A nucleus $\mathrm{A},$ with a finite de-broglie wavelength ${\mathrm{\lambda }}_{\mathrm{A}},$ undergoes spontaneous fission into two nuclei $\mathrm{B}$ and $\mathrm{C}$ of equal mass. $\mathrm{B}$ flies in the same direction as that of $\mathrm{A},$ while $\mathrm{C}$ flies in the opposite direction with a velocity equal to half of that of $\mathrm{B}.$ The de-Broglie wavelengths ${\mathrm{\lambda }}_{\mathrm{B}}$ and ${\mathrm{\lambda }}_{\mathrm{C}}$ of B and C are respectively: