# Half life for beta-gamma decay.

## Homework Statement

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?