A radioactive nucleus can decay by two different processes....

Here the particle is decayed by two processes with decay constant ${\lambda}_{1}$ and ${\lambda}_{2}$.

Radioactive decay rate is directly proportional to number of nucleus present at any time, so total rate of decay is

$\dfrac{d A}{d t} - \left(- {\lambda}_{1}A\right) + \left(- {\lambda}_{2}A\right)$

$⇒ \dfrac{d A}{d t} = - \left({\lambda}_{1} + {\lambda}_{2}\right)A$

$⇒ {\lambda}_{eff} = {\lambda}_{1} + {\lambda}_{2}$

$⇒ \dfrac{\ln 2}{{\left({t}_{\dfrac{1}{2}}\right)}_{eff}} = \dfrac{\ln 2}{{\left(t\dfrac{1}{2}\right)}_{1}} + \dfrac{\left(\ln 2\right)}{{\left(t\dfrac{1}{2}\right)}_{2}}$

$⇒ {\left(t\dfrac{1}{2}\right)}_{off} = \dfrac{4 . 5 \times 3}{7 . 5}$ hours $= 1 . 8$ hours