Question

During $\beta^-$ emission

• A. a neutron in the nucleus decays emitting an electron
• B. an atomic electron is ejected
• C. an electron already present within the nucleus is ejected
• D. part of the binding energy of the nucleus is converted into an electron
• E. a proton in the nucleus decays emitting an electron

Hint:

$\beta^-$ decay: neutron $\rightarrow$ proton + electron + antineutrino Electron is created, not pre-existing.

Answer 1

The Correct Option is A

Concept: Nature of $\beta^-$ decay (Weak Nuclear Interaction)
$\beta^-$ decay is a nuclear transformation governed by the weak interaction, in which a neutron inside the nucleus is converted into a proton with the emission of an electron and an antineutrino. The fundamental reaction is: \[ n \rightarrow p + e^- + \bar{\nu} \] ---

Step 1: Understanding the internal process
At a deeper (quark) level:
• Neutron consists of quarks: $udd$
• Proton consists of quarks: $uud$ During $\beta^-$ decay:
• One down quark ($d$) changes into an up quark ($u$)
• This conversion emits a $W^-$ boson (weak force carrier) \[ d \rightarrow u + W^- \] The $W^-$ boson then decays into: \[ W^- \rightarrow e^- + \bar{\nu} \] Thus overall: \[ n \rightarrow p + e^- + \bar{\nu} \] ---

Step 2: Key physical understanding

• The electron is not originally present inside the nucleus
• It is created at the instant of decay
• Energy for creation comes from the mass difference: \[ m_n > m_p \] This mass difference provides the energy needed for:
• electron creation
• antineutrino emission ---

Step 3: Conservation laws involved
The decay obeys multiple conservation principles:
• Charge conservation: \[ 0 = (+1) + (-1) \]
• Energy conservation: Mass energy converts into kinetic energy
• Lepton number conservation: \[ 0 = (+1) + (-1) \]
• Momentum conservation: Shared between electron and antineutrino ---

Step 4: Detailed option analysis
(A) Correct

• Neutron transforms into proton
• Electron is emitted as part of decay --- (B) Incorrect

• Atomic electrons belong to electron cloud
• $\beta$-decay is a nuclear process --- (C) Incorrect

• Electrons do not exist inside nucleus initially
• They are created during decay --- (D) Incorrect (partially misleading)

• Energy comes from mass defect, not directly “binding energy conversion”
• Electron is created via weak interaction, not simple energy conversion --- (E) Incorrect

• Proton decay would produce positron ($\beta^+$ decay), not electron ---

Step 5: Physical Insight

• $\beta^-$ decay increases atomic number by 1
• Mass number remains unchanged
• Converts neutron-rich nuclei into stable forms --- Final Conclusion: \[ \boxed{\text{A neutron in the nucleus decays emitting an electron}} \]