1. The problem statement, all variables and given/known data A sample of radioactive nuclei of a certain element can decay only by gamma -emission and beta -emission. If the half-life for gamma -emission is 24 minutes and that for beta -emission is 36 minutes, what's the half-life for the sample? 2. The attempt at a solution I don't really know how to go about it. First i thought that may be the half life of the sample should be the half life of beta decay as gamma radiation does not transform the sample into a new element, but only into it's nuclear isomer; but the answer isn't 36 minutes. So clearly it means a new nuclear species by all means. Then I calculated the decay constant, lambda, for both, took the average and converted the constant to half life. that still doesn't match the answer given. How do i do this?