A nucleus with mass number 220 initially at rest emits an $\alpha$ -particle. If the Q-value of the reaction is 5.5MeV, the kinetic energy of the $\alpha$ -particle is  $1.8nMeV$, when n is ___

Let $K_1\&K_2$ and  $P_1\&P_2$ are the K. E and momentum of the  $\alpha$- particle and remaining nucleus, then $K_1+K_2=5.5MeV----\left(i\right)$ 
From conservation of linear momentum  $P_1=P_2$
 $\Rightarrow \sqrt{2K_1\times 4m}=\sqrt{2K_2\times 216m}\Rightarrow K_1=54K_2----\left(ii\right)$
From (i) and (ii) 
$K_1=\frac{5.5\times 54}{55}=5.4MeV$