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Question:

A plot of the number of neutrons (N) against the number of protons (P) of stable nuclei exhibits upward deviation from linearity for atomic number, Z > 20. For an unstable nucleus having N/P ratio less than 1, the possible mode(s) of decay is (are): β⁻- decay (β emission), orbital or K - electron capture, neutron emission, β⁺- decay (positron emission)

β⁻- decay (β emission)

orbital or K - electron capture

neutron emission

β⁺- decay (positron emission)

Solution:

N/P ratio should increase and for that number of neutron should increase and proton should decrease.
0e⁻ + ¹₁P → ¹₀n⁰ (K-electron capture)
¹₁P → ¹₀n⁰ + ¹₁β⁰ (β⁺ decay)
In both cases the number of neutron increase by 1 and proton decrease by 1.