Electron Configuration & Orbitals Quantum Model of the Atom Electrons in Atoms- Where are they Electron Configuration & Orbitals 1s22s22p63s23p64s23d104p65s24d104p65s24d105p66s24f145d106p6… Objectives: To describe the quantum mechanical model of the atom. To describe the relative sizes and shapes of s and p orbitals.

Properties of light We’ve been working with the wave properties of electromagnetic radiation: Wavelength, frequency, etc De Broglie stated: Applied wave-particle theory to electrons electrons exhibit wave properties E=hc/ λ Plank’s equation λ = h/mn DeBroglie’s equation

I. Waves and Particles Wave-Particle Duality of light Einstein and the Photoelectric effect (electrons are ejected when light strikes the surface of a metal, when the frequency is high enough) Proposed the particle nature of light Photons- mass-less packets of energy How can electron be both a particle and a wave? No single experiment can be done to show that the electron behave simultaneously as a wave and a particle

Heisenberg What does wave-particle duality have to do with electrons in atoms? Werner Heisenberg concluded, in what is now known as the Heisenberg uncertainty principle, that it is impossible to fix both the position of an electron in an atom and its energy. Attempting to measure either will alter the path. In order to locate the position of an electron, a picture would need to be taken, this would bounce a particle of light off the electron’s surface, revealing it’s position, but also causing it to move, changing the velocity. His most well-known thought experiment involved photographing an electron. To take the picture, a scientist might bounce a light particle off the electron's surface. That would reveal its position, but it would also impart energy to the electron, causing it to move. Learning about the electron's position would create uncertainty in its velocity; and the act of measurement would produce the uncertainty needed to satisfy the principle.

Quantum Mechanics Heisenberg Uncertainty Principle Impossible to know both the velocity and position of an electron at the same time Werner Heisenberg ~1926 g Microscope Werner Heisenberg (1901 - 1976) The uncertainty principle: a free electron moves into the focus of a hypothetical microscope and is struck by a photon of light; the photon transfers momentum to the electron. The reflected photon is seen in the microscope, but the electron has moved out of focus. The electron is not where it appears to be. A wave is a disturbance that travels in space and has no fixed position. Schrodiner’s cat: cat is both alive and dead, uncertainty – particle position is underdetermined until measured or observed, it is actually in neither state until a measurement is made. For instance, a particle has two possible spins, up or down, but until the actual spin is measured, it is has neither spin. It doesn't "decide" which spin value it has until it is measured The Heisenberg uncertainty principle states that the uncertainty in the position of a particle (Δx) multiplied by the uncertainty in its momentum [Δ(m)] is greater than or equal to Planck’s constant divided by 4: (Δx) [Δ(m)]  h 4 • It is impossible to describe precisely both the location and the speed of particles that exhibit wavelike behavior. Electron

Schrodinger’s cat Schrodinger's Cat was a thought experiment which stated that until we observe the cat in the box (either being dead or alive) we do not actually know that its dead or alive. Schrodinger’s cat: cat is assumed both alive and dead, uncertainty Heisenberg’s- particle position is underdetermined until measured or observed, it is actually in neither state until a measurement is made. For instance, a particle has two possible spins, up or down, but until the actual spin is measured, it is has neither spin. It doesn't "decide" which spin value it has until it is measured.

Heisenberg Uncertainty Principle

Atomic Spectra and electrons Atoms naturally want to take the lowest energy state possible. When atoms absorb energy, electrons move into higher energy levels, and these electrons lose energy by emitting light when they return to lower energy levels. An electron that has absorbed energy and moved up a level is said to be in an ‘excited state’ When at the lowest possible energy level, atoms are said to be in ‘ground state’

Arrangement of Electrons in Atoms Electrons in atoms are arranged as SHELLS (n) SUBSHELLS (l) ORBITALS (ml)

Electron Probability vs. Distance Quantum Mechanics Orbital (“electron cloud”) Region in space where there is 90% probability of finding an electron 90% probability of finding the electron Orbital Electron Probability vs. Distance 40 30 Electron Probability (%) 20 10 50 100 150 200 250 Distance from the Nucleus (pm) Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Energy level Each possible electron orbit has a fixed energy Energy level the specific energies an electron in an atom or other system can have amount of energy possessed by an electron determines its energy level levels farther from nucleus represent higher energy

Energy levels Kind of like the rungs of a ladder. The lowest rung corresponds the lowest energy level. A person can climb up or down a ladder by going from rung to rung. Electrons in an atom can jump from one energy level to another A person can cannot stand between the rungs of a ladder, an electron cannot be between energy levels To move from one rung to another, a person must move just the right distance – an electron must gain or lose just the right amount of energy (known as a quantum) to move. however not equally spaced like the rungs)

Quantum Numbers Four Quantum Numbers: Specify the “address” of each electron in an atom UPPER LEVEL Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Quantum Numbers Four types – they tell us how to describe an electron and its probable location Principal Quantum Number ( n ) Angular Momentum Quantum # ( l ) Magnetic Quantum Number ( ml ) Spin Quantum Number ( ms ) Schrödinger used three quantum numbers (n, l, and ml) to specify any wave functions. • Quantum numbers provide information about the spatial distribution of the electron.

Quantum Numbers 1. Principal Quantum Number ( n ) energy level occupied by the electrons (distance from the nucleus) In an address analogy, this would be the state in which the electron would probably be found Size of the orbital n2 = # of orbitals in the energy level 1s 2s s Orbitals – Orbitals with l = 0 are s orbitals and are spherically symmetrical, with the greatest probability of finding the electron occurring at the nucleus. – All orbitals with values of n > 1 and l  0 contain one or more nodes. – Three things happen to s orbitals as n increases: 1. they become larger, extending farther from the nucleus 2. they contain more nodes 3. for a given atom, the s orbitals become higher in energy as n increases due to the increased distance from the nucleus 3s Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Prinicpal quantum number – (n) – The principal quantum number has positive integer values (1, 2, 3, and so on). These numbers represent the periods of the periodic table, which correspond to the energy levels in which electrons are located. If the quantum numbers were a complete address for a house, the principle quantum number would be analogous to the name of the city.

Quantum Numbers n shell l subshell ml orbital ms electron spin 1, 2, 3, 4, ... l subshell 0, 1, 2, ... n - 1 ml orbital - l ... 0 ... +l ms electron spin +1/2 and - 1/2

Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 334 Relative Sizes 1s and 2s 1s 2s Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 334

Atomic Orbitals

Quantum Numbers f d s p 2. Angular Momentum Quantum # ( l ) shape of the orbital (s, p, d, f) In the address analogy, this would be the city in which the electron would probably be found. f d s p Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Quantum Numbers n shell l subshell ml orbital ms electron spin 1, 2, 3, 4, ... l subshell 0, 1, 2, ... n - 1 ml orbital - l ... 0 ... +l ms electron spin +1/2 and - 1/2

Shapes of s, p, and d-Orbitals s orbital p orbitals • p orbitals – Orbitals with l = 1 are p orbitals and contain a nodal plane that includes the nucleus, giving rise to a “dumbbell shape.” – The size and complexity of the p orbitals for any atom increase as the principal quantum number n increases. • d orbitals – Orbitals with l = 2 are d orbitals and have more complex shapes with at least two nodal surfaces. • f orbitals – Orbitals with l = 3 are f orbitals, and each f orbital has three nodal surfaces, so their shapes are complex. d orbitals

Quantum Numbers 2s 2px 2py 2pz Orbitals combine to form a spherical shape. 2s 2pz 2py 2px Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Quantum Numbers 3. Magnetic Quantum Number ( ml ) orientation of the orbital around the nucleus specifies the exact orbital within each subshell Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Quantum Numbers n shell l subshell ml orbital ms electron spin 1, 2, 3, 4, ... l subshell 0, 1, 2, ... n - 1 ml orbital - l ... 0 ... +l ms electron spin +1/2 and - 1/2

Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 335 p-Orbitals px pz py Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 335

Copyright © 2007 Pearson Benjamin Cummings. All rights reserved.

Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 336 d-orbitals Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 336

Quantum Numbers 4. Spin Quantum Number ( ms ) The direction the electron is spinning An orbital can hold 2 electrons that spin in opposite directions. In the address analogy, this would be the street on which the electron would probably be found. Analyzing the emission and absorption spectra of the elements, it was found that for elements having more than one electron, nearly all the lines in the spectra were pairs of very closely spaced lines. Each line represents an energy level available to electrons in the atom so there are twice as many energy levels available than predicted by the quantum numbers n, l, and ml. Applying a magnetic field causes the lines in the pairs to split apart. Uhlenbeck and Goudsmit proposed that the splittings were caused by an electron spinning about its axis. Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Quantum Numbers n shell l subshell ml orbital ms electron spin 1, 2, 3, 4, ... l subshell 0, 1, 2, ... n - 1 ml orbital - l ... 0 ... +l ms electron spin +1/2 and - 1/2

Electron Spin: The Fourth Quantum Number When an electrically charged object spins, it produces a magnetic moment and behaves like a magnet. A magnetic moment is called electron spin. An electron behaves like a magnet that has one of two possible orientations, aligned either with the magnetic field or against it. In the address analogy, this would be the house number of the electron Copyright © 2006 Pearson Benjamin Cummings. All rights reserved.

Copyright © 2006 Pearson Benjamin Cummings. All rights reserved.

Electron Configurations Electron configuration-arrangement of electrons in an atom Most chemical systems are going to tend towards the lowest energy states The lowest energy arrangement of the electrons is called the “ground state” electron configuration

Aufbau Principle The Aufbau principle states that an electron will always occupy the lowest energy orbital that will receive it Any orbital can only hold 2 electrons Once the orbital is full electrons have to occupy higher energy orbitals

Fill in the chart

Orbital Filling Technique 7s 6s 6p 6d 5s 5p 5d 5f 4s 4p 4d 4f 3s 3p 3d 2s 2p 1s memorize!

Orbital Filling Technique 7s 6s 6p 6d 5s 5p 5d 5f 4s 4p 4d 4f 3s 3p 3d 2s 2p 1s memorize!

Other Filling Rules . . . Pauli Exclusion Principle: no two electrons in the same orbital can have the same spin. Hund’s Rule: orbitals of equal energy are each occupied by one electron before any orbital is occupied by a second electron.

Quantum Numbers Pauli Exclusion Principle No two electrons in an atom can have the same 4 quantum numbers. Each electron has a unique “address”: Wolfgang Pauli 1. Principal #  2. Ang. Mom. #  3. Magnetic #  4. Spin #  energy level sublevel (s,p,d,f) orbital electron Wolfgang Pauli determined that each orbital can contain no more than two electrons. Pauli exclusion principle: No two electrons in an atom can have the same value of all four quantum numbers (n, l, ml , ms). By giving the values of n, l, and ml, we specify a particular orbit. Because ms has only two values (+½ or -½), two electrons (and only two electrons) can occupy any given orbital, one with spin up and one with spin down. Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Notation Orbital Notation: graphical method that uses lines or boxes to represent orbitals and arrows to represent electrons Electron Configuration Notation: simplified method that simply uses orbital names with the appropriate number of electrons Noble Gas Notation: a short-hand e.c. notation which uses noble gases’ configurations to simplify high atomic number configurations

Orbital Notation

More Orbital Notation . . .

Describe the electron configuration for the atoms of any element using orbital notation, electron configuration notation, and noble-gas notation. Magnesium ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ 1s 2s 2p 3s 1s22s22p63s2 [Ne] 3s2

Write the electron configuration notation and the noble gas notation for a barium atom. 2. Identify the elements having the following electron configuration: 1s22s22p63s23p3 [Ar]4s1 ↑↓ ↑↓ ↑↓ ↑↓ ↑ 1s 2s 2p

Orbital Shapes

Allowed Sets of Quantum Numbers for Electrons in Atoms Level n 1 2 3 Sublevel l Orbital ml Spin ms 1 -1 2 -2 = +1/2 = -1/2 Allowed Sets of Quantum Numbers for Electrons in Atoms

"Teacher, may I be excused? My brain is full." Feeling overwhelmed? Read chapter 4.2! Chemistry "Teacher, may I be excused? My brain is full." Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

H = 1s1 He = 1s2 Li = 1s2 2s1 Be = 1s2 2s2 C = 1s2 2s2 2p2 S 2px 2py 2pz S = 1s2 2s2 2p4 1s 2s 2px 2py 2pz 3s 3px 3py 3pz

H = 1s1 1s e- +1 He = 1s2 1s e- +2 e- Coulombic attraction holds valence electrons to atom. Be = 1s2 2s2 1s 2s e- e- +4 Coulombic attraction holds valence electrons to atom. e- e- Valence electrons are shielded by the kernel electrons. Therefore the valence electrons are not held as tightly in Be than in He.

Fe = 1s1 2s22p63s23p64s23d6 26 Iron has ___ electrons. Arbitrary 2px 2py 2pz 3s 3px 3py 3pz 4s 3d 3d 3d 3d 3d Arbitrary Energy Scale 18 32 8 2 1s 2s 2p 3s 3p 4s 4p 3d 5s 5p 4d 6s 6p 5d 4f NUCLEUS e- e- e- e- e- e- e- e- e- e- e- e- e- +26 e- e- e- e- e- e- e- e- e- e- e- e- e-

Electron Configurations Orbital Filling Element 1s 2s 2px 2py 2pz 3s Configuration Orbital Filling Element 1s 2s 2px 2py 2pz 3s Configuration Electron Electron H He Li C N O F Ne Na H He Li C N O F Ne Na 1s1 1s1 1s2 1s2 NOT CORRECT Violates Hund’s Rule 1s22s1 1s22s1 1s22s22p2 1s22s22p2 The aufbau principle 1. For hydrogen, the single electron is placed in the 1s orbital, the orbital lowest in energy, and electron configuration is written as 1s1. The orbital diagram is H: 2p _ _ _ 2s _ 1s  2. A neutral helium atom, with an atomic number of 2 (Z = 2), contains two electrons. Place one electron in the lowest-energy orbital, the 1s orbital. Place the second electron in the same orbital as the first but pointing down, so the electrons are paired. This is written as 1s2. He: 2p _ _ _ 1s  3. Lithium, with Z = 3, has three electrons in the neutral atom. The electron configuration is written as 1s22s1. Place two electrons in the 1s orbital and place one in the next lowest-energy orbital, 2s. The orbital diagram is Li: 2p _ _ _ 2s  4. Beryllium, with Z = 4, has four electrons. Fill both the 1s and 2s orbitals to achieve 1s22s2: Be: 2p _ _ _ 2s  1s  5. Boron, with Z = 5, has five electrons. Place the fifth electron in one of the 2p orbitals. The electron configuration is 1s22s22p1 B: 2p  _ _ 2s  1s  6. Carbon, with Z = 6, has six electrons. One is faced with a choice — should the sixth electron be placed in the same 2p orbital that contains an electron or should it go in one of the empty 2p orbitals? And if it goes in an empty 2p orbital, will the sixth electron have its spin aligned with or be opposite to the spin of the fifth? 7. It is more favorable energetically for an electron to be in an unoccupied orbital rather than one that is already occupied due to electron-electron repulsions. According to Hund’s rule, the lowest-energy electron configuration for an atom is the one that has the maximum number of electrons with parallel spins in degenerate orbitals. Electron configuration for carbon is 1s22s22p2 and the orbital diagram is C: 2p   _ 8. Nitrogen (Z = 7) has seven electrons. Electron configuration is 1s22s22p3. Hund’s rule gives the lowest-energy arrangement with unpaired electrons as N: 2p    9. Oxygen, with Z = 8, has eight electrons. One electron is paired with another in one of the 2p orbitals. The electron configuration is 1s22s22p4: O: 2p    2s  10. Fluorine, with Z = 9, has nine electrons with the electron configuration 1s22s22p5: F: 2p    11. Neon, with Z = 10, has 10 electrons filling the 2p subshell. The electron configuration is 1s22s22p6 Ne: 2p    1s22s22p3 1s22s22p3 1s22s22p4 1s22s22p4 1s22s22p5 1s22s22p5 1s22s22p6 1s22s22p6 1s22s22p63s1 1s22s22p63s1

Maximum Number of Electrons In Each Sublevel Sublevel Number of Orbitals of Electrons s 1 2 p 3 6 d 5 10 f 7 14 LeMay Jr, Beall, Robblee, Brower, Chemistry Connections to Our Changing World , 1996, page 146

Quantum Numbers n shell l subshell ml orbital ms electron spin 1, 2, 3, 4, ... l subshell 0, 1, 2, ... n - 1 ml orbital - l ... 0 ... +l ms electron spin +1/2 and - 1/2