Lecture 9 - Quantum Theory II

Tuesday, February 6, 2024

7:19 AM

The task is not so much to see what no one has yet seen; but to think what nobody has yet thought, about that which everybody sees. - Erwin Schrödinger Class notes can now be found here: https://bricejurban.github.io/CHEM111/ Assignments due this week: ﷟HYPERLINK "https://boisestatecanvas.instructure.com/courses/28699/assignments/990937"HW 4 - Quantum Part 1 (Aktiv Chemistry) (Sun 2/11) Finish reading Chapter 4 Read Chapter 5 Assignments due next week: ﷟HYPERLINK "https://boisestatecanvas.instructure.com/courses/28699/assignments/990975"HW 5 - Quantum Part 2 (Aktiv Chemistry) (Fri 2/16) Reading quiz TBD New Activity TBD Read Chapter 6, Preview 7 Office Hours: Friday 11-1 CIC ﷟HYPERLINK "https://calendly.com/bricejurban/office-hours"By appointment ﷟HYPERLINK "https://www.youtube.com/watch?v=uWMTOrux0LM"IDTIMWYTIM: Schrodinger's Cat (start at 1:15) IDTIMWYTIM: Schrodinger's Cat Press enter to activate, SCHRODINGER'SCAT There will be some equations below. Focus on the concepts Today's Schedule: Thursday (2/8) Quantum Numbers and Orbitals Electron Configuration Ground state Excited State Looking Ahead Tuesday (2/13) Schedule Electron Configuration Transition metals Atomic Radii Ionic Bonding Coulombic Energy Nomenclature Part II Ionic Radii Thursday (2/15) Schedule Covalent Bonding Electronegativity Lewis Structures Part I Formal Charge An Inconvenient Truth - The Planetary Model of the Atom cannot exist Newtonian Mechanics says that an electron orbiting a nucleus must be constantly accelerated in order to maintain its orbit Maxwell's Electromagnetic Theory requires an accelerated charged particle to emit radiation Thus, the electron would simply spiral into the nucleus in a fraction of a second. Bohr's Model, which had electrons occupying certain quantized fixed orbits, was a temporary band-aid to this problem But this was soon replaced by quantum mechanical models, namely, Heisenberg's matrix mechanics, and the Schrödinger equation.
But this was soon replaced by quantum mechanical models, namely, Heisenberg's matrix mechanics, and the Schrödinger equation. The Schrödinger equation We learned in the last class that electrons exhibit wave-particle duality. That is, they behave as both a wave and a particle. The Schrödinger equation is a mathematical formula that calculates the wave function of an electron. The wave function is a complex expression that contains all the information about the electron's state such as its position and energy The solutions to the Schrödinger equation for an atom yield specific energy levels that the electron can occupy. These are quantized meaning they can only have certain specific energy values. The solutions also define atomic orbitals, which are regions around the nucleus where the electron is most likely to be found. Each atomic orbital has a characteristic shape and energy level ψ is the wave function of the particle m is the mass of the particle V is the potential energy as a function of position E is the total energy of the system ﷐−﷐ℎ﷮2﷯﷮8﷐𝜋﷮2﷯𝑚﷯﷐﷐𝑑﷮2﷯𝜓﷮𝑑﷐𝑥﷮2﷯﷯+𝑉𝜓=𝐸𝜓 Each quantum state solution of the Schrödinger equation provides a wave function ﷐𝜓﷮𝑛ℓ𝑚﷯﷐𝑟,𝜃,𝜙﷯= Total Wave Function ﷐𝑅﷮𝑛ℓ﷯﷐𝑟﷯ = Radial Part (influence energy) ﷐𝑌﷮ℓ𝑚﷯﷐𝜃,𝜙﷯ = Angular part (influence shape) ﷐𝜓﷮𝑛ℓ𝑚﷯﷐𝑟,𝜃,𝜙﷯=﷐𝑅﷮𝑛ℓ﷯﷐𝑟﷯﷐𝑌﷮ℓ𝑚﷯(𝜃,𝜙) The wave function is a product of a radial and angular component defined by three quantum numbers (n, ℓ, and m) We do not measure the wave function itself, but the physically significant quantity ﷐𝜓﷮2﷯ ﷐𝝍﷮𝟐﷯ represents the probability density for locating the electron at a particular point in the atom ﷐﷐(𝜓﷮𝑛ℓ𝑚﷯)﷮2﷯𝑑𝑉=﷐[﷐𝑅﷮𝑛ℓ﷯﷐𝑟﷯]﷮2﷯﷐﷐﷐𝑌﷮ℓ𝑚﷯﷐𝜃,𝜙﷯﷯﷮2﷯𝑑𝑉 The spherical volume element dV= ﷐𝑟﷮2﷯𝑠𝑖𝑛𝜃𝑑𝑟𝑑𝜃𝑑𝜙 as shown to the right Untitled picture.png sin 9 dr r sin O dd) rdO rdct)
The wave function for a one-electron atom in the state (n, ℓ, m) is called an orbital Although the term orbital resembles the circular orbits of the Bohr atom there is no real resemblance. An orbital is not a trajectory traced by an individual electron. Rather it is the probability of finding the electron at the point ﷐𝑟,𝜃,𝜙﷯ given by the square of its wavefunction ﷐﷐𝜓﷮2﷯﷮𝑛ℓ𝑚﷯﷐𝑟,𝜃,𝜙﷯ For shorthand, we say the electron is in the an (n, ℓ, m) orbital. The quantum numbers (n, ℓ, m) define the atomic orbital Quantum number n is called the principle quantum number and defines the energy for the electron in a hydrogen atom n can take the values 1, 2, 3, and so on. These correlate to the various shells of the atom n = 1 is the lowest allowed value and the ground state of the hydrogen atom The ground state depends only on the distance from the proton and is written 𝜓﷐𝑟﷯ The probability density falls of rapidly from the nucleus and because it does not depend on direction in space it is said to be spherically symmetric Untitled picture.png (e) Untitled picture.png 0.4 0.3 (빟훃 0.2 0.1 0 0 50 100 150 r/pm 200 250 Quantum number ℓ is called the azimuthal quantum number and defines the shape of an orbital ℓ is restricted to the values 0, 1, 2, . . . n - 1 The values for ℓ are denoted by the letters s, p, d, f, g, h . . . . Untitled picture.png designation It is common to pair these with the principle quantum number (see right) In a hydrogen atom, the 2s and 2p orbitals are considered degenerate meaning they have the same energy value. This is not the case for other atoms . . . Untitled picture.png Designation Is 31) 301 41) Untitled picture.png Untitled picture.png Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings
In a hydrogen atom, the 2s and 2p orbitals are considered degenerate meaning they have the same energy value. This is not the case for other atoms . . . Untitled picture.png Designation Is 31) 301 41) Untitled picture.png 2p orbital Untitled picture.png 2p orbital showing probability density (note the node) Quantum number m (or ﷐𝒎﷮ℓ﷯) is called the magnetic quantum number and determines the spatial orientation of an orbital m is restricted to the values 0, ±1, ±2, . . . , ±ℓ. The three 2p (ℓ=1) orbitals are shown to the right They have the same shape, but different orientation Each is oriented along a different axis ﷐𝒎﷮ℓ﷯ = -1, 0 , +1 Untitled picture.png px Untitled picture.png pz Untitled picture.png py There is a fourth quantum number ﷐𝑚﷮𝑠﷯ ms called the spin quantum number This does not arise from the wave equation but was determined empirically (Stern-Gerlach experiment page 147) ﷐𝑚﷮𝑠﷯ can take the values +﷐1﷮2﷯ or −﷐1﷮2﷯ In summary these are the allowed values for the quantum numbers: Untitled picture.png I (1-1) 1, -ı 2 Concept Check: Deduce the maximum number of electrons that can occupy the n = 1 shell, the n = 2 shell, the n = 3 shell, and the n = 4 shell. subshell n ℓ m ms Max # e- Total e- in shell 1s 1 0 0 +½ or –½ 2 (1, 0, 0, +½) or (1, 0, 0, -½) n=1 2 electrons 2s 2 0 0 +½ or –½ 1 * 2 = 2 electrons n =2 8 electrons Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings
2s 2 0 0 +½ or –½ 1 * 2 = 2 electrons n =2 8 electrons 2p 2 1 -1, 0, +1 +½ or –½ 3 * 2 = 6 electrons 3s 3 0 0 +½ or –½ 2 electrons n = 3 2+6+10 = 18 electrons 3p 3 1 -1, 0, +1 +½ or –½ 6 electrons 3d 3 2 -2, -1, 0, +1, +2 +½ or –½ 5 orbitals w/ 2 e- each = 10 e- 4s 4 0 0 +½ or –½ 2 n= 4 2+6+10+14 = 32 electrons 4p 4 1 -1, 0, +1 +½ or –½ 6 4d 4 2 -2, -1, 0, +1, +2 +½ or –½ 10 4f 4 3 -3, -2, -1, 0, +1, +2, +3 +½ or –½ 14 Trend for determining the total number of electrons for any shell: 2n2 Trend for determining the total number of orbitals for any shell: n2 Trend for determining the total number of subshells for any shell: n Shapes of the s, p, d, and f orbitals s-subshell Untitled picture.emf p-subshell Untitled picture.emf
d-subshell Untitled picture.emf 월寸寸§넣화 f-subshell Untitled picture.emf |전立寸*鞏§4宖| The energy states of atoms with two or more electrons depends on both n and l Untitled picture.png Is (a) Hydrogen Is (b) Multielectron atoms Untitled picture.emf Ener Of Atomic Orbitals AO
Untitled picture.png Is (a) Hydrogen Is (b) Multielectron atoms Untitled picture.emf Ener Of Atomic Orbitals AO This nifty chart will help you determine the electronic configuration of any ground state element The rules for how atomic orbitals get filled by electrons Aufbau Principle (building up) Lowest energy orbitals fill up first Pauli Exclusion Principle Maximum of two electrons per Atomic orbital (AO) Hund's Rule Fill up empty orbitals of same energy first All electrons should be same spin up first Untitled picture.emf Here's a trick to filling orbitals: Use the periodic table to predict the electron configuration of an atom or ion. s block p block d block f block When you don't have the chart you can use the periodic table as your guide Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings
Untitled picture.emf Here's a trick to filling orbitals: Use the periodic table to predict the electron configuration of an atom or ion. s block p block d block f block Core Electrons Inner electrons. We abbreviate these in short form by the noble gas. Valence Electrons Electrons in the highest energy electron shell. These are involved with bonding and determine chemical properties Hydrogen Untitled picture.png Is Long Form: # of Protons: # of Total Electrons: # of Valence Electrons: Oxygen Untitled picture.png Is Long Form: Short Form: # of Protons: # of Total Electrons: # of Core electrons: # of Valence Electrons: Silicon Untitled picture.png XOCQD Is Long Form: # of Protons: # of Total Electrons: Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings
Untitled picture.png XOCQD Is Short Form: # of Core electrons: # of Valence Electrons: Untitled picture.png QX)Qč Long Form: Short Form: # of Protons: # of Total Electrons: # of Core electrons: # of Valence Electrons: Arsenic Untitled picture.png 2s IS Long Form: Short Form: # of Protons: # of Total Electrons: # of Core electrons: # of Valence Electrons: Uranium Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings
Uranium Untitled picture.png Energy of Atomic Orbitals (A 7006000000000000 6000b0000boocooo 6s 500000000 0000000 36000 Is # of Total Electrons: Long Form: Short Form: When an atom is one away from filling a subshell (see group 11) or one away from half-filling a subshell (see group 6) the electron from a similar energy level (the previous s subshell) may donate one of its electrons. This lowers electron-electron repulsion and tends to be more stable Being familiar with these exceptions will help you understand the chemistry of these elements better Here is a list of exceptions: Electron Configuration Exceptions.jpg Machine generated alternative text: Exceptions to Madelung's Rule The exact ground-state electronic configuration of most atoms can be found by use of aufbau principle and Madelung's energy ordering rule. However exact ground-state electronic configurations of some atoms denoted by yellow in the below periodic table can't be found in this way. 1 H Li a 19 K 37 55 s 37 2 M 20 56 88 No Violation 3 sc 57-71 lantha- .00ids j _ 89-103 acti- 4 5 6 24 Cr 7 n 8 Violation 9 10 11 29 Cu 72 104 105 106 57 58 La Ce 89 90 91 Ac Th Pa 75 78 79 Re os 1 Pt Au 107 108 109 Bh Hs •at JDs 64 Sm E Gd 94 9S 96 Cm 12 80 112 b 7 13 14 13 14 31 32 81 82 j 113 114 Dy Ho | 98 99 15 N 15 33 As 83 115 100 16 16 34 Se 52 84 PO 116 Tm 101 17 F 17 35 53 85 At 117 10 18 10 N 18 36 54 86 118 103 Ground-State electronic configurations of exceptions to Madelung's rule: cr: IAr13dS 4s cu: IAr13d10 4s Nb: [Kr14d4 5s MO: IKr14dS 5S Ru: 1Kr14d7 5s Notes: Rh: IKr14d* 5s PCI: 1Kr14d10 _Ag: IKr14d10 5s 2 La: IXe15d 6s Ce: IXe14f5d 6s Gd: IXe14f7 5d 6s2 pe 5d9 6s Au: IXe14d4 5d10 6s Ac: [Rn16d 7s Th: IRn16d2 7s2 Pa: [Rn15f2 6d 7s2 U: IRn15/ 6d 7s2 Np: IRn15fA 6d 7s2 cm: IRn15f7 6d Is Lr: 7s2 71) 0 *There is dispute over nickel (Ni), although chemistry textbooks quote the ground-state electronic configuration of nickel as IAr13d84s , some calculations result in the alternative IAr13d9 4s. *The ground-state electronic configurations of 7th-period atoms with higher atomic numbers (Mt and afterwards) are predicted (and not observed) to obey Madelung's rule.J/%3/tammac/ Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings
Electron Configuration Exceptions.jpg Machine generated alternative text: Exceptions to Madelung's Rule The exact ground-state electronic configuration of most atoms can be found by use of aufbau principle and Madelung's energy ordering rule. However exact ground-state electronic configurations of some atoms denoted by yellow in the below periodic table can't be found in this way. 1 H Li a 19 K 37 55 s 37 2 M 20 56 88 No Violation 3 sc 57-71 lantha- .00ids j _ 89-103 acti- 4 5 6 24 Cr 7 n 8 Violation 9 10 11 29 Cu 72 104 105 106 57 58 La Ce 89 90 91 Ac Th Pa 75 78 79 Re os 1 Pt Au 107 108 109 Bh Hs •at JDs 64 Sm E Gd 94 9S 96 Cm 12 80 112 b 7 13 14 13 14 31 32 81 82 j 113 114 Dy Ho | 98 99 15 N 15 33 As 83 115 100 16 16 34 Se 52 84 PO 116 Tm 101 17 F 17 35 53 85 At 117 10 18 10 N 18 36 54 86 118 103 Ground-State electronic configurations of exceptions to Madelung's rule: cr: IAr13dS 4s cu: IAr13d10 4s Nb: [Kr14d4 5s MO: IKr14dS 5S Ru: 1Kr14d7 5s Notes: Rh: IKr14d* 5s PCI: 1Kr14d10 _Ag: IKr14d10 5s 2 La: IXe15d 6s Ce: IXe14f5d 6s Gd: IXe14f7 5d 6s2 pe 5d9 6s Au: IXe14d4 5d10 6s Ac: [Rn16d 7s Th: IRn16d2 7s2 Pa: [Rn15f2 6d 7s2 U: IRn15/ 6d 7s2 Np: IRn15fA 6d 7s2 cm: IRn15f7 6d Is Lr: 7s2 71) 0 *There is dispute over nickel (Ni), although chemistry textbooks quote the ground-state electronic configuration of nickel as IAr13d84s , some calculations result in the alternative IAr13d9 4s. *The ground-state electronic configurations of 7th-period atoms with higher atomic numbers (Mt and afterwards) are predicted (and not observed) to obey Madelung's rule.J/%3/tammac/
Electron Configuration Exceptions.jpg Machine generated alternative text: Exceptions to Madelung's Rule The exact ground-state electronic configuration of most atoms can be found by use of aufbau principle and Madelung's energy ordering rule. However exact ground-state electronic configurations of some atoms denoted by yellow in the below periodic table can't be found in this way. 1 H Li a 19 K 37 55 s 37 2 M 20 56 88 No Violation 3 sc 57-71 lantha- .00ids j _ 89-103 acti- 4 5 6 24 Cr 7 n 8 Violation 9 10 11 29 Cu 72 104 105 106 57 58 La Ce 89 90 91 Ac Th Pa 75 78 79 Re os 1 Pt Au 107 108 109 Bh Hs •at JDs 64 Sm E Gd 94 9S 96 Cm 12 80 112 b 7 13 14 13 14 31 32 81 82 j 113 114 Dy Ho | 98 99 15 N 15 33 As 83 115 100 16 16 34 Se 52 84 PO 116 Tm 101 17 F 17 35 53 85 At 117 10 18 10 N 18 36 54 86 118 103 Ground-State electronic configurations of exceptions to Madelung's rule: cr: IAr13dS 4s cu: IAr13d10 4s Nb: [Kr14d4 5s MO: IKr14dS 5S Ru: 1Kr14d7 5s Notes: Rh: IKr14d* 5s PCI: 1Kr14d10 _Ag: IKr14d10 5s 2 La: IXe15d 6s Ce: IXe14f5d 6s Gd: IXe14f7 5d 6s2 pe 5d9 6s Au: IXe14d4 5d10 6s Ac: [Rn16d 7s Th: IRn16d2 7s2 Pa: [Rn15f2 6d 7s2 U: IRn15/ 6d 7s2 Np: IRn15fA 6d 7s2 cm: IRn15f7 6d Is Lr: 7s2 71) 0 *There is dispute over nickel (Ni), although chemistry textbooks quote the ground-state electronic configuration of nickel as IAr13d84s , some calculations result in the alternative IAr13d9 4s. *The ground-state electronic configurations of 7th-period atoms with higher atomic numbers (Mt and afterwards) are predicted (and not observed) to obey Madelung's rule.J/%3/tammac/ Excited State Configurations The configurations we have been working on were all in the ground state. When a photon of sufficient energy is absorbed one or more electrons can be moved into a higher energy level. Under this condition the atom is considered to be in an excited state configuration. Examples of excited states: Simplest: Flipping the spin state of an electron Pairing up an electron when Hund's rule would suggest otherwise Moving an electron from one orbital to another Here is a depiction of this with oxygen Ground State Oxygen Flipped spin state Electrons are paired up when not expected Electron is promoted Untitled picture.png XOCQD Is Untitled picture.png XOCQD Is Untitled picture.png XOCQD Is Untitled picture.png XOCQD Is Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings

 

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