Effect of beta decay (β− or β+): how does the neutron-to-proton ratio (n/p) of a radioactive nuclide change under β-decay?

Introduction / Context:
Beta decay alters the composition of a nucleus by converting a neutron to a proton (β−) or a proton to a neutron (β+ or electron capture). Understanding how the neutron-to-proton ratio (n/p) changes clarifies why certain isotopes move toward the valley of stability through β-decay processes.

Given Data / Assumptions:

• β− decay: n → p + e− + v̄ (antineutrino).
• β+ decay (or electron capture): p → n + e+ + v (or p + e− → n + v).
• We compare n/p before and after decay.

Concept / Approach:
In β− decay, one neutron converts to a proton. Neutrons decrease by 1 and protons increase by 1, so n/p = (n−1)/(p+1). This tends to decrease n/p. In β+ decay (or electron capture), one proton converts to a neutron: n/p = (n+1)/(p−1), which tends to increase n/p. Therefore, without specifying which beta mode occurs, the best general statement is that n/p may increase or decrease depending on whether the nuclide undergoes β− or β+ decay.

Step-by-Step Solution:
Write the particle balance for β− and β+ processes.Compute qualitative effect on numerator and denominator of n/p.Conclude direction of change for each mode.Choose the conditional statement covering both possibilities.

Verification / Alternative check:
Charts of the nuclides show neutron-rich nuclides moving toward stability via β− decay (lowering n/p) and proton-rich nuclides via β+ or EC (raising n/p) to approach stable ratios.

Why Other Options Are Wrong:
Always increases/always decreases: ignores the two beta modes.Remains the same: composition changes by definition.Becomes exactly 1: stability does not mandate n/p = 1; it varies with mass number.

Common Pitfalls:
Assuming “beta decay” always means β−; many nuclides undergo β+ or electron capture depending on energy conditions.

Final Answer:
May increase or decrease depending on whether it is β− or β+ decay