One mole of a monoatomic gas is mixed with three moles of a...

Molecular specific heat at constant volume in terms of degrees of freedom is given by ${C}_{V} = \dfrac{f}{2}R$

Molecular specific heat of mixture at constant volume is ${C}_{V} / mix = \dfrac{{n}_{1}{C}_{{V}_{1}} + {n}_{2}{C}_{{V}_{2}}}{{n}_{1} + {n}_{2}}$

$= \dfrac{1 \times \dfrac{3R}{2} + 3 \times \dfrac{5R}{2}}{1 + 3}$

$= \dfrac{9R}{4} = \dfrac{{\alpha}^{2}}{4}R$

$⇒ \alpha = 3$