One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture at constant volume is $\frac{\alpha^2}{4} \mathrm{R} \mathrm{J} / \mathrm{mol} \mathrm{K}$; then the value of $\alpha$ will be $\_\_\_\_$ (Assume that the given diatomic gas has no vibrational mode.)