A radioactive isotope has a half-life of T years How long will it take the activity to reduce to - Physics - Nuclei

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?

Ajay Shukla · Accepted Answer

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:

Where, λ = Decay constant t = Time

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:

Since, λ = 0 693/T

Hence, the isotope will take about 6 645T years to reduce to 1% of its original value

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?