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 provided options depict potential nuclear processes. Selection of the correct option necessitates adherence to the principles of conservation of charge and baryon number. The presented options illustrate neutron decay 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{u} $

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

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

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

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

However, lepton number conservation is violated. Both the electron and neutrino possess a lepton number of +1, with no corresponding negative lepton number source on the reactant side.

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

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

Charge is not conserved, rendering this process invalid.

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

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

Charge is again not conserved, thus this process is invalid.

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

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