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?
(a) Let the half-life be T years. original amount of isotope is No after decay, the remaining amount is N now as per given values, N/No=3.125%=1/32 also, N/No=e−λt where λ is decay constant also λ=0.693/T so, t=3.4657/λ=5T years. (b) Let the half-life be T years. original amount of isotope is No after decay, the remaining amount is N now as per given values, N/No=1%=1/100 also, N/No=e−λt where λ is decay constant also λ=0.693/T so, t=4.6052/λ=6.645T years.
