(a) Let the half-life be \\\\(T\\\\) years.original amount of isotope is \\\\(N_o\\\\)after decay, the remaining amount is \\\\(N\\\\)now as per given values, \\\\(N/N_o=3.125\\%=1/32\\\\)also, \\\\(N/N_o=e^{-\\lambda t}\\\\)where \\\\(\\lambda\\\\) is decay constantalso \\\\(\\lambda=0.693/T\\\\)so, \\\\(t=3.4657/\\lambda=5T\\\\) years.(b) Let the half-life be \\\\(T\\\\) years.original amount of isotope is \\\\(N_o\\\\)after decay, the remaining amount is \\\\(N\\\\)now as per given values, \\\\(N/N_o=1\\%=1/100\\\\)also, \\\\(N/N_o=e^{-\\lambda t}\\\\)where \\\\(\\lambda\\\\) is decay constantalso \\\\(\\lambda=0.693/T\\\\)so, \\\\(t=4.6052/\\lambda=6.645T\\\\) years.