A radioactive element undergoes two different types of radioactive disintegration, one with disintegration constant λ₁ and the other with λ₂. The half-life of the element is

$\frac{0.693}{\lambda_1 + \lambda_2}$

Let equivalent decay constant is $\lambda$

$ \lambda N = \lambda_1 N + \lambda_2 N$

$ \Rightarrow \lambda = \lambda_1 + \lambda_2$

$ \tau = \frac{0.693}{\lambda}= \frac{0.693}{\lambda_1 + \lambda_2}$