Question

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?

Answer 1

Half-life of the radioactive isotope = T years
Original amount of the radioactive isotope = N₀
(a) After decay, the amount of the radioactive isotope = N 

It is given that only 3.125% of N₀ remains after decay. Hence, we can write:

Hence, the isotope will take about 5T years to reduce to 3.125% of its original value.

(b) After decay, the amount of the radioactive isotope = N 

It is given that only 1% of N₀ remains after decay. Hence, we can write:

Hence, the isotope will take about 6.645T years to reduce to 1% of its original value.