Apply energy conservation
1/2mv2 + 0 = -kQ2/R + 1/2mV2
Now since there is only electrostatic force between them so the net force always pass through the line joining their centres hence the torque about centre of sphere =0 so angular momentum is conserved about this point
According to conservation of momentum
=mv(2R)=mVR
or V=2v
Substitute this in first eqn and use the value of alpha given in the question we get
v=\(\sqrt \frac{2\alpha}{3}\)