# V.Montgomery & R.Smith1 DEVELOPMENT of Quantum Mechanic.

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V.Montgomery & R.Smith1 DEVELOPMENT of Quantum Mechanic

V.Montgomery & R.Smith2 Wave Nature of Electrons We know electrons behave as particles

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5 de Broglies Equation A free e- of mass (m) moving with a velocity (v) should have an associated wavelength: = h/mv Linked particle properties (m=mass, and v=velocity) with a wave property ( )

V.Montgomery & R.Smith6 Example of de Broglies Equation Calculate the wavelength associated with an e- of mass 9.109x10 -28 g traveling at 40.0% the speed of light.

V.Montgomery & R.Smith7 Answer C=(3.00x10 8 m/s)(.40)=1.2x10 8 m/s = h/mv = (6.626 x 10 -34 J s) =6.06x10 -12 m (9.11x10 -31 kg)(1.2x10 8 m/s) Remember 1J = 1(kg)(m) 2 /s 2

V.Montgomery & R.Smith8 Wave-Particle Duality de Broglies suggested that e- has wave-like properties. Thomsons experiments suggested that e- has particle-like properties measured charge-to-mass ratio

Davisson and Germer experiment They were the first to prove experimentally that the electrons have both wave and particle nature. V.Montgomery & R.Smith9

Davisson and Germer experiment They showed in their experiment that a beam of electrons are diffracted on a crystal, just like X-rays and could measure the wavelength of electrons. V.Montgomery & R.Smith10

V.Montgomery & R.Smith11 In this experiment, electrons produced the interference pattern jut like in Youngs experiment with light.

Conclusion Since electrons produce the same pattern with the light, the electrons also have the wave nature. V.Montgomery & R.Smith12

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V.Montgomery & R.Smith14 Quantum mechanical model Schr Ö dinger Heisenberg Pauli Hund

V.Montgomery & R.Smith15 Where are the e- in the atom? e- have a dual wave-particle nature If e- act like waves and particles at the same time, where are they in the atom? First consider a theory by German theoretical physicist, Werner Heisenberg.

V.Montgomery & R.Smith16 Heisenbergs Idea e- are detected by their interactions with photons Photons have about the same energy as e- Any attempt to locate a specific e- with a photon knocks the e- off its course ALWAYS a basic uncertainty in trying to locate an e-

V.Montgomery & R.Smith17 Heisenbergs Uncertainty Principle Impossible to determine both the position and the momentum of an e- in an atom simultaneously with great certainty.

V.Montgomery & R.Smith18 Schr Ö dingers Wave Equation An equation that treated electrons in atoms as waves Only waves of specific energies, and therefore frequencies, provided solutions to the equation Quantization of e- energies was a natural outcome

V.Montgomery & R.Smith19 Schr Ö dingers Wave Equation Solutions are known as wave functions Wave functions give ONLY the probability of finding and e- at a given place around the nucleus e- not in neat orbits, but exist in regions called orbitals

V.Montgomery & R.Smith20 Schr Ö dingers Wave Equation Here is the equation Dont memorize this or write it down It is a differential equation, and we need calculus to solve it -h (ә 2 Ψ )+ (ә 2 Ψ )+( ә 2 Ψ ) +Vψ =Eψ 8(π) 2 m (әx 2) (әy 2) (әz 2 ) Scary???

V.Montgomery & R.Smith21 Probability likelihood Orbital wave function; region in space where the probability of finding an electron is high Schr Ö dingers Wave Equation states that orbitals have quantized energies But there are other characteristics to describe orbitals besides energy Definitions

V.Montgomery & R.Smith22 Quantum Numbers Definition: specify the properties of atomic orbitals and the properties of electrons in orbitals There are four quantum numbers The first three are results from Schr Ö dingers Wave Equation

V.Montgomery & R.Smith23 Quantum Numbers (1) Principal Quantum Number, n

V.Montgomery & R.Smith24 Quantum Numbers Principal Quantum Number, n Values of n = 1,2,3,… Positive integers only! Indicates the main energy level occupied by the electron

V.Montgomery & R.Smith25 Quantum Numbers Principal Quantum Number, n Values of n = 1,2,3,… Describes the energy level, orbital size As n increases, orbital size increases.

V.Montgomery & R.Smith26 Principle Quantum Number n = 1 n=2 n=3 n=4 n=5 n=6 Energy

V.Montgomery & R.Smith27 Principle Quantum Number More than one e- can have the same n value These e- are said to be in the same e- shell The total number of orbitals that exist in a given shell = n 2

V.Montgomery & R.Smith28 Quantum Numbers (2) Angular momentum quantum number, l

V.Montgomery & R.Smith29 Quantum Numbers Angular momentum quantum number, l Values of l = n-1, 0

V.Montgomery & R.Smith30 Quantum Numbers Angular momentum quantum number, l Values of l = n-1, 0 Describes the orbital shape

V.Montgomery & R.Smith31 Quantum Numbers Angular momentum quantum number, l Values of l = n-1, 0 Describes the orbital shape Indicates the number of sublevel (subshells) (except for the 1 st main energy level, orbitals of different shapes are known as sublevels or subshells)

V.Montgomery & R.Smith32 Orbital Shapes For a specific main energy level, the number of orbital shapes possible is equal to n. Values of l = n-1, 0 Ex. Orbital which n=2, can have one of two shapes corresponding to l = 0 or l=1 Depending on its value of l, an orbital is assigned a letter.

V.Montgomery & R.Smith33 Orbital Shapes Angular magnetic quantum number, l If l = 0, then the orbital is labeled s. s is spherical.

V.Montgomery & R.Smith34 Orbital Shapes If l = 1, then the orbital is labeled p. dumbbell shape

V.Montgomery & R.Smith35 Orbital Shapes If l = 2, the orbital is labeled d. double dumbbell or four-leaf clover

V.Montgomery & R.Smith36 Orbital Shapes If l = 3, then the orbital is labeled f.

V.Montgomery & R.Smith37 Energy Level and Orbitals n=1, only s orbitals n=2, s and p orbitals n=3, s, p, and d orbitals n=4, s,p,d and f orbitals Remember: l = n-1

V.Montgomery & R.Smith38 Atomic Orbitals Atomic Orbitals are designated by the principal quantum number followed by letter of their subshell Ex. 1s = s orbital in 1 st main energy level Ex. 4d = d sublevel in 4 th main energy level

V.Montgomery & R.Smith39 Quantum Numbers (3) Magnetic Quantum Number, m l

V.Montgomery & R.Smith40 Quantum Numbers Magnetic Quantum Number, m l Values of m l = + l …0…- l

V.Montgomery & R.Smith41 Quantum Numbers Magnetic Quantum Number, m l Values of m l = + l …0…- l Describes the orientation of the orbital Atomic orbitals can have the same shape but different orientations

V.Montgomery & R.Smith42 Magnetic Quantum Number s orbitals are spherical, only one orientation, so m=0 p orbitals, 3-D orientation, so m= -1, 0 or 1 (x, y, z) d orbitals, 5 orientations, m= -2,-1, 0, 1 or 2

V.Montgomery & R.Smith43 Quantum Numbers (4) Electron Spin Quantum Number,m s

V.Montgomery & R.Smith44 Quantum Numbers Electron Spin Quantum Number,m s Values of m s = +1/2 or –1/2 e- spin in only 1 or 2 directions A single orbital can hold a maximum of 2 e-, which must have opposite spins

V.Montgomery & R.Smith45 Electron Configurations Electron Configurations: arragenment of e- in an atom There is a distinct electron configuration for each atom There are 3 rules to writing electron configurations:

V.Montgomery & R.Smith46 Pauli Exclusion Principle No 2 e- in an atom can have the same set of four quantum numbers (n, l, m l, m s ). Therefore, no atomic orbital can contain more than 2 e-.

V.Montgomery & R.Smith47 Aufbau Principle Aufbau Principle: an e- occupies the lowest energy orbital that can receive it. Aufbau order:

V.Montgomery & R.Smith48 Hunds Rule Hunds Rule: orbitals of equal energy are each occupied by one e- before any orbital is occupied by a second e-, and all e- in singly occupied orbitals must have the same spin

V.Montgomery & R.Smith49 Electron Configuration The total of the superscripts must equal the atomic number (number of electrons) of that atom. The last symbol listed is the symbol for the differentiating electron.

V.Montgomery & R.Smith50 Differentiating Electron The differentiating electron is the electron that is added which makes the configuration different from that of the preceding element. The last electron. H1s 1 He1s 2 Li1s 2, 2s 1 Be1s 2, 2s 2 B1s 2, 2s 2, 2p 1

V.Montgomery & R.Smith51 Orbital Diagrams These diagrams are based on the electron configuration. In orbital diagrams: Each orbital (the space in an atom that will hold a pair of electrons) is shown. The opposite spins of the electron pair is indicated.

V.Montgomery & R.Smith52 Orbital Diagram Rules 1. Represent each electron by an arrow 2. The direction of the arrow represents the electron spin 3. Draw an up arrow to show the first electron in each orbital. 4. Hunds Rule: Distribute the electrons among the orbitals within sublevels so as to give the most unshared pairs. Put one electron in each orbital of a sublevel before the second electron appears. Half filled sublevels are more stable than partially full sublevels.

V.Montgomery & R.Smith53 Orbital Diagram Examples H _ 1s Li _ 1s 2s B __ __ 1s 2s 2p N _ 1s 2s 2p

V.Montgomery & R.Smith54 Dot Diagram of Valence Electrons When two atom collide, and a reaction takes place, only the outer electrons interact. These outer electrons are referred to as the valence electrons. Because of the overlaying of the sublevels in the larger atoms, there are never more than eight valence electrons.

V.Montgomery & R.Smith55 Rules for Dot Diagrams :Xy:. S sublevel electrons P x orbital P y orbital P z orbital

V.Montgomery & R.Smith56 Rules for Dot Diagrams Remember: the maximum number of valence electrons is 8. Only s and p sublevel electrons will ever be valence electrons. Put the dots that represent the s and p electrons around the symbol. Use the same rule (Hunds rule) as you fill the designated orbitals.

V.Montgomery & R.Smith57 Examples of Dot Diagrams H He Li Be

V.Montgomery & R.Smith58 Examples of Dot Diagrams C N O Xe

V.Montgomery & R.Smith59 Summary Both dot diagrams and orbital diagrams will be use full to use when we begin our study of atomic bonding. We have been dealing with valence electrons since our initial studies of the ions. The number of valence electrons can be determined by reading the column number. Al = 3 valence electrons Br = 7 valence electrons All transitions metals have 2 valence electrons.