An unstable heavy nucleus at rest breaks into two nuclei which move away with velocities in the ratio of 8 : 27. The ratio of the radii of the nuclei (assumed to be spherical) is :

If the de Broglie wavelengths associated with a proton and an $$\alpha $$-particle are equal, then the ratio of velocities of the proton and the $$\alpha $$-particle will be :