Soumendra Nath Thakur | ORCiD: 0000-0003-1871-7803 | Tagore’s Electronic Lab, India | postmasterenator@gmail.com
August 24, 2025
A bound or free electron is a negatively charged subatomic particle that carries a single, fundamental negative elementary charge, denoted by −e, equivalent to approximately −1.602 × 10⁻¹⁹ coulombs (C). An atom or molecule becomes ionised when it gains or loses electrons, thereby acquiring a net positive or negative charge.
In Extended Classical Mechanics (ECM), the transition of an electron between a bound state and a free state is governed by the gain or loss in the magnitude of ΔMᴍ ≡ Mᵃᵖᵖ. A corresponding displacement −ΔMᴍ ≡ −Mᵃᵖᵖ, linked to the electron’s fundamental charge, determines whether the electron remains confined by the attractive potential of the atomic nucleus or is liberated as a free particle.
Appendix 25 provides the detailed basis for this condition [1] by equationally presenting the attractive nuclear potential and showing how confinement produces an apparent mass deficit. Bound electrons occupy quantized states with significantly reduced net energy compared to free electrons. For example, in hydrogen the discrete energy levels are:
E₁ = −13.6 eV, E₂ = −3.4 eV, E₃ = −1.51 eV, etc.
ECM interprets these reduced bound-state energies as a negative apparent mass contribution, such that:
Mᵃᵖᵖ = Mᴍ − mₑ < 0.
Liberation of an electron corresponds to a positive mass displacement:
ΔMᴍ = mₑ − Mᴍ > 0,
which directly governs both kinetic and radiative outcomes. Thus, confinement and release are two aspects of the same mass–energy displacement law in ECM [1].
From this perspective:
Thermionic emission occurs when thermal energy input satisfies the displacement condition:
hf (or thermal input) ≥ |−Mᵃᵖᵖ|c².
Here, the work function φ aligns with the confinement-induced apparent mass, φ ≈ |−Mᵃᵖᵖ|c² [1].
Photoelectric emission occurs when incident photon energy meets the same criterion:
hf = −Mᵃᵖᵖc² = ΔMᴍc² [1][2].
This shows that whether the input is thermal or photonic, the decisive factor is not a direct electron–photon coupling, but rather the mass–energy interaction at the atomic level, expressed as ΔMᴍ displacement.
Furthermore, when electrons drop between quantized levels (nᵢ → n𝑓), the energy loss manifests as photon emission with:
ΔE = hf = Eₙᵢ − Eₙ𝑓 = −ΔPEᴇᴄᴍ = −ΔKEᴇᴄᴍ.
Here, the photon is not an abstract mediator but the externalized carrier of displaced internal mass (ΔMᴍ = hf/c²) [3]. In contrast, a free electron (Mᴍ = mₑ) lacks confinement and cannot radiate via inertial motion in vacuum, confirming that only bound states support radiative quantum events [1].
Therefore, ECM demonstrates that both thermionic and photoelectric effects emerge from the same atom–energy interaction, rooted in the apparent mass displacement of bound electrons [2][5]. The notion of direct photon–electron interaction, isolated from nuclear confinement, is thus an incomplete and weak assumption, and should be discarded in favour of ECM’s unified confinement-based framework.
Consideration of a Photon Striking a Free Electron versus a Bound Electron
In conventional descriptions of the photoelectric effect, it is often proposed that a photon strikes an electron and directly transfers its energy, enabling the electron to overcome the metal’s binding energy (the work function, φ) and be ejected. In this view, the condition for emission is simply that the photon’s energy exceeds the work function, with any excess manifesting as the kinetic energy of the emitted electron.
However, this proposition assumes that a photon can effectively transfer its entire quantum of energy directly to an electron as though the electron were free in vacuum. In ECM, this assumption is invalid [3]. A truly free electron (Mᴍ = mₑ) does not exist in a confined quantized state, and therefore cannot absorb a discrete photon and undergo emission transitions or continue propagation through such an interaction. Without confinement, there is no quantized orbital structure to mediate energy exchange, and thus photon absorption by a free electron in vacuum is prohibited as a stable interaction.
In contrast, when an electron is bound within an atom, its reduced energy state is characterized by negative apparent mass (Mᵃᵖᵖ < 0), reflecting confinement by the nuclear potential [1]. Only under these conditions can quantized absorption or emission occur, since the atom–electron system provides a conservative framework for energy redistribution. A photon interacting with such a bound system does not simply “hit an electron” but excites the atom–electron system through vibrational and mass–energy displacement, ΔMᴍ [5]. Liberation occurs only if the displacement condition ΔMᴍc² ≥ |−Mᵃᵖᵖ|c² is satisfied [1][2].
This distinction is decisive. In ECM, the effective process of both thermionic and photoelectric emission is not reducible to photon–electron collisions, but to atom–energy interactions mediated by vibrational dynamics and mass displacement [5]. Thermal excitation and photon input are merely two pathways delivering external energy into the same confinement system [2].
Evaluation:
Photon striking a free electron: no confined state, no quantized transitions, interaction unstable and insignificant [3].
Photon interacting with a bound electron via atomic confinement: quantized transitions possible, ΔMᴍ displacement governs release, consistent with observed discrete energy levels and emission thresholds [1][2].
Energy interacting through induced atomic vibration (thermal route): equally valid pathway, with emission again determined by ΔMᴍ displacement rather than a direct electron–photon collision [5].
Conclusion:
This provides concrete evidence that, whereas the application of a potential difference surrounding a free electron can set it in motion—as experimentally demonstrated in Thermionic Emission within CRT systems [4]—the direct striking of a free electron by a sufficiently energetic photon cannot set the electron in motion or sustain its propagation via photon absorption [3]. In ECM, such a process is prohibited as a stable interaction, reaffirming that photon-induced transitions are only possible in bound, quantized states, not in free electron dynamics. Consequently, the conventional photoelectric proposition of direct photon–electron impact is an inadequate description and must be replaced with ECM’s unified confinement-based framework [2][5].
References
[1] Appendix 25: Apparent Mass Displacement and Energy-Mass Transitions of Electrons — An ECM Framework for Bound States, Emission, and Photon Generation. DOI: https://doi.org/10.13140/RG.2.2.28129.62565
(Provides the explicit equational presentation of nuclear attractive potential, bound vs. free electron states, and the role of ΔMᴍ in emission.)
[2] Appendix 42: Both the previously developed thermionic emission and the later photoelectric effect are inevitably based on the same mechanism. DOI: https://doi.org/10.13140/RG.2.2.29392.01280
(The foundational statement that both effects arise from the same ΔMᴍ-governed confinement mechanism.)
[3] Appendix 19: Photon Mass and Momentum — ECM's Rebuttal of Relativistic Inconsistencies through Apparent Mass Displacement. DOI: https://doi.org/10.13140/RG.2.2.36775.46242
(Supports the treatment of photons as carriers of displaced mass ΔMᴍ, essential in distinguishing bound-state emission from free-electron motion.)
[4] Appendix 40: Empirical Support for ECM Frequency-Governed Kinetic Energy via Thermionic Emission in CRT Systems. DOI: https://doi.org/10.13140/RG.2.2.31184.42247
(Provides experimental grounding for ECM by demonstrating that electron liberation and motion in CRT systems follow the ΔMᴍ-based displacement condition. Shows that thermionic emission, a well-established physical phenomenon, validates the frequency-governed kinetic energy formulation of ECM, thereby linking the theoretical framework directly to measurable laboratory effects and reinforcing its unification with the photoelectric effect and quantized bound-state transitions.)
[5] Appendix 42 Part-2: A Unified ECM Framework of Atomic Vibration. DOI: https://doi.org/10.13140/RG.2.2.30001.49766
(Extends Appendix 42 by clarifying that external energy inputs — thermal or photonic — act through atomic vibrational mediation, not direct photon–electron collisions.)
