the radioactive sample is 0.22 years.

b) It will take 0.16 years to sample to decay to 40% of its original amount.

Explanation:

a) Initial amount of radioactive substance =

Final amount of radioactive substance after 1 year=

Decay constant = k

Decaying of radio active sample follows first order kinetics:

Half life of the sample =

The half life of the radioactive sample is 0.22 years.

b)

Initial amount of radioactive substance =

Final amount of radioactive substance after t years=

Decay constant = k =

Decaying of radio active sample follows first order kinetics:

Solving for t:

t =  0.1587 years ≈ 0.16 years

It will take 0.16 years to sample to decay to 40% of its original amount.