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## 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?