When a radioactive nucleus emits 1 α-particle mass number decreases by 4 and the atomic number decreases by 2.So after the emission of \\\\(3 - \\alpha\\\\) particlesNew atomic mass, \\\\(A' = A - 4 \ imes 3 = A - 12\\\\) New atomic number \\\\(Z'= Z - 6\\\\)When this nucleus emits \\\\(1 β\\\\)-particle (positron), the atomic mass remains unchanged but the atomic number decreases by 1.So after emission of 2 positrons \\\\(A" = A' = A-12\\\\) \\\\(Z" = Z'-2×1 = Z-8\\\\)So, the ratio of neutrons to protons-\\\\(\\dfrac{n}{p} = \\dfrac{A-Z-4}{Z-8}\\\\)