A radioactive nucleus can decay by two different processes. The half-life for the first process is `t_1` and that for the second process is `t_2`. Show that the effective half-life `t` of the nucleus is given by
`1/t = 1/t_1 + 1/t_2`.

Explanation

To solve the problem, we need to show that the effective half-life \( t \) of a radioactive nucleus that can decay by two different processes is given by the equation:

\[ \frac{1}{t} = \frac{1}{t_1} + \frac{1}{t_2} \]

where \( t_1 \) and \( t_2 \) are the half-lives for the first and second decay processes, respectively.

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