Module 1 Electronic Structure of the Atom (revised Sept 2024) PDF

Module 1 Electronic Structure of the Atom History of Chemistry John Dalton (1766 - 1844) showed that ratios of masses of an element combining with a gram of another element can always be reduced to small whole numbers https://en.wikiped...

Module 1 Electronic Structure of the Atom History of Chemistry John Dalton (1766 - 1844) showed that ratios of masses of an element combining with a gram of another element can always be reduced to small whole numbers https://en.wikipedia.org Dalton’s Atomic Theory 1. Each element is made up of tiny particles called atoms. Dalton’s Atomic Theory 2. The atoms of a given element are identical; the atoms of different elements are different in some fundamental way or ways. Dalton’s Atomic Theory 3. Chemical compounds are formed when atoms of different elements combine with each other. A given compound always has the same relative numbers and types of atoms. Dalton’s Atomic Theory 4. Chemical reactions involve reorganization of atoms – changes in the way they are bound together. The atoms themselves are not changed in a chemical reaction. If elements are made up of atoms, how come different elements have different atoms? History of Chemistry Joseph John Thomson (1856 - 1940) studied electrical discharges in partially evacuated tubes (CRT) discovered the electron (corpuscles) e/m = –1.76 x 108 C/g https://en.wikipedia.org Thomson’s Experiment History of Chemistry Thomson’s Plum Pudding Model culturesciences.chimie.ens.fr History of Chemistry Robert Millikan (1868 - 1953) performed experiments using oil drops calculated the mass of an electron me = 9.11 x 10–31 kg https://en.wikipedia.org History of Chemistry Ernest Rutherford (1871 - 1937) performed an experiment to test Thomson’s atomic model α particle bombardment of a metal foil https://en.wikipedia.org History of Chemistry Rutherford’s Experiement www.missclub.info History of Chemistry Rutherford’s Experiement EXPECTATION REALITY Zumdahl, 8th ed. History of Chemistry Ernest Rutherford (1871 - 1937) “…It was almost as incredible as if your fired a 15-inch shell at a piece of tissue paper and it came back and hit you.” https://en.wikipedia.org Rutherford’s Experiment Most of the alpha particles passed through the gold foil, without any deflection. Most of the space in the atom is empty. Rutherford’s Experiment Some of the alpha particles were deflected by large angles. The alpha particles probably approached a positively large region responsible for the deflection. Rutherford’s Experiment Few alpha particles experienced deflection. The volume occupied by the positively charged region is small. History of Chemistry Rutherford’s Nuclear Model History of Chemistry James Chadwick (1891 - 1972) performed an experiment that led to the discovery of neutrons α particle bombardment of a beryllium sheet www.elpueblodigital.es History of Chemistry large.stanford.edu Recap Dalton’s Solid Sphere Model recognized that atoms of a particular element differ from other elements atoms are not indivisible – they are composed of subatomic particles www.compoundchem.com Recap Thomson’s Plum Pudding Model recognized electrons as components of atoms no nucleus www.compoundchem.com Recap Rutherford’s Nuclear Model realized that a positive charge was localized in the nucleus of the atom did not explain why electrons orbit the nucleus www.compoundchem.com What is a wave? “A wave is a vibrating disturbance by which energy is transmitted.” Properties of a Wave wavelength, λ amplitude, A frequency, ν Chang, 10th ed. Electromagnetic Radiation “An electromagnetic radiation is an emission or transmission of energy in the form of electromagnetic waves.” Electromagnetic Radiation www.ces.fau.edu Characteristics all have wave-like properties all travel through a vacuum at the speed of light (3.00 x 108 m/s) 𝑐 = λν different types of electromagnetic radiation have different wavelengths Exercise The brilliant red colors seen in fireworks are due to the emission of light with wavelengths around 650 nm when strontium salts are heated. Calculate the frequency of red light. Answer: 4.62 x 1014 Hz Interference An interference is the net effect of the combination of two or more waves moving on intersecting or coincident paths. Interference Constructive Destructive (in phase) (out of phase) https://commons.wikimedia.org Diffraction Diffraction is a phenomenon resulting from interference where waves spread around an obstacle. Diffraction https://roguephysicist.com History of Chemistry Max Planck (1858 - 1947) discovered that atoms and molecules emit energy only in certain discrete quantities (quanta) https://en.wikipedia.org Heated Solids Problem Heated solids emit electromagnetic radiation of specific wavelengths when heated to a certain temperature. image from the youtube video of Ric Furrer Blackbody Radiation The blackbody spectrum depends only on T, not on the material being heated. The maxima shifts to the left as T increases. Quantum Theory Energy is always emitted in integral multiples of hν. where h = Planck’s constant 𝐸 = ℎν = 6.63 x 10–34 J∙s 𝑐 ν= Energy is quantized on such λ a small scale that the 𝑐 gradations between allowed 𝐸=ℎ values are so small. λ Exercise The blue color in fireworks is often achieved by heating CuCl to about 1200°C. Then the compound emits blue light having a wavelength of 450 nm. What is the energy emitted at this wavelength? Answer: 4.42 x 10–19 J History of Chemistry Albert Einstein (1879 - 1955) explained the photoelectric effect suggested that a beam of light is made of particles (representing a quantum of light) called photons https://en.wikipedia.org What is the photoelectric effect? “The photoelectric effect is a phenomenon in which electrons are ejected from the surface of certain metals exposed to light of at least a certain minimum frequency (threshold frequency).” Photoelectric Effect The threshold frequency (ν0) is the minimum frequency required to remove an electron from the metal surface. Energy of the incident 𝟏 𝟐 photon 𝑲𝑬 = 𝒎𝒗 = 𝒉𝝂 − 𝒉𝝂𝟎 𝟐 Energy needed to remove an electron Photoelectric Effect https://education.pasco.com What is the photoelectric effect? The ability of the light to eject an electron depends only on frequency and not on the intensity. 𝐸 = ℎν Only a photon of sufficient energy can eject an electron. Dual Nature of Light Electromagnetic radiation exhibits wave properties and particulate properties. https://chem.libretexts.org https://www.sparaft.com Wave-Particle Duality youtube video by OpenMind If light (electromagnetic radiation) has particulate properties, can matter (particle) exhibit wave- like properties? Continuous Spectrum www.diy.fyi Line Spectrum www.diy.fyi Line Spectrum of Hydrogen Only certain energies are allowed for the electron in a hydrogen atom. The energy of the electron is quantized. https://archive.cns.org Atomic Emission Spectrum www.diy.fyi Line Spectrum of Hydrogen www.diy.fyi Line Spectrum of Hydrogen 𝑩𝒎𝟐 where B = 364.6 nm 𝝀= 𝟐 𝒎 − 𝒏𝟐 n=2 www.diy.fyi Line Spectrum of Hydrogen www.diy.fyi Line Spectrum of Hydrogen Light is emitted as an electron moves from a high energy level to a low energy level. 𝟐 𝒁 𝑬𝒏 = −𝑹𝑯 𝒏𝟐 where: RH = 2.18 x 10–18 J (Rydberg constant) Z = nuclear charge n = an integer Line Spectrum of Hydrogen Since a hydrogen atom has a nuclear charge of +1: –18 1 𝐸𝑛 = −2.18 𝑥 10 𝑛2 Line Spectrum of Hydrogen For an electronic transition: Δ𝐸 = 𝐸𝑓 − 𝐸𝑖 1 1 𝐸𝑛 = −2.18 𝑥 10–18 2 − −2.18 𝑥 10 –18 𝑛𝑓 𝑛𝑖2 1 1 𝐸𝑛 = −2.18 𝑥 10–18 2− 2 𝑛𝑓 𝑛𝑖 𝟏 𝟏 𝑬𝒏 = 𝟐. 𝟏𝟖 𝒙 𝟏𝟎–𝟏𝟖 𝟐− 𝟐 𝒏𝒊 𝒏𝒇 History of Chemistry Niels Bohr (1885 - 1962) explained the emission spectrum of the hydrogen atom postulated that an electron is allowed to occupy only orbits of specific energy https://en.wikipedia.org History of Chemistry Niels Bohr (1885 - 1962) The electron moves about the nucleus with speed u in one of a fixed set of circular orbits The electron’s angular momentum is an integer multiple of h/2π An atom emits energy as a photon when an electron falls from an orbit of higher energy and larger radius Line Spectrum of Hydrogen 𝑐 Δ𝐸 = ℎ λ www.diy.fyi Exercise Calculate the energy required to excite the hydrogen electron from level n = 1 to level n = 2. Also calculate the wavelength of light that must be absorbed by a hydrogen atom in its ground state to reach this excited state. Answers: E1 = – 2.178 x 10–18 J; E2 = – 5.445 x 10–19 J ΔE = 1.633 x 10–18 J Exercise Energy for an electronic transition: Δ𝐸 = 𝐸𝑓 − 𝐸𝑖 = 𝐸2 − 𝐸1 –𝟏𝟖 𝟏 𝟏 ∆𝑬 = 𝟐. 𝟏𝟖 𝒙 𝟏𝟎 𝑱 𝟐− 𝟐 𝒏𝒊 𝒏𝒇 1 1 ∆𝐸 = 2.18 𝑥 10–18 𝐽 2 − 2 1 2 ∆𝐸 = 1.635 𝑥 10–18 𝐽 Exercise Calculating the wavelength: ℎ𝑐 ℎ𝑐 Δ𝐸 = λ= λ ∆𝐸 6.63𝑥10−34 𝐽 · 𝑠 3.00𝑥108 𝑚/𝑠 λ= 1.635𝑥10−18 𝐽 λ = 1.217𝑥10−7 𝑚 History of Chemistry Bohr’s Planetary Model proposed stable electron orbits; explained the emission spectra of some elements model did not work well for heavier atoms www.compoundchem.com History of Chemistry Louis de Broglie (1892 - 1977) particles (like electrons) have wave properties glimpse.clemson.edu History of Chemistry youtube video by Crash Chemistry Academy History of Chemistry https://i.ytimg.com de Broglie Equation 𝑐 𝐸=ℎ 𝐸 = 𝑚𝑐 2 λ 𝒉 𝝀= 𝒎𝒗 Exercise Compare the wavelength for an electron (mass = 9.11 x 10–31 kg) traveling at a speed of 1.0 x 107 m/s with that of a ball (mass = 0.10 kg) traveling at 35 m/s. Planck’s constant = 6.626 x 10–34 kg m2/s Answers: electron = 7.27 x 10–11 m; ball = 1.90 x 10–34 m Exercise Wavelength of the moving electron: 𝒉 𝝀= 𝒎𝒗 6.626𝑥10−34 𝑘𝑔 · 𝑚2 /𝑠 𝜆= 9.11𝑥10−31 𝑘𝑔 1.0𝑥107 𝑚/𝑠 𝜆 = 7.3𝑥10−11 𝑚 Exercise Wavelength of the moving ball: 𝒉 𝝀= 𝒎𝒗 6.626𝑥10−34 𝑘𝑔 · 𝑚2 /𝑠 𝜆= 0.10 𝑘𝑔 35 𝑚/𝑠 𝜆 = 1.9𝑥10−34 𝑚 Recap Planck: Energy is quantized Einstein: Light is quantized light has particle-like properties de Broglie: Electron energy is quantized electrons display wave-like properties History of Chemistry Werner Heisenberg (1901 - 1976) “It is impossible to know simultaneously both the momentum and the position of a particle with certainty.” https://en.wikipedia.org Heisenberg’s Uncertainty 𝒑 = 𝒎𝒗 𝑝 = 𝑚𝑣 𝑝 = 𝑚𝑣 large momentum = short wavelength 𝒉 𝝀= 𝒎𝒗 Heisenberg’s Uncertainty 𝒑 = 𝒎𝒗 atoms and electrons exhibit wavelengths that can be measured Heisenberg’s Uncertainty when we overlap waves, regions that coincide with each other increases in amplitude, and those that do not cancel https://socratic.org Heisenberg’s Uncertainty adding more waves with varying wavelengths will cause the waves to be localized forming a wave packet https://socratic.org Heisenberg’s Uncertainty the more waves combined, the more precisely the particle is located but momentum becomes more uncertain https://socratic.org Heisenberg’s Uncertainty 𝒉 𝜟𝒙𝜟𝒑 ≥ 𝟒𝝅 to determine the position with certainty, you need more waves to determine the momentum, you need a larger wave packet History of Chemistry Erwin Schrödinger (1887 - 1961) formulated wave mechanics which laid the foundation for modern quantum theory https://en.wikipedia.org History of Chemistry Erwin Schrödinger (1887 - 1961) suggested that an electron exhibiting wave properties should be described by a mathematical equation called a wave function, Ψ https://en.wikipedia.org Schrödinger Equation ĤΨ = 𝑬Ψ where Ψ is called a wave function, a function of the coordinates of the electron’s position in three- dimensional space https://chemistry.stackexchange.com History of Chemistry Max Born (1882 - 1970) The total probability of finding a particle in a small volume of space is the product of the square of the wave function, Ψ2 (probability density) https://en.wikipedia.org Particle in a 3D Box 𝒉𝟐 𝒏𝟐𝒙 𝒏𝟐𝒚 𝒏𝟐𝒛 𝑬 𝒏𝒙 𝒏𝒚 𝒏 𝒛 = 𝟐 + 𝟐+ 𝟐 𝟖𝒎 𝑳𝒙 𝑳𝒚 𝑳𝒛 for a three-dimensional system, the particle can move in three directions each dimension must have one quantum number a three-dimensional system will need three quantum numbers  The Hydrogen Atom ℎ2 δ 2 δψ 1 δ δψ 1 δ2 ψ 𝑍𝑒 2 − 2 2 𝑟 + 𝑠𝑖𝑛θ + 2 2 − 𝜓 = 𝐸𝜓 8π μ𝑟 δ𝑟 δ𝑟 𝑠𝑖𝑛θ δθ δθ 𝑠𝑖𝑛 θ δϕ 4𝜋𝜀0 𝑟 open-inorganic-chemistry.digitalscholarship.utsc.utoronto.ca The Hydrogen Atom orbitals: wave functions that are solutions to the Schrödinger equation spherical polar system: orbitals are expressed as products of radial factor and angular factor Radial wave function ψ(𝑟, θ, ϕ) = 𝑅 𝑟 𝑌(θ, ϕ) Angular wave function History of Chemistry Quantum Mechanical Model introduces the concept of an electron density which gives the probability that an electron will be found in a particular region of an atom www.compoundchem.com Quantum Numbers What are quantum numbers? “Quantum numbers are mathematical solutions of the Schrödinger equation for a hydrogen atom that describe the properties of an orbital (wave function).” What is an orbital? The square of the wave function indicates the probability of finding an electron near a particular point in space (probability distribution). What is an orbital? The probability of finding an electron in this s orbital is greatest near the nucleus. electron density map electron density electron probability socratic.org What is an orbital? Nodes are regions of no electron density. https://chemistry.stackexchange.com What is an orbital? https://chemistry.stackexchange.com What are quantum numbers? 1. Principal quantum number, n 2. Angular momentum quantum number,  3. Magnetic quantum number, m What are quantum numbers? Principal quantum number, n has positive non-zero integral values 1, 2, 3… related to the size and energy of the orbital related to the average distance of the electron from the nucleus What are quantum numbers? Principal quantum number, n principal electronic shell – orbitals with the same value of n What are quantum numbers? Angular momentum quantum number,  has integral values from 0 to n – 1 for every value of n related to the shape of the orbital What are quantum numbers? Angular momentum quantum number,  What are quantum numbers? Angular momentum quantum number,  subshell – orbitals with a given angular momentum quantum number the number of subshells in a principal shell is equal to n What are quantum numbers? Angular momentum quantum number,  Value of  0 1 2 3 Letter s p d f designation What are quantum numbers? Magnetic quantum number, m has integral values from –  to +  including zero related to the orientation of an orbital in space relative to the other orbitals What are quantum numbers? Magnetic quantum number, m https://chemistry.stackexchange.com What are quantum numbers? chemiday.com What are quantum numbers? Number Sublevel n  m of designation orbitals 1 0 1s 0 1 2 0 2s 0 1 1 2p –1, 0, +1 3 What are quantum numbers? https://chemistry.stackexchange.com Exercise Number Sublevel n  m of designation orbitals 4 What are quantum numbers? Electron spin quantum number, ms proposed by George Eugene Uhlenbeck and Samuel Abraham Goudsmit has values of + ½ or – ½ describes the electron occupying an orbital instead of the actual orbital What are quantum numbers? Electron spin quantum number, ms https://chem.libretexts.org What are quantum numbers? Electron spin quantum number, ms ms does not depend on n,  , and m quantum number characterizing an electron: s: magnitude of the magnetic field ms : orientation of the magnetic field What are quantum numbers? Electron spin quantum number, ms for an electron: s = ½ for a photon: s = 1 possible values of ms are: – s, – s + 1, – s + 2, …, s What are quantum numbers? Stern and Gerlach Experiment https://chem.libretexts.org What are quantum numbers? Pauli’s Exclusion Principle in any given atom, no two electrons can have the same set of four quantum numbers an orbital can only hold two electrons and these electrons must have opposite spins Exercise ( n ,  , m , ms ) What are the four quantum numbers of the second electron occupying the 3d orbital? Electronic Configuration Electronic Configuration For a one-electron species, the energies depend only on n. –𝟏𝟖 𝟏 𝑬𝒏 = −𝟐. 𝟏𝟖 𝒙 𝟏𝟎 𝒏𝟐 https://sparknotes.com Electronic Configuration Energy contributions for multielectron systems kinetic energy of the electrons potential energy of attraction between nucleus and electrons potential energy of repulsion between the electrons  Hydrogen-like orbitals have the same general shapes as the orbitals of hydrogen, but their sizes and energies are different. Petrucci, et al., 2017 Electronic configuration The maxima indicates the maximum probability that an electron will be at that specific distance from the nucleus. Electronic configuration The penetration effect causes an electron in a 3s orbital to be attracted to the nucleus more strongly than an electron in a 3p orbital. Electronic configuration Aufbau Principle as protons are added one by one to the nucleus to build up the elements, electrons are similarly added to the orbitals Electronic configuration (n + ) Rule lower (n + ) value = lower energy lower energy orbitals are filled up first Electronic configuration www.klejonka.info Electronic configuration The electronic configuration describes how electrons are distributed among the various atomic orbitals 1 1𝑠 1𝑠 Electronic configuration Recall: Pauli’s Exclusion Principle 2 1𝑠 1𝑠 Electronic configuration Recall: Pauli’s Exclusion Principle 2 1 1𝑠 2𝑠 1𝑠 2𝑠 Exercise Write the electronic configuration of carbon. What are the four quantum numbers of the last entering electron of carbon? Electronic configuration Hund’s Rule of Multiplicity the most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins 3 2𝑝 2𝑝 Summary No two electrons in the same atom can have the same set of four quantum numbers. Each orbital can have a maximum of two electrons, and these must have opposite spins. The most stable arrangement of electrons in a subshell is the one that has the greatest number of parallel spins. Exercise Write the electronic configuration of the ground state of sodium. What are the four quantum numbers of the last entering electron of sodium? Electronic configuration consider fluorine (Z = 9) 1𝑠 2 2𝑠 2 2𝑝5 1𝑠 2𝑠 2p 2 2 2 2 1 1𝑠 2𝑠 2𝑝𝑥 2𝑝𝑦 2𝑝𝑧 expanded notation 2 2 5 1𝑠 2𝑠 2𝑝 condensed notation Electronic configuration consider neon (Z = 10) 1𝑠 2 2𝑠 2 2𝑝6 1𝑠 2𝑠 2p 2 2 2 2 2 1𝑠 2𝑠 2𝑝𝑥 2𝑝𝑦 2𝑝𝑧 expanded notation 1𝑠 2 2𝑠 2 2𝑝6 condensed notation Electronic configuration consider sodium (Z = 11) 2 2 6 1 1𝑠 2𝑠 2𝑝 3𝑠 condensed notation for Na 1𝑠 2 2𝑠 2 2𝑝6 condensed notation for Ne [Ne] 3𝑠1 noble gas notation for Na Electronic configuration consider aluminum (Z = 13) 2 2 6 2 1 condensed notation for Al 1𝑠 2𝑠 2𝑝 3𝑠 3𝑝 1𝑠 2 2𝑠 2 2𝑝6 condensed notation for Ne [Ne] 3𝑠 2 3𝑝1 noble gas notation for Al Electronic configuration https://files.mtstatic.com Electronic configuration https://sciencenotes.org What are valence electrons? “Valence electrons are the electrons in the outermost principal quantum level of an atom.” Valence electron configuration s-block elements: 𝒏𝒔𝒙 p-block elements: 𝒏𝒔𝟐 𝒏𝒑𝒙 d-block elements: 𝒏𝒔𝟐 (𝒏 − 𝟏)𝒅𝒙 f-block elements: 𝒏𝒔𝟐 𝒏 − 𝟏 𝒅𝟏 𝒏 − 𝟐 𝒇𝒙 where: 𝒏 = row number 𝒙 = column number in the block Magnetic Properties paramagnetic – contain net unpaired spins (attracted by a magnet) diamagnetic – do not contain net unpaired spins (slightly repelled by a magnet) Exercise Write the electronic configuration of the following: K+ Cl– Ar Ca+2 Electronic configuration the anomaly of chromium (Z = 24) [Ar] 4𝑠 2 3𝑑 4 expected configuration [Ar] 4𝑠1 3𝑑 5 observed configuration the anomaly of copper (Z = 29) [Ar] 4𝑠 2 3𝑑 9 expected configuration [Ar] 4𝑠1 3𝑑10 observed configuration Periodic Trends Size of atoms and ions Ionization energy Electron affinity Electronegativity Atomic radius The atomic radius is one-half the distance between the two nuclei in two adjacent metal atoms (metallic radius) or in a diatomic molecule (covalent radius). https://chem.libretexts.org Atomic radius Atomic radius decreases across a period. Atomic radius increases down a group. https://socratic.org What is effective nuclear charge? The effective nuclear charge is the nuclear charge felt by an electron when both the actual nuclear charge and the repulsive effects of the other electrons are taken into account. 𝒁𝒆𝒇𝒇 = 𝒁 − 𝝈 What is effective nuclear charge? wps.prenhall.com Atomic radius decreases across a period electrons occupy the same shell (n) σ is almost constant; Zeff = Z higher Zeff = electrons are more attracted to the nucleus https://socratic.org Atomic radius Zeff Z σ for p electron 2.60 5 2.40 3.25 6 2.75 3.90 7 3.10 4.55 8 3.45 5.20 9 3.80 5.85 10 4.15 https://socratic.org Atomic radius increases down a group increasing shell (n) higher n = electrons occupy orbitals farther from the nucleus; larger atomic radius https://socratic.org Ionization energy Ionization energy is the minimum energy required to remove an electron from a gaseous atom in its ground state. 𝑿(𝒈) → 𝑿 + + 𝒆 – (𝒈) Ionization energy Consider the IE of aluminum: 𝑨𝒍(𝒈) → 𝑨𝒍+ (𝒈) + 𝒆– IE1 = 580 kJ/mol + +𝟐 + 𝑨𝒍 (𝒈) → 𝑨𝒍 (𝒈) + 𝒆– IE2 = 1815 kJ/mol +𝟐 +𝟑 + 𝑨𝒍 (𝒈) → 𝑨𝒍 (𝒈) + 𝒆– IE3 = 2740 kJ/mol For Al, IE4 = 11,580 kJ/mol! Why? Ionization energy Petrucci, et al., 2017 Ionization energy Element Atomic Radius, Ionization pm Energy, kJ/mol Li 155 520 Na 190 496 K 235 419 Rb 248 403 Cs 267 376 Ionization energy increases across a period increasing effective nuclear charge; electrons are more difficult to remove decreases down a group the electrons being removed are farther from the nucleus; electrons are easier to remove Electron affinity Electron affinity is the energy change associated with the addition of an electron to a gaseous atom. 𝑿(𝒈) + 𝒆 – → 𝑿 – (𝒈) Electron affinity Electron affinity Electron affinity Period 2 vs Period 3 the atomic orbitals of the second period elements are much smaller or more compact the additional electron encounters stronger repulsive forces from the electrons in the compact orbitals Electron affinity Electron affinity Group 2 and Group 18 the added electron will enter the orbital of the next subshell, or the next orbital in the next shell Electron affinity increases across a period increasing effective nuclear charge; added electron experiences attraction to the nucleus decreases down a group the electrons being added are farther from the nucleus; electrons are less attracted to the nucleus Ionic radius Ionic Radius for isoelectronic cations the greater the positive charge, the smaller is the ionic radius for isoelectronic anions the grater the negative charge, the larger is the ionic radius Electronegativity Electronegativity refers to the tendency of an atom to pull an electron in a covalent bond. Electronegativity Principal Author Method of Calculation Pauling Bond energy Mulliken Average of electron affinity and ionization energy Alfred and Rochow Electrostatic attraction proportional to Zeff/r2 Sanderson Electron density of atoms Pearson Average of electron affinity and ionization energy Allen Average energy of valence shell electrons Jaffe Orbital electronegativities