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?

Half-life of the radioactive isotope = T yearsOriginal amount of the radioactive isotope = N0(a) After decay, the amount of the radioactive isotope = NIt is given that only 3.125% of N0 remains after decay. Hence, we can write:Where, = Decay constantt= TimeThus, 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 = NIt is given that only 1% of N0 remains after decay. Hence, we can write:Since, = 0.693/T yearsHence, the isotope will take about 6.645Tyears to reduce to 1% of its original value.