Notes

Outline

Atomic Structure Electronic Structure of Atoms

Theory of Electromagnetic Radiation Developed by Ernst Maxwell Radiation is a wave manifestation resulting from an interaction between an electrical and magnetic field perpendicular to one another Waves are transverse Wave train is infinite in both directions

Properties Of Electromagnetic Waves Frequency (f or n )-The number of waves that pass a stationary point in a unit of time Wavelength( l )- The linear distance between one point on a wave and the corresponding point on the next wave. f~ 1/ l f = c / l                                                where c = speed of light = 3.00 X 10 8 m/s Example

T-7.5 Electromagnetic Spectrum

Quantum Theory Developed by Max Planck When energy is absorbed or liberated by matter it is exchanged with the environment in packets of energy(quanta) discontinuously (microcosmic) From a macrocosmic view energy appears to be exchanged continuously (flowing) because atoms are out of sync when exchanging the energy resulting in an appearance of continuity Impressionistic painting analogy

T-7.2 Emission(Line)Spectra

Photoelectric Effect Discovered by Albert Einstein Used to support Plank’s Quantum Theory Determined the Threshold Frequency where energy was absorbed by electrons Proved that energy was not exchanged at the atomic level continuously

Energy of Electromagnetic Radiation E~ f E=h f    where h = Planck’s Constant = 6.29 X 10 –34 j-sec Since f = c / l Then DE = h f = h c / l For 1 mol of Photons: DE = N h f             where N = 6.023 X 10 23 atoms Example

Bohr Model of Atom Solar System Model Attempts To Justify Classical Physics with Quantum Physics Basic Premise Electrons travel around nucleus in defined elliptical orbits associated with a energy level The closer orbit is to nucleus the less energy associated with it Atoms of matter absorb or liberate energy by electrons moving from one orbit to another

Bohr Model (cont) A minimum packet of energy must be absorbed or liberated to go from one orbit to another

T-59  Line Spectrum of Common Elements

Energy State of a Bohr Hydrogen Atom En = - Rh / n 2 where n = orbit number; Rh = 2.179 X 10 –18 J E1 = -B / (1)2 = -B / 1

E2 = -Rh / (2)2 = -B / 4 E3 = -Rh / (3)2 = -B / 9 Example

T-58 The Visible Emission Spectrum of Hydrogen

T-61 Energy Levels and Spectral Lines of Hydrogen

Determining Energy of Transition (D E) Using Bohr Model D E 1,2 = E2 – E1 = (- Rh / 4) – (-B / 1) =   - Rh(1/4-1/1) D E 1,3 = E3 – E1 = - Rh(1/9 – 1/1) D E 2,3 =E3 – E2= - Rh (1/9 – ¼) Example

Determining the Frequency of Emission Of An Excited State D  E = h f f = D E / h Example

of Emission Of An Excited Hydrogen Atom D E = h c / l l  = h c / D E Must convert c = speed of light to nm/sec 3.0 X 10 8 m/s X 1 X 10 9 nm / 1 m = 3.0 X 10 17 nm/s Example

DeBrogli’s Dual Nature of Sub-Atomic Particles l  =  h / mv    where m = mass of particle; v = velocity; h = Planck’s Constant; l = wavelength Matter has both particle like (mass) and wave like characteristics Electrons, neutrons, and protons exhibit both particle like and wave like characteristics(diffraction)

Heisenberg’s Uncertainty Principle It is impossible to know the position and momentum (mv) of an electron at the same time.  Since we do know with absolute certainty the mass and velocity of an electron, this means that its position can not be known with absolute certainty.There will always be a degree of uncertainty as to its exact position.

T-63 Experimental Justification of Uncertainty Principle

Highlights of Scrodinger’s Quantum Mechanical Theory of Matter Basic Premise: The position of an electron in an atom has a probability region which can be defined by : A wave function (eigen function)( y ) A wave equation which is a differential equation  HY  =  EY Where H = Hamiltonian Differential operator; E = Energy state of the probability region

Quantum Mechanical Theory (cont) When the Hamiltonian operates mathematically upon the wave function it generates a differential equation Solving the differential equation requires using approximation methods which result in approximate solutions (4) The four solutions are referred to as the quantum numbers of the probability region of an electron

Quantum Mechanical Theory (cont) The set of quantum numbers when taken together approximately describe the Physical Features of the probability region In the 1930’s mathematical group theory was applied that resulted in the extraction of the fourth solution.

Quantum Numbers Principle Quantum Number (shell)(n) Azimuthal  Quantum Number (sub-shell)(l) Magnetic Quantum Number (orbital)(ml) Spin Quantum (ms)

Principle Quantum Number(n) n = 1, 2, 3, 4, ….. Physically represents the radial extension(effective volume) of the region from the nucleus The greater the n value the further extended the region is. Max # of e = 2n 2 n = 1  max # e = 2(1)2 n = 2 max # e = 2(2)2 Relative Energy State n=1 < n=2 < n=3

Azimuthal Quantum Number(L) Accepted Values Physically represents the shape of the probability region L =0, 1, 2,……..n-1 L = 0 spherically shaped(mono lobed) L = 1 Two speroids tangent to each other (double lobed) L = 2 quadra-lobed L=3 Octa-lobed

Limits of Azimuthal Q.N. L=0     2 electron max L = 1    6 electron max L = 2   10 electron max L = 3   14 electron max

Spdf Notational Symbol L = 0 is an “s” notation L = 1 is a “p” notation L = 2 is a “d” notation L = 3 is an “f” notation For a given n value the relative energy states: s < p < d < f

Magnetic Quantum Number(ml) Physically represents the spatial orientation or direction of the probability regions Values- ML = -L, -L+1, -L+2,…..0, 1, 2, 3, …+L Limits Maximum of two electrons having the same m value Energy States: All degenerate (having the same energy state) when not in an electromagnetic field

Spin Quantum Number (ms) Physically represents the spin of an electron on an imaginary axis Values +1/2 -1/2 In a given orbital (m value) electrons occupying the same orbital (same n,l, and m value)will have opposite spins

T-7.24 Comparison of 1s and 2s orbitals

T-7.26 The 2p orbitals

T-7.27 The 3d orbitals

Quantum Rules For Assigning Electrons To Orbitals Aufbau Principle- In assigning quantum numbers begin with the lowest energy state. Pauli Exclusion Principle-No two electrons may have the exact same set of quantum numbers in an atom.Two electrons in the same orbital must have opposite spins

Quantum Rules For Assigning Electrons To Orbitals(cont) Hunds Rule- When two or more orbitals have the same energy (degenerate) then one electron must be assigned to each before a second electron can be assigned.

Electronic spdf Notation Nl #e Orbital Occupancy Sequence 1s2, 2s2, 2p6, 3s2,3p6,4s2,3d10,4p6,5s2,4d10,5p6,6s2,5d1,4f14,5d9, 6p6, 7s2, 6d1, 5f14, 6d9

T-68 Periodic Table Illustrating spdf Build-Up Order

T-8.1 Electronic Configurations of Atoms

T-8.2 Orbital Diagrams of Atoms