Question

Choose the correct nuclear process from the below options:
\( [ p : \text{proton}, n : \text{neutron}, e^- : \text{electron}, e^+ : \text{positron}, \nu : \text{neutrino}, \bar{\nu} : \text{antineutrino} ] \)

• A. \(n \rightarrow p + e^- + \nu\)
• B. \(n \rightarrow p + e^+ + \nu\)
• C. \(n \rightarrow p + e^- + \overline{\nu}\)
• D. \(n \rightarrow p + e^+ + \overline{\nu}\)

Hint:

Remember that in beta decay, an electron is emitted along with an antineutrino, not a neutrino or positron.

Answer 1

The Correct Option is C

The given options represent possible nuclear processes. We need to choose the correct one based on the principle of conservation of charge and baryon number. The options given represent the decay of a neutron into a proton.

Particle Properties:

• Neutron: Charge = 0, Baryon number = 1
• Proton: Charge = +1, Baryon number = 1
• Electron: Charge = -1, Baryon number = 0
• Positron: Charge = +1, Baryon number = 0
• Neutrino: Charge = 0, Baryon number = 0
• Antineutrino: Charge = 0, Baryon number = 0

Option (3):
$ n \rightarrow p + e^- + \bar{\nu} $

• Charge: $ 0 \rightarrow +1 + (-1) + 0 = 0 $ (Conserved)
• Baryon number: $ 1 \rightarrow 1 + 0 + 0 = 1 $ (Conserved)

This process is known as beta-minus decay and is valid.

Option (2):
$ n \rightarrow p + e^- + \nu $

• Charge: $ 0 \rightarrow +1 + (-1) + 0 = 0 $ (Conserved)
• Baryon number: $ 1 \rightarrow 1 + 0 + 0 = 1 $ (Conserved)

However, lepton number conservation is violated. The electron and neutrino each have a lepton number of +1, but there is no source of negative lepton number on the left side.

Option (1):
$ n \rightarrow p + e^+ + \bar{\nu} $

• Charge: $ 0 \rightarrow +1 + (+1) + 0 = +2 $ (Not conserved)
• Baryon number: $ 1 \rightarrow 1 + 0 + 0 = 1 $ (Conserved)

Charge is not conserved, so this process is invalid.

Option (4):
$ n \rightarrow p + e^+ + \nu $

• Charge: $ 0 \rightarrow +1 + (+1) + 0 = +2 $ (Not conserved)
• Baryon number: $ 1 \rightarrow 1 + 0 + 0 = 1 $ (Conserved)

Again, charge is not conserved, so this process is invalid.

Conclusion:
Only option (3) satisfies all conservation laws: charge, baryon number, and lepton number.

Final Answer:
The final answer is $ (3) $.