A travelling nucleus $A$ having a de-Broglie wavelength ${\lambda }_{\mathrm{A}}$ spontaneously splits into two nuclei $B$ and $C$ of equal masses. After the split, $B$ travels in the same direction while $C$ travels in the opposite direction with a speed equal to half of $B$. The values of the de-Broglie wavelengths ${\lambda }_{\mathrm{B}}$ and ${\lambda }_{\mathrm{C}}$ will be