Chapter 9: Electrons in Atoms

Contents 9-1Electromagnetic Radiation 9-2Atomic Spectra 9-3Quantum Theory 9-4The Bohr Atom 9-5Two Ideas Leading to a New Quantum Mechanics 9-6Wave Mechanics 9-7Quantum Numbers and Electron Orbitals

Contents 9-8Quantum Numbers 9-9Interpreting and Representing Orbitals of the Hydrogen Atom 9-9Electron Spin 9-10Multi-electron Atoms 9-11Electron Configurations 9-12Electron Configurations and the Periodic Table Focus on Helium-Neon Lasers

9-1 Electromagnetic Radiation Electric and magnetic fields propagate as waves through empty space or through a medium. A wave transmits energy.

EM Radiation Low High

Frequency, Wavelength and Velocity Frequency ( ) in Hertz—Hz or s -1. Wavelength (λ) in meters—m. cm  m nm  pm (10 -2 m)(10 -6 m)(10 -9 m)( m)( m) Velocity (c)—  10 8 m s -1. c = λ λ = c/ = c/λ

Electromagnetic Spectrum

R ed O range Y ellow G reen B lue I ndigo V iolet ROYGBIV 700 nm450 nm

Constructive and Destructive Interference

Refraction of Light

9-2 Atomic Spectra

Atomic Spectra

9-3 Quantum Theory Blackbody Radiation: Max Planck, 1900: Energy, like matter, is discontinuous. є = h

The Photoelectric Effect Light striking the surface of certain metals causes ejection of electrons. > o threshold frequency e -  I e k 

The Photoelectric Effect

At the stopping voltage the kinetic energy of the ejected electron has been converted to potential. mu 2 = eV s 1 2 At frequencies greater than o : V s = k ( - o )

The Photoelectric Effect E o = h o E k = eV s o = eV o h eV o, and therefore o, are characteristic of the metal. Conservation of energy requires that: h = mu 2 + eV o 2 1 mu 2 = h - eV o eV s = 2 1 E photon = E k + E binding E k = E photon - E binding

9-4 The Bohr Atom E = -R H n2n2 R H =  J

Energy-Level Diagram ΔE = E f – E i = -R H nf2nf2 ni2ni2 – = R H ( ni2ni2 1 nf2nf2 – 1 ) = h = hc/λ

Ionization Energy of Hydrogen ΔE = R H ( ni2ni2 1 nf2nf2 – 1 ) = h As n f goes to infinity for hydrogen starting in the ground state: h = R H ( ni2ni2 1 ) = R H This also works for hydrogen-like species such as He + and Li 2+. h = -Z 2 R H

Emission and Absorption Spectroscopy

9-5 Two Ideas Leading to a New Quantum Mechanics Wave-Particle Duality. –Einstein suggested particle-like properties of light could explain the photoelectric effect. –But diffraction patterns suggest photons are wave-like. deBroglie, 1924 –Small particles of matter may at times display wavelike properties.

deBroglie and Matter Waves E = mc 2 h = mc 2 h /c = mc = p p = h/λ λ = h/p = h/mu

X-Ray Diffraction

The Uncertainty Principle Δx Δp ≥ h 4π4π Werner Heisenberg

9-6 Wave Mechanics 2L n Standing waves. –Nodes do not undergo displacement. λ =, n = 1, 2, 3…

Wave Functions ψ, psi, the wave function. –Should correspond to a standing wave within the boundary of the system being described. Particle in a box.

Probability of Finding an Electron

Wave Functions for Hydrogen Schrödinger, 1927 Eψ = H ψ –H (x,y,z) or H (r,θ,φ) ψ (r,θ,φ) = R(r) Y(θ,φ) R(r) is the radial wave function. Y(θ,φ) is the angular wave function.

Principle Shells and Subshells Principle electronic shell, n = 1, 2, 3… Angular momentum quantum number, l = 0, 1, 2…(n-1) l = 0, s l = 1, p l = 2, d l = 3, f Magnetic quantum number, m l = - l …-2, -1, 0, 1, 2…+ l

Orbital Energies

9-8 Interpreting and Representing the Orbitals of the Hydrogen Atom.

s orbitals

p Orbitals

d Orbitals

9-9 Electron Spin: A Fourth Quantum Number

9-10 Multi-electron Atoms Schrödinger equation was for only one e -. Electron-electron repulsion in multi- electron atoms. Hydrogen-like orbitals (by approximation).

Penetration and Shielding Z eff is the effective nuclear charge.

9-11 Electron Configurations Aufbau process. –Build up and minimize energy. Pauli exclusion principle. –No two electrons can have all four quantum numbers alike. Hund’s rule. –Degenerate orbitals are occupied singly first.

Orbital Energies

Orbital Filling

Aufbau Process and Hunds Rule

Filling p Orbitals

Filling the d Orbitals

Electon Configurations of Some Groups of Elements

9-12 Electron Configurations and the Periodic Table

Focus on He-Ne Lasers