If a radioactive element having half-life of 30 min is undergoing...

Given: Half life of radioactive element $t\dfrac{1}{2} = 30min$.

In $90min$, there will be three half lives, so $n = 3$.

Using radioactive decay law, fraction of radioactive element remains undecayed is

$\dfrac{N}{{N}_{0}} = {\left(\dfrac{1}{2}\right)}^{n} = {\left(\dfrac{1}{2}\right)}^{3}$

$⇒ \dfrac{N}{{N}_{0}} = \dfrac{1}{8}$