Matter units {atom, matter}| are small and have chemical properties. Atoms have same properties as larger amounts of same element.
types
Most atoms are metals. There are 22 non-metal elemental solids, liquids, and gases.
number
Nature has 90 atoms, and particle accelerators can make more than 13 heavy atoms.
mass
Hydrogen atom has mass 10^-24 grams. Heaviest atom is 250 times more massive.
size
Atoms are 99.99% empty space. Atoms have diameter 10^-8 centimeters. Largest-atom volume is 10 times hydrogen-atom volume.
parts: nucleus
Atoms have positively charged protons and neutral neutrons in orbits at central atom nucleus. Number of protons determines atom properties. Nuclei have diameter 10^-12 centimeters. Protons and neutrons have diameter 10^-13 centimeter.
parts: electrons
Electrons rapidly orbit nucleus at varying distances. Electron mass is 10^-27 grams. In neutral atom, protons equal electrons.
energy
Average kinetic energy equals binding energy. If electromagnetic force is same as now, too-small atoms fly apart, because electron velocities are greater. Too-large atoms cannot exist, because electron velocities are too slow to stay in orbit.
magnetism
Atoms have magnetism, because charges move at relativistic speeds. Most atoms have symmetrical electron and proton arrangements, so magnetic effects cancel. Atoms can have odd numbers of protons and/or neutrons and have net magnetism.
large elements
Carbon nucleus can form from three helium nuclei. Elements higher than carbon can form, because carbon atoms have resonance energy at which three helium nuclei are stable and can add more protons and neutrons.
model
Atom models can have infinite number of linear vibrators, which represent all atom frequencies, momenta, and positions.
Atomic nucleus has mass less than sum of proton and neutron masses {mass defect}, because some mass has become energy.
Atoms have number {atomic number}| of protons.
Atom masses {atomic weight}| {atomic mass} are in atomic mass units.
Atoms have number {mass number}| of protons and neutrons.
Atom centers {nucleus, atom}| have protons and neutrons.
ratio
In the most-massive atoms, neutron number can be up to 1.5 times proton number. In light atoms, neutron number equals proton number.
alpha particles
Light nuclei have alpha particles.
layers
Nuclei lighter than aluminum have no interior and no special surface. Heavier nuclei have surface neutron layer.
shape
Most atomic nuclei are spherical, but some are ellipsoids. If outer shell fills, nucleus is spherical. If outer shell is half-filled, nucleus is ellipsoidal. Spherical and ellipsoidal nuclei can rotate, but other shapes oscillate.
force
Strong nuclear force holds protons and neutrons in nuclear orbits, against electric force repulsions.
force: particle speed
Protons and neutrons have speed 6 x 10^7 meters per second.
force: orbit
Protons have orbits, and neutrons have orbits. Orbits have shells, angular momenta, orientations, and spins.
models
Atomic nuclei can be like charged drops {liquid drop model}, with charge spread evenly throughout. Nuclei can be like radial fields from nucleus center {shell model}.
Nuclei with odd number of protons and odd number of neutrons can break apart {radioactivity}|. Nuclei with even numbers of both protons and neutrons are stable, because orbits are full. Bigger nuclei are less stable, because neutron number is more than proton number. Radioactive decay happens randomly. Temperature, pressure, and other substances do not affect it. However, it can increase above 10^6 K.
Radioactive material takes time {half-life, radioactivity}| to become half as radioactive. Half-life can be several hours to billions of years. Short-half-life isotopes emit high-velocity alpha particles. Long-half-life atoms emit low-velocity alpha particles.
Radioactive nuclei can lose clusters {alpha particle, radiation} with two protons and two neutrons. Paper can stop alpha particles.
Radioactive nuclei can lose electron {beta particle}|. Neutron to proton and electron conversion makes beta particles. Aluminum foil can stop beta particles.
Radioactive nuclei can lose high-energy radiation {gamma particle}|. Five meters of concrete can stop gamma particles.
Devices {Geiger counter} can measure inert-gas ionization in 2000-V potential. Ionization causes current cascade. Current is proportional to ionization.
Devices {proportional counter} can measure gas ionization in 1000-V potential. Current is sensitive to voltage change.
Devices {scintillation counter} can measure sodium-iodide, anthracene, or naphthalene fluorescence. Photomultiplier detects visible light.
Radioactivity detection can use tiny bubbles in saturated fluid {bubble chamber}.
Radioactivity detection can use condensation trails in saturated vapor {cloud chamber}.
Radioactivity detection can combine bubble and spark chamber {streamer chamber}.
Atoms {isotope}| can have same number of protons but different numbers of neutrons. Element isotopes have same physical properties, except for mass differences.
Most isotopes are not radioactive, such as 2H [2 is superscript] {deuterium}.
Isotopes {radioactive isotope}| can be radioactive. Tritium is 3H [3 is superscript]. Carbon-14 is 14C [14 is superscript]. Nitrogen-15 is 15N [15 is superscript]. Phosphorus-32 is 32P [32 is superscript]. Sulfur-35 is 35S [35 is superscript]. Strontium-90 is 90Sr [90 is superscript]. Uranium-235 is 235U [235 is superscript]. Plutonium is 239Pu [239 is superscript].
Because electrons are wave-like, they do not have trajectories but have cloud-like or blurry orbits {orbit, electron} {electron orbit}|. Electron repulsions also spread orbits.
energy
Electron energy has quanta, so electrons have minimum energy. Uncertainty principle requires that energy cannot be zero. Shell, orbital, spin-orbit interaction, and spin angular momentum contribute angular momentum and energy quanta to orbital electrons. Energy levels depend on angular momentum squared.
rotation
Rotations can be spins or orbits. Spins have orientation, frequency, and angular momentum. Orbits have orientation, frequency, angular momentum, and spin-orbit angular-momentum interactions. Spins and orbits have no net linear momentum, because motion is in all directions equally. Rotation is around point or line. Rotation defines plane perpendicular to rotation axis. Rotation axes have orientations in space.
rotation: compared to vibration
Vibrations are oscillations or waves. Vibration is between two extremes. Vibration along length has spatial orientation. Vibration around angle is in plane. Vibrations have frequency. Waves have motion direction. Wave vibration can be transverse to, or longitudinal with, motion direction.
angular momentum
Spins and orbits have angular momentum, because motion is around rotation axis. Orbitals have axis orientation.
width
Orbit width is same as atom diameter, by uncertainty principle. Electrons move all over orbit, by uncertainty principle, but most motion is near shell radius.
independent
Orbitals are orthogonal to all others, with no overlap or interaction, because electrons are fermions and cannot be together in same place (Pauli exclusion principle).
time
Orbitals do not change with time.
speed
Electron orbital speed is 600,000 meters per second and so is not relativistic.
large atoms
For large atoms, inner electrons shield outer electrons from atomic nucleus, so outer electrons have orbits farther from nucleus and have less kinetic energy than with no shielding.
Electrostatic force between nucleus and electron causes electrons to orbit atomic nuclei in main regions {shell, atom}| {atomic shell} at specific distances. Atoms have up to seven shells, from one to seven unit distances from nucleus.
energy
Electron kinetic energy E depends on reciprocal of shell number n squared: E = 1 / n^2. For first shell, n = 1 and E = 1/1 = 1 unit. For second shell, n = 2 and E = 1/4 = 0.25 unit. For third shell, n = 3 and E = 1/9 = 0.11 unit. For fourth shell, n = 4 and E = 1/16 = 0.07 unit, For fifth shell, n = 5 and E = 1/25 = 0.04 unit. For sixth shell, n = 6 and E = 1/36 = 0.03 unit. For seventh shell, n = 7 and E = 1/49 = 0.02 unit. Energy levels are closer together at higher shells, because force depends directly on reciprocal of radius squared.
K shell is 10^4 times atomic-nucleus radius. L shell is 1.5 times farther from nucleus than K shell. M shell is 1.67 times farther from nucleus than K shell. N shell is 1.75 times farther from nucleus than K shell.
electrons
Shells farther from nucleus can hold more electrons, because they allow more quanta combinations. Shells can hold 2 * n^2 electrons, where n is shell number. First shell {K shell} can hold two electrons. Second shell {L shell} can hold eight electrons. Third shell {M shell} can hold 18 electrons. Fourth shell {N shell} can hold 32 electrons. Fifth shell {O shell} can hold 50 electrons. Sixth shell {P shell} can hold 72 electrons. Seventh shell {Q shell} can hold 98 electrons.
shell
Atomic-electron orbits have different radii and energy levels {shell, orbital}. From lowest to highest potential energy, and highest to lowest kinetic energy, radius is 1, 2, 3, 4, 5, 6, and 7 units. Orbit radii increase linearly. Units differ for different atoms. Potential energy depends on radius, so quantum energy changes between shells are equal.
wavelength
Smallest orbit has circumference equal to one wavelength. Wavelength depends on radial force and resistance to force. Smallest orbit has highest frequency. Second-smallest orbit has circumference with wavelength equal to two original wavelengths. Second-smallest orbit has half original frequency. Third-smallest orbit has circumference with wavelength equal to three original wavelengths. Third-smallest orbit has one-third original frequency, and so on.
Atom electrons are in shells with orbit types {orbital}|. Orbital can have zero, one, or two electrons.
energy level
Electron orbitals have different energy levels. From lowest to highest, they are one 1s, one 2s, three 2p, one 3s, three 3p, one 4s, five 3d, three 4p, one 5s, five 4d, three 5p, one 6s, seven 4f, five 5d, three 6p, one 7s, seven 5f, five 6d, and three 7p. Number in parentheses is number of possible orbits with that energy. Before using f orbitals, orbital hybridization causes one electron to go into a d orbital.
electronic transitions
Electrons can jump from orbital to higher or lower orbital. Both orbitals must be anti-symmetric to allow angular-momentum conservation. Angular-momentum units are the same for orbiting and spinning.
angular momentum
Same-shell electrons can have different orbital angular momenta {orbital angular momentum, atom}. Angular momentum adds centrifugal force to electrostatic force. Orbital angular momentum has units h / (2 * pi), where h is Planck constant. First shell allows only 0 units. Second shell allows 0 and 1 units. Third shell allows 0, 1, and 2 units. Fourth shell allows 0, 1, 2, and 3 units, and so on.
shape
In shells, orbit shape determines orbital angular momentum. Spherical s orbital allows zero angular momentum. Double-ellipsoid p orbital allows zero or one angular-momentum unit. Quadruple-ellipsoid or double-ellipsoid/torus d orbital allows zero, one, or two angular-momentum units. Octuple-ellipsoid f orbital allows zero, one, two, or three angular momentum units, and so on.
First shell can only have spherical orbital, because it has minimum potential energy and cannot alter. Second shell can have spherical orbital and three oriented orbitals. Shells above first shell can have spherical orbital, three oriented orbitals, and five, seven, and so on, multiply oriented orbitals.
interactions
Orbital orientation and spin orientation interaction changes angular momentum by precession. Spin-axis orientation is always along z-axis. If orbital-axis orientation is along z-axis, no interaction happens, and total angular momentum does not change. If orbital-axis orientation is perpendicular to z-axis, torque interaction {spin-orbit interaction} effects add or subtract angular momentum units. Electric coupling forces cause torque that causes orbital to precess around orbital vertical axis. Spin-orientation interaction can change angular momentum by -3, -2, -1, 0, +1, +2, or +3 units.
Atom electrons are in orbitals {electron configuration}|. Orbitals {degenerate orbital} can have same energy levels.
Electrons fill orbitals from lowest energy to highest energy {Aufbau principle}. Before using f orbitals, orbital hybridization causes one electron to go into a d orbital.
Electrons tend to enter all shell orbitals before they fill any orbital with two opposite-spin electrons {Hund's rule} {Hund rule}. Hund's rule is true for small atoms, because it takes more energy to put two electrons into one orbital than into two different orbitals.
Fermions are electrons, neutrons, protons, and the like. Because fermions have half-unit spins, when identical fermions interchange, their wavefunctions become the negative of the other. Therefore, no two fermions can have same energy quanta {Pauli exclusion principle, fermion}|.
Hund's rule is true for small atoms. Other rules {Slater's rules} {Slater rules} apply for large atoms.
Orbital shape can be spherical {s orbital}, with zero crossing points. Because spheres are radially symmetric, with electron orbits in all directions and so filling space, spherical orbits have no net orientation, so no interaction with spin makes added angular momentum 0. There can only be one kind of spherical orbital, because it must have radial symmetry.
Orbital shape can be double ellipsoidal along straight line {p orbital}, with one crossing point and one rotation axis. p orbital has two elongated lobes along line with one crossing in middle. Double-ellipsoidal orbit can orient in three spatial directions. If axis is along z-axis, aligned with spin, added angular momentum is 0. If axis is along x-axis or y-axis, perpendicular to spin, added angular momentum is -1 or +1. There can only be three kinds of double-ellipsoidal orbital, because one axis can have only three independent spatial orientations, which fill space. For same shell and same orbital angular momentum, all orientations are equally probable and have equal energy. All orientations add to make spherical orbital with zero net angular momentum.
Orbital shape can be quadruple-ellipsoidal four-leaf clover {d orbital}, with two crossing points and two rotation axes. d orbitals have four elongated lobes, two each along both orthogonal lines, with two crossings in middle. Four-leaf-clover quadruple ellipsoidal orbit can align with x-axis and y-axis; between xy-axis, xz-axis, or yz-axis; or with z-axis, as double ellipsoid and torus. If with x and y or between xy, added angular momentum is -2 or +2, because both axes are perpendicular to z-axis. If between xz or yz, added angular momentum is -1 or +1, because one axis is perpendicular to z-axis. If with z, added angular momentum is 0, because axis aligns with spin axis. There can only be five kinds of quadruple-ellipsoidal orbital, because axes can have only five independent spatial orientations, which fill space. For same shell and same orbital angular momentum, all orientations are equally probable and have equal energy. All orientations add to make spherical orbital with zero net angular momentum.
Orbital shape can be octuple-ellipsoidal eight-lobed clover {f orbital}, with three crossing points and three rotation axes. f orbitals have six elongated lobes, with two each along three orthogonal lines, with three crossings in middle. Successive and more complex clover-leaf-shaped orbits can have 7, 9, or 11 distinct orientations. For same shell and same orbital angular momentum, all orientations are equally probable and have equal energy. All orientations add to make spherical orbital with zero net angular momentum.
Elementary particles have intrinsic angular momentum {spin, particle}| {particle, spin} {intrinsic angular momentum}. Spin conserves energy, momentum, and angular momentum.
axis
Particles always travel at light speed along a space-time motion line. Spin axis is parallel to motion line and is either counter-clockwise or clockwise around that space-time momentum vector.
classical mechanics
In classical mechanics, spin has linear continuous projections onto other axes (and orthogonal axes have no spin components). For example, if object spins around z-axis, observers can measure spin around xz-axis and yz-axis, but spin around x-axis and y-axis (both orthogonal to z-axis) is zero.
Fundamental particles are points (or strings or loops with negligible radius), and some have no mass, so fundamental-particle intrinsic angular momentum is not due to mass rotating at a distance around an axis. Classical mechanics cannot account for elementary-particle spin.
quantum mechanics
Elementary-particle spin is quantum-mechanical and special relativistic. To reconcile quantum mechanics and special relativity, quantum-mechanical-wavefunction components are matrices, not just numbers. Matrices have transformations that are equivalent to spin angular momentum. Reconciling quantum mechanics and general relativity requires that momentum (energy) and position (time) affect each other, so matrices have complex-number elements.
In quantum mechanics, observers can measure spin around any axis. Measurement of elementary-particle spin around any axis finds that spin is an angular-momentum quantum unit, either clockwise or counterclockwise around axis. For example, measuring independent-electron intrinsic angular momentum finds spin equals (0.5 * h) / (2 * pi), where h is Planck constant, which is 1/2 angular-momentum quantum unit. (Electron spin cannot be zero, because electrons have mass.) Spin counterclockwise around motion axis adds 1/2 angular momentum unit, so spin is +1/2. Spin clockwise around motion axis subtracts 1/2 angular-momentum unit, so spin is -1/2.
Measuring independent-photon intrinsic angular momentum finds spin equals (0.5 * h) / pi, where h is Planck constant, which is 1 angular-momentum quantum unit. (Photon spin cannot be zero, because photons have energy.) Spin counterclockwise around motion axis adds 1 angular-momentum unit, so spin is +1. Spin clockwise around motion axis subtracts 1 angular-momentum unit, so spin is -1.
spin: vectors and spinors
Real-number vectors have magnitude, one direction (component), and one orientation (in that direction): (a). Rotating real-number vectors 360 degrees makes the same vector, because vector direction and orientation return to original direction and orientation. Spinning real-number vectors any number of degrees makes the same vector, because vectors have no extensions in perpendicular directions. For example, turning a straight line around its axis keeps the same shape.
Complex-number vectors have magnitude, one direction (in local two-dimensional space), and one orientation (in that direction): (a + b*i). Rotating complex-number vectors 360 degrees makes the same vector, because vector direction and orientation return to original direction and orientation. Spinning complex-number vectors any number of degrees makes the same vector, because vectors have no extensions in perpendicular directions.
Spinors have two complex-number (or quaternion) components: (a + b*i, c + d*i). Spinors have magnitude, two directions, and one orientation that depends on which component goes first. Rotating spinors 360 degrees makes original direction but opposite orientation, like rotating around a Möbius strip, because parity changes. Spinor rotation differs from vector rotation because spinor rotation has phase effects. Spinning spinors any number of degrees makes a different spinor, because spinors have extensions in perpendicular directions.
spin: rotation
Fermion odd-half-integer-spin particles have different statistics than boson integer-spin particles. For bosons, spin and rotation are independent and add. For fermions, spin and rotation are dependent and multiply.
spin: symmetries
Elementary-particle intrinsic angular momentum is about wavefunction symmetries.
Spin-0 particles are scalars (not vectors). Scalars have no direction and so have same physics under any rotation. Because intrinsic angular momentum is zero, clockwise and counterclockwise have no meaning. Spheres have all symmetries: any-degree rotational symmetry, mirror symmetry, radial symmetry, and inversion symmetry. Turning a sphere through any angle, reflecting it through any plane through any diameter, and spinning around any axis results in the same shape and behavior. Around any axis and orientation, observers see no net spin, so spin-rotation interaction is zero. See Figure 1.
Spin-1 particles are vectors, with one symmetry axis. Spin-rotation interaction is non-zero, so observers see opposite spin (anti-symmetry) after 180-degree rotation. Turning a clockwise spinning sphere upside down reverses its orientation and changes clockwise to counterclockwise. Vectors have same physics under 360-degree (and 720-degree, 1080-degree, and so on) rotation (360-degree rotational symmetry). Turning the sphere upside down again puts it back to original orientation and clockwise spin. See Figure 2.
Spin-2 particles are tensors, with two symmetry axes. Spin 2 particles have mirror symmetry. Spin 2 has 90-degree anti-symmetry. Turning the sphere to right angle interchanges axes, so one axis keeps clockwise motion and one axis changes from clockwise to counter-clockwise, reversing the orientation. Two spin-rotation interactions are non-zero but symmetric, so flipping plane over returns system to same spin-rotation interactions. Spin-2 particles have same physics under 180-degree (and 360-degree, 540-degree, 720-degree, and so on) rotation. Turning a sphere spinning clockwise around an axis and clockwise around a perpendicular axis upside down changes clockwise to counterclockwise around both axes but also reverses both axes, so the sphere returns to its original state. See Figure 3.
Spin-1/2 particles are vectors, with two axes sharing one symmetry. Because they share one symmetry, spin-1/2 particles have different spin-rotation interactions than vector bosons, which have no shared symmetry and so spin 1. Spin-rotation interaction is perpendicular at 180-degree rotation, reversed at 360-degree rotation, and opposite perpendicular at 540-degree rotation, and original at 720-degree rotation. Spin 1/2 particles have 360-degree anti-symmetry, like rotating around a Möbius strip, changing parity. Turning a sphere spinning clockwise around an axis, clockwise around a perpendicular axis, and clockwise around a second perpendicular axis completely around changes clockwise to counterclockwise around two axes and reverses both axes, but changes clockwise to counterclockwise around the third axis, which has the same orientation, so the sphere reverses orientation. Spin 1/2 has 720-degree rotational symmetry. Turning the sphere completely around again changes clockwise to counterclockwise around two axes and reverses both axes, but changes counterclockwise to clockwise around the third axis, which has the same orientation, so the sphere returns to original state. See Figure 4.
spin: speculation
Perhaps, elementary-particle intrinsic angular momentum is imaginary-number mass rotating at imaginary-number radius around particle axis, through imaginary-number angle with imaginary-number angular velocity, perhaps through imaginary-number time. Multiplying imaginary numbers results in positive real-number momentum and energy. Hyperbolas have imaginary-number radii, because they have negative curvature. Hyperbolic-curve angles are imaginary-number angles: cos(i*A) = cosh(A) and e^A = cosh(A) + sinh(A), where A is real-number angle. Higgs field has imaginary mass. Imaginary-number time rotations make special-relativity Lorentz transformations. Using imaginary-number time can establish absolute general-relativity space-time.
spin: bosons and fermions
At high concentration and/or low temperature, with Heisenberg uncertainty, for thermal-equilibrium non-interacting bosons, exchange of two particles does not change wavefunction (Bose-Einstein statistics), because particle wavefunction product is commutative (symmetric rank-two tensor): f(a) * f(b) - f(b) * f(a). Combining two spins returns the system to original orientation: f(a) * f(b) = ((-1)^(2*spin)) * (f(b) * f(a)), where spin = +1 or -1. Relativistically applying a rotation operator in imaginary time to integer spin particles results in no Pauli exclusion principle. Bosons are indistinguishable. Only system states matter. It is incorrect to talk about first one and second one, or particle 1 and particle 2. Many bosons can have same energy, momentum, and angular momentum.
At high concentration and/or low temperature, with Heisenberg uncertainty, for thermal-equilibrium non-interacting fermions, exchange of two particles changes wavefunction (Fermi-Dirac statistics), because particle wavefunction product is anti-commutative (anti-symmetric rank-two tensor): f(a) * f(b) + f(b) * f(a). Combining two spins takes the system to opposite orientation: f(a) * f(b) = ((-1)^(2*spin)) * (f(b) * f(a)), where spin = +1/2 or -1/2. Relativistically applying a rotation operator in imaginary time to half-integer spin particles results in Pauli exclusion principle. Fermions are distinguishable. Only system states matter. It is correct to talk about first one and second one, or particle 1 and particle 2. Two particles can have same energy but must have different momentum and/or angular momentum.
Note: At low concentration and/or high temperature, without Heisenberg uncertainty, thermal-equilibrium non-interacting particles have Maxwell-Boltzmann statistics. Exchange of two particles does not matter, because wavefunction has no effect. Particles can have same energy and same or different momentum and angular momentum.
spin: measurement
To measure spin, experimenters must establish a spatial axis, and then measure angular momentum around that axis. (Experimenters cannot know electron trajectories, because electrons have wavefunctions.) Around any chosen axis, instruments measure spin as exactly +1/2 unit or exactly -1/2 unit. By uncertainty principle, instruments measuring spin simultaneously around axes perpendicular to that axis get +1/2 unit or -1/2 unit with equal probability, meaning that those spin measurements have 100% uncertainty.
Instruments cannot measure spin when two electrons are interacting, because system then includes measuring apparatus. Instruments measure after particle creation or interaction. After particle creation or interaction, instruments decohere wavefunction and so destroy particle system and make particles independent.
spin: measurement angle
For electrons (spin 1/2), if measuring axis is at angle A to a clockwise spin-vector (spin -1/2), the probability that the measurement will be spin -1/2 is (cos(A/2))^2. Perhaps, because spin-vector has two axes but shares one symmetry, it is like the spin-vector projects onto an angle A/2 axis as cos(A/2), and the angle A/2 axis vector projects onto the angle A measuring axis as cos(A/2), so the net projection is (cos(A/2))^2.
If a zero-spin state emits entangled electrons in opposite directions (conserving momentum and angular momentum), and one direction is measured at angle A and the other at angle B (with angle difference C), the both-same-spin probability is (sin(C/2))^2, and the each-opposite-spin probability is (cos(C/2))^2.
For photons (spin 1), if measuring axis is at angle A to a clockwise spin-vector (spin -1), the probability that the measurement will be spin -1 is (cos(A))^2. Perhaps, because spin-vector has one axis, it is like the spin-vector projects onto an angle A axis as cos(A) twice, so the net projection is (cos(A))^2.
If a zero-spin state emits entangled photons in opposite directions (conserving momentum and angular momentum), and one direction is measured at angle A and the other at angle B (with angle difference C), the both-same-spin probability is (sin(C))^2, and the each-opposite-spin probability is (cos(C))^2.
orbitals
Orbitals with two electrons typically have one electron with positive spin and one electron with negative spin {anti-symmetric spin state}, so net spin angular momentum is zero, and ground-state orbital is symmetric. In orbitals, paired electron spins {spin pair} cancel magnetic fields.
Outside energy can add spin angular momentum. The first excited orbital state has two electrons with positive spin or two electrons with negative spin {symmetric spin state}. Net spin angular momentum is 1, and excited-state orbital is anti-symmetric.
In orbitals, two electrons have probability 0.25 to have total spin 0 and 0.75 to have total spin 1.
In different orbitals, electrons can have same lower-energy spins. Two electrons enter two different orbitals before going into same orbital, because electrostatic repulsions are greater in energy than magnetic interactions, energy differences between orbitals are small, and repulsions between electrons in different orbitals are smaller than repulsions in same orbital.
Electron has spin and can precess {spin dragging}| or move in electric fields.
Low-temperature materials can behave like ice {spin ice}|. Magnetic poles can become unaligned.
Atom electrons have coupling {spin-orbit coupling} {Russell-Sanders coupling} {jj coupling} between orbit and spin magnetic fields.
Elements have unique electron configurations around atomic nucleus. Element electron configurations have groups and sequences {periodic table}|, from smallest to largest.
columns
Named columns are alkali metal, alkaline earth metal, chalcogen, halogen, and noble gas.
rows
First row has lightest elements, with electrons in first electron shell, 1s: elements 1 and 2.
Second row has common light elements with electrons in second electron shell, 2s and 2p: elements 3 to 10.
Third row has less common elements with electrons in third electron shell, 3s and 3p: elements 11 to 18.
Fourth row has elements with electrons in third and fourth electron shells, from 19 to 36.
Fifth row has elements with electrons in fourth and fifth electron shells, from 37 to 54.
Sixth row has elements with electrons in fifth and sixth electron shells, from 55 to 86.
Seventh row has elements with electrons in sixth and seventh electron shells, from 87 to 118.
large atoms
Uranium is element 92 and is the largest natural element. Manmade elements go up to 116, but as of 2011 people have not yet made elements 113 and 115. Neptunium is element 93. Plutonium is element 94. Americium is element 95. Curium is element 96. Berkelium is element 97. Californium is element 98. Einsteinium is element 99. Fermium is element 100. Mendelevium is element 101. Nobelium is element 102. Lawrencium is element 103.
6d orbital
Rutherfordium is element 104. Dubnium is element 105. Seaborgium is element 106. Bohrium is element 107. Hassium is element 108. Meitnerium is element 109. Darmstadtium is element 110. Roentgenium is element 111. Copernicium is element 112.
7p orbital
Ununtrium (not made as of 2011) is element 113. Ununquadium is element 114. Ununpentium (not made as of 2011) is element 115. Ununhexium is element 116. Ununseptium (not made as of 2011) is element 117. Ununoctium (not made as of 2011) is element 118.
orbitals
1s orbital has H and He.
2s orbital has Li and Be.
2p orbital has B, C, N, O, F, and Ne.
3s orbital has Na and Mg.
3p orbital has Al, Si, P, S, Cl, and Ar.
4s orbital has K and Ca.
3d orbital has Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn.
4p orbital has Ga, Ge, As, Se, Br, and Kr.
5s orbital has Rb and Sr.
4d orbital has Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, and Cd. Tc 43 is not in nature.
5p orbital has In, Sn, Sb, Te, I, and Xe.
6s orbital has Cs and Ba. 5d orbital has La.
4f orbital has Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu. Pm 61 is not in nature.
5d orbital has Hf, Ta, W, Re, Os, Ir, Pt, Au, and Hg. 6p orbital has Tl, Pb, Bi, Po, At, and Rn. At 85 is not in nature.
7s orbital has Fr and Ra. Fr 87 is not in nature.
6d orbital has Ac.
5f orbital has Th, Pa, U, Np, Pu, Am, Cm, Bk, Cf, Es, Fm, Md, No, and Lr. Np, Pu, Am, Cm, Bk, Cf, Es, Fm, Md, No, and Lr {actinoid} are not in nature.
6d orbital has Rf, Db, Sg, Bh, Hs, Mt, Ds, Rg, and Cn and are not in nature.
7p orbital has Uut, Uuq, Uup, Uuh, Uus, and Uuo {transactinide element} {super heavy element} and are not in nature.
Stable artificial elements have a number {magic number} of protons or neutrons. Some {doubly magic isotope} have special numbers of both protons and neutrons. Lead-208 has 82 protons and 126 neutrons and is doubly magic. Elements 114, 120, or 126 can be doubly magic, with 184 neutrons.
Periodic table has columns {chemical group}|. Periodic table has 18 columns, one for each orbital.
Leftmost column or 1A column has soft metals {alkali metal} with low densities and melting points.
Second-from-left column or 2A column has harder, higher-density, and higher-melting-point metals {alkaline earth metal}.
Third-from-right column or 6A column has reactive elements {chalcogen} with slight colors.
Second-from-right column or 7A column has colorful and highly reactive gases, liquids, and solids {halogen}|.
Rightmost column or 8A column has inert colorless gases {noble gas}|.
Fourth and fifth rows have reactive elements {transition metal}, with many ionic forms, whose outermost electrons are in d orbitals, not in higher p orbitals. Metals in columns 4 to 16 have 10 d electrons.
Sixth row has elements {inner transition metal} with one or two electrons in d orbital and outermost electrons in f orbitals. Lanthanides and actinides {rare earth}, as well as scandium and yttrium, are solids.
First inner-transition-metal row {lanthanide series}, from element 58 to 71, is solids.
Second inner-transition-metal row {actinide series}, from element 90/91 to 103, is solids.
Large nucleus can split into two nuclei {fission, physics}| {nuclear fission}. Fission releases million times more energy per mass than burning. In nuclear reactions, neutrons collide with uranium or plutonium nuclei to cause fission.
Neutron can decay into proton, electron, and anti-neutrino {beta decay}| {beta radiation}. Beta decay causes nucleus to lose neutron and gain proton.
Nuclear reactors {breeder reactor} can use neutrons from fission to form plutonium from uranium.
Electron and positron collision {electron-positron collision} makes two real photons, positive pion and negative pion, proton and anti-proton, or virtual photon that becomes rho vector meson that makes two pions. Process must make two particles to conserve energy and momentum.
High-energy photon and atomic nucleus can collide to make electron and positron {pair production}. Protons and neutrons absorb photons 200 times less than hyperons.
Particle decays {decay, particle} {particle decay}| always make two particles, to conserve energy and momentum.
Proton and proton collisions {proton-proton collision} at high energies make larger subatomic particles. Scattering happens if both protons have same spin, but not if protons have opposite spins.
Particles can collide and rebound {scattering, collision}|.
path
In gas, particles go average distance, through mean free path, before they hit another particle.
elastic
Both particles can collide, bounce off, and remain intact, with no new particles {elastic scattering}.
inelastic
Both particles can collide to make new particles {inelastic scattering}. Created particles go off in pairs in jets perpendicular to colliding-particle paths. Increased amplitude at collision resonance energy indicates particle creation at that mass.
Small particles scatter through wider angles than larger particles, because cross-sectional area is less. Cross-sectional area increases with energy.
particle size
Particles have minimum diameter at 70 to 300 MeV. Particles grow rapidly in diameter up to at least 1500 MeV. At collision energy 2 GeV, particles reach maximum diameter.
Crystals exposed to radioactivity trap electrons in crystal faults. By heating material, luminescence {thermo-luminescence} measures number trapped. Thermo-luminescence can date from recent times to hundreds of thousands of years ago. Electron-spin resonance also measures number trapped.
Two small nuclei can merge into one nucleus {fusion, physics} {nuclear fusion}|. Fusion releases million times more energy per mass than burning.
products
Nuclear fusion makes all atoms up to and including iron.
efficiency
Nuclear hydrogen fusion to helium makes 0.007 of mass into energy, so efficiency is 0.007. Other fusions make 0.017 of mass into energy. If efficiency is less, universe has no or less helium and heavy atoms. If efficiency is more, universe has more helium and heavy atoms, but no hydrogen. Carbon production also depends on ratio, because it involves resonance energy.
Main fusion reaction {proton-proton cycle} unites two protons. In stars, hydrogen fusion to helium requires 10^6 K. Two protons change to deuterium and proton. These two nuclei combine to make helium 3. Two helium 3 make helium 4 and two protons.
The second-most-important fusion reaction {carbon-nitrogen cycle} makes helium starting from protons and carbon. Carbon acts like catalyst to make lithium, beryllium, and boron, which combine or decay to helium. Carbon-nitrogen cycle is not chain reaction.
Reactions {chain reaction, fusion}| that have proton reactants and make protons can be self-sustaining. Chain reaction continues until limiting reactant amount becomes zero or system disrupts physically.
Minimum mass {critical mass} starts chain reactions. Below minimum mass, too many proton initiators do not collide and escape to outside.
Absorbing protons {damping} slows fusion reactions. In nuclear reactors, metal rods absorb proton initiators to slow reaction.
Non-reactive gases {inert gas}| can have full electron shells.
Common metal atoms {metal atom}, in order of increasing mass, are lithium, sodium, magnesium, aluminum, potassium, calcium, titanium, chromium, manganese, iron, cobalt, nickel, copper, zinc, molybdenum, silver, cadmium, tin, cesium, barium, tungsten, platinum, gold, mercury, lead, radium, and uranium. Metals are shiny, crystalline, and conductive.
In order of increasing mass, non-metallic atoms {non-metal atom} in first two periodic-table rows are hydrogen gas, helium non-reactive gas, boron solid, carbon solid, nitrogen gas, oxygen gas, fluorine gas, and neon inert gas. Heavier ones are silicon solid, sulfur solid, phosphorus solid, chlorine gas, argon inert gas, germanium solid, arsenic solid, selenium solid, antimony solid, bromine solid, krypton inert gas, iodine solid, and zenon inert gas. Non-metal solids are crystals with various properties.
Increased amplitudes {resonance energy} at frequencies indicate particle masses, which are energy concentrations.
Hydrogen emits light in frequency series {spectra, atomic} {atomic spectra} {line spectrum}.
series
Frequencies 82000 cm^-1 to 110000 cm^-1 {Lyman series} are ultraviolet and start from ground state in shell 1. Frequencies 15000 cm^-1 to 28000 cm^-1 {Balmer series} are visible and start from ground state in shell 2. Frequencies 5000 cm^-1 to 12500 cm^-1 {Paschen series} are infrared and start from ground state in shell 3. Frequencies {Brackett series} can start from ground state in shell 4. Frequencies {Pfund series} can start from ground state in shell 5.
Rydberg formula
Hydrogen spectra, and similar electron-transition energy series, are regular {Rydberg formula}.
cause
Heat energy can put electrons into higher orbitals. Materials emit electromagnetic radiation when electrons fall back to lower orbitals.
temperature
In low-density gas, temperature change changes intensities but not frequencies. Intensity E at frequency is proportional to temperature T to fourth power: E = k * T^4.
density
Dense matter emits continuous frequency spectrum, because molecules interact. Dense-matter spectra depend only on temperature, because temperature determines interactions.
radiation temperature
Light at definite wavelength has definite temperature, because light is kinetic energy. Radiation temperature depends on beam solid angle and intensity, as well as wavelength.
Elements absorb light frequencies {absorption spectra}|.
Absorption lines {Fraunhofer line} of Sun elements make absorption spectrum.
Elements emit light frequencies {emission spectra}|.
Moving charges in atoms make magnetic fields that split spectrum peaks {fine structure}| {fine spectra}. Bigger nuclei make bigger magnetic fields and so make larger fine structure. Spin-orbit coupling and Zeeman effect also contribute to fine structure.
Atoms and molecules have temperature-caused random movements, so emission frequencies shift by Doppler effect {Doppler broadening}. Higher temperature makes more Doppler broadening. Higher mass makes less Doppler broadening. Higher frequency makes more Doppler broadening. Microwaves have lower frequencies than optical waves and so have lower Doppler broadening.
Hydrogen-atom electrons can be in 1s orbital or 1p orbital. Hydrogen-atom 1s-to-1p electronic transition has the smallest electronic-transition energy, equivalent to microwave photons. Microwaves have lower frequencies than optical waves and so have smaller Doppler broadening. This system is optimum to measure the fine-structure constant. Microwaves excite hydrogen-atom same-spin electrons from 1s to 1p orbitals {Lamb shift, electron} [1947] (Willis E. Lamb, Jr., and Robert Retherford) (Hans Bethe) to measure the fine-structure constant, which indicates virtual photons.
Electrons in outermost atom orbitals can jump to orbital with higher or lower energy level {electron transition}| {electronic transition} {transition, electron}, if new orbital is not full. Lower-energy orbital electron acquires energy from photon to go to higher-energy orbital. Higher-energy orbital electron loses energy to photon to fall to lower-energy orbital.
time
Collision, radiation, and other energies can send electron to higher-energy orbital in atom in 10^-12 seconds. Electron takes 10^-8 seconds to return to lower-energy orbital, emitting photon. Electronic transitions are random.
channel
Transition from one energy level to another emits or absorbs photons with quanta. Electronic transition can be direct and take one step {direct channel, transition} or go through intermediate steps {cross channel, transition}.
Electronic transitions naturally happen between orbitals differing by one angular-momentum unit {allowed state}, because photon carries that amount.
Transitions take longer to happen between certain orbits {forbidden state}|, because they differ by several angular-momentum units and one photon can carry only one unit.
Strong electric field can shift rotational-frequency lines {Stark effect}.
External magnetic field causes atom electrons to align and splits electron-energy level into slightly higher and slightly lower levels {Zeeman effect}. Magnetic field displaces spectral lines.
Outline of Knowledge Database Home Page
Description of Outline of Knowledge Database
Date Modified: 2022.0225