Choose the correct nuclear process from the below options [p: proton, n : neutron, $$e^{-}$$:electron, $$e^{+}$$ : positron, $$\upsilon$$ : neutrino, $$\overline{\upsilon}$$ : antineutrino]

We need to identify the correct nuclear process for beta-minus decay of a neutron.

Key Concept: Beta-minus ($$\beta^-$$) Decay

In beta-minus decay, a neutron inside a nucleus (or a free neutron) transforms into a proton by emitting an electron and an antineutrino:

$$n \rightarrow p + e^- + \bar{\nu}$$

Conservation Laws:

Charge conservation: Neutron (charge 0) $$\rightarrow$$ proton (charge +1) + electron (charge -1) + antineutrino (charge 0). Total: $$0 = +1 - 1 + 0$$ $$\checkmark$$

Lepton number conservation: Left side: lepton number = 0. Right side: electron (lepton number +1) + antineutrino (lepton number -1) = 0. $$\checkmark$$

Baryon number conservation: Left side: 1. Right side: 1 + 0 + 0 = 1. $$\checkmark$$

Why other options are wrong:

- Option 1: $$n \rightarrow p + e^+ + \bar{\nu}$$ -- The positron ($$e^+$$) has charge +1, giving total charge +2 on the right. Charge not conserved.

- Option 2: $$n \rightarrow p + e^+ + \nu$$ -- Same charge violation as above.

- Option 3: $$n \rightarrow p + e^- + \nu$$ -- Lepton number: right side = +1 + 1 = +2 $$\neq$$ 0. Lepton number not conserved.

The correct answer is Option 4: $$n \rightarrow p + e^- + \bar{\nu}$$.