Electron

Semiconductors' number of mobile charge carriers (electrons, holes) are finely tuned by adding impurities (doping), temperature control, applying voltage and radiation exposure.

Electrons can exist as free particles. As particle beams in a vacuum, accelerated free electrons, used for cathode ray tubes, electron microscopes, electron beam welding, lithography and particle accelerators creating radiations like electromagnetic, gamma rays, X-rays, synchrotron radiation.

• mobile charge: charge carrier (like electron, ion) free to move through a material to conduct electricity

  • mobile (shorthand for mobility: μ = Vd/E): how easily something moves; μ is the value of ease/efficiency with which those charges move 

• finely: divided as very small particles/pieces (e.g., powder, thinly chopped substance)

• tuned: adjusted/controlled

• doping: to add other small property amounts

• free electrons: electrons inbound to an atom and move freely

• particle beam: concentrated beam of accelerated particles (electrons/protons, moving in same direction)

• cathode ray tube: device creating images via electron beam hitting a screen

• electron microscope: microscope using electrons IO light for high-resolution imaging

• electron beam welding: welding process via focused electron beam to melt, join metals

  • welding: to join metals by by heat/pressure

• lithography: technique for printing patterns, often using light or electrons to etch designs on surfaces

• synchrotron radiation: intense electromagnetic radiation emitted when charged particles move at near-light speeds in a curved path

  • synchrotron: particle accelerator moving charged particles at high speeds along a circular path, creating synchrotron radiation

    • etm: "synchro-" = magnetic fields + "-tron" = device for particle acceleration

Characterization

[2] Unlike protons and neutrons, electrons are almost massless, only being 9.11x10-31 kg. Unlike them also they surround and bound to an atom's nucleus IO being part of it, due to being negatively charged and attracted to an atomic nucleus' positive charge. A neutral atom electrons' number is the same as proton's (positive) charges in its nucleus, so its negative and the proton's positive charges balance. All the elements of the Periodic Table are neutral (by default), they can gain (negatively charged) or lose (positively charged) electrons to becoming ions (anions or cations respectively).

• Note: Not to be confused with anode (positive electrode) and cathodes (negative electrode).

Charged atoms are ions, with 2 types: 

1. Anions are negatively charged ions by gaining electron.

2. Cations are positively charged ions by losing electron.

If electrons gain extra energy, it becomes excited, occuring if an electron absorbs a photon (light packet) or collides to an atom/particle. They can get enough energy to leave atomic nuclei behin, becoming free electrons, mixed to ions to form a plasma.

We used to think electrons orbited nuclei like how the moon orbits Earth. But now they actually surround nuclei in a cloud divided into an atom's shells, which are akin to Earth atmosphere's different layers, but aren't fixed points, i.e., they spread out in a cloud of probable locations, reflecting Heisenberg Uncertainty Principle. The wave-particle duality applies to electrons - they act as points and waves, thus inner shells have various chances to have electrons.

[1] Lab tools can trap individual electrons and electron plasma via electromagnetic fields. Special telescopes can detect electron plasma in outer space. Electrons are involved in tribology/frictional charging, electrolysis, electrochemistry, battery techs, electronics, welding, cathode-ray tubes, photoelectricity, photovoltaic solar panels, electron microscopes, radiation therapy, lasers, gaseous ionization detectors, and particle accelerators.

• electron plasma: a partially or fully ionized gas consisting mainly of free electrons and positive ions

• tribology: study of friction, wear, lubrication between interacting surfaces

• frictional charging: electric charge buildup caused by rubbing different materials

• electrolysis: electric current usage to drive non-spontaneous chemical reaction

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[1] Interactions involving electrons to other subatomic particles are of interest in fields like chemistry and nuclear physics. Atoms are made of positive protons in atomic nuclei and negative electrons without, held together by Coulomb force interaction. Ionization state (contrast in negative electrons' proportions versus positive nuclei) or electrons sharing between 2+ atoms are main chemical bonding causes.

• Coulomb force interaction: electric force between charged particles

• ionization state: atom/molecule's condition based on how many electrons it lost/gained

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Properties

Mass

[1] An electron's invariant mass is ~9.109×10-31 kg, or 5.486×10-4 Da. Due to mass–energy equivalence, this corresponds to a rest energy of 8.19×10-14 J (0.511 MeV). The ratio between a proton's mass and an electron is ~1836. Astronomical measurements show the proton-to-electron mass ratio held the same value, as predicted by the Standard Model, for half the universe's age.

• Dalton (Da): unified atomic mass unit (u); unit of mass equal to 1/12 of a free carbon-12 atom at rest's mass

• mass–energy equivalence: relationship that mass and energy are interchangeable forms if 1 thing, depicted by E = mc2

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Charge

[1] Electrons have an electric charge of −1.602176634×10-19 C, a constant used as a standard subatomic particles' charges unit, the elementary charge. In experimental accuracy limits, an electron charge is identical to a proton's charge, but of opposite sign.

The electron is often symbolized by e- to indicate its negative charge (an electron's anti-particle, the positron, is symbolized by e+ to indicate its identical but positive charge).

Angular momentum

[1] An electron has an intrinsic angular momentum or spin of ⁠ħ/2⁠, a property often stated by referring to the electron as a spin-1/2 particle. Such particles' spin magnitudes are ⁠ħ/2⁠, while the result of the measurement of a projection of the spin on any axis can only be ±⁠ ħ/2⁠. The electron also has an intrinsic magnetic moment along its spin axis. It's ~equal to 1 Bohr magneton, a physical constant of 9.2740100657(29)×10-24 J⋅T−1. The spin's orientation with respect to the the electron's momentum defines elementary particles' property, helicity.

Structure

[1] An electron has no known substructure. Regardless, in condensed matter physics, spin–charge separation can occur in some materials. In such cases, electrons 'split' into 3 independent particles, the spinon, the orbiton and the holon (or chargon). The electron can always be theoretically considered as a bound state of the three, with the spinon carrying the spin of the electron, the orbiton carrying the orbital degree of freedom and the chargon carrying the charge, but in certain conditions they can behave as independent quasiparticles.

Size

[1] Electron–electron scattering shows no deviation from Coulomb's law: experimentally the electron is structureless and point-like. 1 electron's observation in a Penning trap suggests the upper limit of the particle's radius as 10-22 m. An electron radius' upper bound of 10-18 m can be derived via the uncertainty relation in energy.

[1] Theoretical concepts of the electron size are ambiguous. In relativisitic quantum mechanics, the Dirac equation treats the electron as a point charge, but the equivalent Newton–Wigner form does not. In quantum field theory mathematical treatments of self-energy involve a minimal distance cutoff or equivalent energy. Shorter distances (high energies) involve adding more terms. 

[1] Attempts to create non-quantum mechanical, non-point models lead to contradictions. E.g., A mechanically spinning electron with the classical electron radius and an electron's observed gyromagnetic ratio will have a tangential velocity exceeding the light speed. The classical electron radius, with a much larger value 2.8179×10-15 m (above a proton's radius), is used as a physical constant but is not a measure of the electron's fundamental structure.

Lifetime 

[1] In the Standard Model, an electron is considered stable. It's the least massive known particle with non-zero electric charge: assuming energy conservation, its decay can violate charge conservation. Many experiment efforts have looked for Standard Model's failures and of charge conservation by looking for electron decay. The experimental lower bound for the electron's mean lifetime is 6.6×1028 years, at a 90% confidence level.

Wave-Particle Duality: Electrons do not just act as solid spheres; they behave as both particles and waves. Their wavelength is inversely proportional to their momentum (de Broglie hypothesis).Intrinsic Spin: Every electron has a fundamental property called "spin," with a value of either \(+1/2\) or \(-1/2\). This internal angular momentum is crucial for magnetism and the organization of atoms.The Pauli Exclusion Principle: A critical rule for university courses is that no two electrons in the same system can occupy the exact same quantum state (i.e., have the same four quantum numbers).

Quantum properties

• Intrinsic spin: Any electron has a "spin," a fundamental property with a value of either +1/2 or - 1/2, an internal angular momentum crucial for magnetism and atoms organization.

• The Pauli Exclusion Principle: no 2 electrons in the same system can occupy the exact same quantum state (i.e., have the same four quantum numbers).

• Quantized energy: Atoms' electrons can only occupy some discrete energy levels, where they "jump" among by absorbing/emitting photons of some frequencies.

• Quantum Numbers: 4 numbers define an electron's state:

1. 1. n (Principal): Defines the energy shell and distance from the nucleus.

   2. l (Azimuthal): Defines the shape of the orbital (s, p, d, f).

   3. ml (Magnetic): Defines the orbital's orientation in space.

   4. ms (Spin): Defines an electron spin's direction.

Theoretical concepts

• The wave function (ψ) is a mathematical representation depicting an electron's state. Its magnitude's square(|ψ|2) gives the probability density for an electron's location.

• Heisenberg Uncertainty Principle: It is fundamentally impossible to precisely know both an electron's position and momentum simultaneously; measuring one accurately will inherently disturb the other.

• Quantum tunneling: Due to their wave nature, electrons can "tunnel" through energy barriers that would be impossible to cross according to classical physics.

• Entanglement: Electrons can become "entangled," thus one's state can't be depicted independently of another, even across vast distances.

History

References

• [1] Wikipedia

• [2] U.S Department of Energy

• [3] Britannica

• [4] 

Quizzes

• [1]