A radioactive isotope has a half-life of T years. How long will it take the activity to reduce to a) 3.125%, b) 1% of its original value?


Suppose, Initially the amount of radioactive isotope is N0

After time t if x% of it’s original value remains, and let λ be the decay constant


Then, we can write


λt = ln[100/x]


we know that,


Hence,


Given that


a) If x = 3.125% then t = = ≈ 5T years


b) If x = 1% then, t = = 6.645T years


7
1