An inductor of 10 mH , capacitor of $0.1 \mu \mathrm{~F}$ and a resistor of $100 \Omega$ are connected in series across an $a . c$ power supply $220 \mathrm{~V}, 70 \mathrm{~Hz}$. The power factor of the given circuit is 0.5 . The difference in the inductive reactance and capacitance reactance is $\sqrt{3} \alpha \Omega$. The value of $\alpha$ is $\_\_\_\_$ .