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) $.

Answer 2

Step 1: Understand the question.
We are asked to identify the correct nuclear process among the given options. The given symbols are:
\( p \): proton, \( n \): neutron, \( e^- \): electron, \( e^+ \): positron, \( \nu \): neutrino, \( \bar{\nu} \): antineutrino.

Step 2: Recall beta decay processes.
There are two main types of beta decay:
1. Beta-minus (β⁻) decay: In this process, a neutron converts into a proton, emitting an electron and an antineutrino.
The reaction is:
\[ n \rightarrow p + e^- + \bar{\nu} \]
2. Beta-plus (β⁺) decay: In this process, a proton converts into a neutron, emitting a positron and a neutrino.
The reaction is:
\[ p \rightarrow n + e^+ + \nu \]

Step 3: Analyze the given process.
The question specifies the correct nuclear process that fits the description. The process:
\[ n \rightarrow p + e^- + \bar{\nu} \] represents beta-minus decay, which is the correct and physically valid process where a neutron decays into a proton, an electron, and an antineutrino.

Step 4: Conclusion.
Hence, the correct nuclear process is:
\[ n \rightarrow p + e^- + \overline{\nu} \]

Final Answer:
\[ \boxed{n \rightarrow p + e^- + \overline{\nu}} \]