Chapter 6Electronic Structure of AtomsCHEMISTRY

The Wave Nature of LightAll waves have a characteristic wavelength, l, and amplitude, A.The frequency, v, of a wave is the number of cycles which pass a point in one second.

The Wave Nature of LightThe speed of a wave, v, is given by its frequency multiplied by its wavelength: v = v l

For light, speed = c (3 x 108 m/s)

The Wave Nature of Light

The Wave Nature of Light

The Wave Nature of LightModern atomic theory arose out of studies of the interaction of radiation with matter.Electromagnetic radiation moves through a vacuum with a speed of 2.99792458 108 m/s.

The Wave Nature of LightElectromagnetic waves have characteristic wavelengths and frequencies.Example: visible radiation has wavelengths between 400 nm (violet) and 750 nm (red).

The Wave Nature of Light

The Wave Nature of Light

Quantized Energy and PhotonsPlanck: energy can only be absorbed or released from atoms in certain amounts called quanta.The relationship between energy and frequency is E = hv

Quantized Energy and Photonswhere h is Plancks constant (6.626 10-34 J.s).To understand quantization consider walking up a ramp versus walking up stairs:For the ramp, there is a continuous change in height whereas up stairs there is a quantized change in height.

Quantized Energy and PhotonsThe Photoelectric Effect and PhotonsThe photoelectric effect provides evidence for the particle nature of light -- quantization.If light shines on the surface of a metal, there is a point at which electrons are ejected from the metal.

Quantized Energy and PhotonsThe electrons will only be ejected once the threshold frequency is reached.Below the threshold frequency, no electrons are ejected.Above the threshold frequency, the number of electrons ejected depend on the intensity of the light.

Quantized Energy and Photons

The Photoelectric Effect and PhotonsEinstein assumed that light traveled in energy packets called photons.The energy of one photon: E = hv

Line Spectra and the Bohr Model

Line SpectraRadiation composed of only one wavelength is called monochromatic.Radiation that spans a whole array of different wavelengths is called continuous.

Line Spectra and the Bohr Model

Line SpectraWhite light can be separated into a continuous spectrum of colors.Note that there are no dark spots on the continuous spectrum that would correspond to different lines.

Line Spectra and the Bohr Model

Bohr ModelRutherford assumed the electrons orbited the nucleus analogous to planets around the sun.However, a charged particle moving in a circular path should lose energy.

Line Spectra and the Bohr Model

Bohr ModelThis means that the atom should be unstable according to Rutherfords theory.Bohr noted the line spectra of certain elements and assumed the electrons were confined to specific energy states. These were called orbits.

Bohr ModelColors from excited gases arise because electrons move between energy states in the atom.

Line Spectra and the Bohr Model

Line Spectra and the Bohr Model

Bohr ModelSince the energy states are quantized, the light emitted from excited atoms must be quantized and appear as line spectra.n is the principal quantum number (i.e., n = 1, 2, 3, and nothing else).

Line Spectra and the Bohr ModelBohr ModelThe first orbit in the Bohr model has n = 1, is closest to the nucleus, and has negative energy by convention.The furthest orbit in the Bohr model has n close to infinity and corresponds to zero energy.

Line Spectra and the Bohr ModelBohr ModelElectrons in the Bohr model can only move between orbits by absorbing and emitting energy in quanta (hn).The amount of energy absorbed or emitted on movement between states is given by

Line Spectra and the Bohr ModelLimitations of the Bohr ModelCan only explain the line spectrum of hydrogen adequately.Electrons are not completely described as small particles.

The Wave Behavior of Matter

Knowing that light has a particle nature, it seems reasonable to ask if matter has a wave nature.Using Einsteins and Plancks equations, de Broglie showed:

The Wave Behavior of Matter

The momentum, (mass x velocity)mv, is a particle property, whereas is a wave property.de Broglie summarized the concepts of waves and particles, with noticeable effects if the objects are small.

The Wave Behavior of Matter

The Uncertainty PrincipleHeisenbergs Uncertainty Principle: It is impossible to know exactly both the velocity and position of a particle at the same time.

The Wave Behavior of Matter

The Uncertainty PrincipleAs the measurement of the velocity is made more accurately, the measurement of the position must be less accurate.

Quantum Mechanics and Atomic OrbitalsSchrdinger proposed an equation that contains both wave and particle terms.Solving the equation leads to wave functions.

Quantum Mechanics and Atomic OrbitalsThe wave function gives the shape of the electronic orbital.The square of the wave function, gives the probability of finding the electron,that is, gives the electron density for the atom.

Quantum Mechanics and Atomic Orbitals

Quantum Mechanics and Atomic OrbitalsOrbitals and Quantum NumbersIf we solve the Schrdinger equation, we get wave functions and energies for the wave functions.We call wave functions orbitals.

Quantum Mechanics and Atomic OrbitalsOrbitals and Quantum NumbersSchrdingers equation requires 3 quantum numbers:Principal Quantum Number, n. This is the same as Bohrs n. As n becomes larger, the atom becomes larger and the electron is further from the nucleus.

Quantum Mechanics and Atomic Orbitals

Orbitals and Quantum NumbersAzimuthal Quantum Number, l. This quantum number depends on the value of n. The values of l begin at 0 and increase to (n - 1). We usually use letters for l (s, p, d and f for l = 0, 1, 2, and 3). Usually we refer to the s, p, d and f-orbitals.

Quantum Mechanics and Atomic Orbitals

Orbitals and Quantum NumbersMagnetic Quantum Number, ml. This quantum number depends on l. The magnetic quantum number has integral values between -l and +l. Magnetic quantum numbers give the 3D orientation of each orbital.

Orbitals and Quantum Numbers

Quantum Mechanics and Atomic Orbitals

Quantum Mechanics and Atomic Orbitals

Orbitals can be ranked in terms of energy to yield an Aufbau diagram.Note that the following Aufbau diagram is for a single electron system.As n increases, note that the spacing between energy levels becomes smaller.

Orbitals and Quantum NumbersQuantum Mechanics and Atomic Orbitals

Orbitals and Quantum Numbers

Quantum Mechanics and Atomic Orbitals

Representations of Orbitals

The s-OrbitalsAll s-orbitals are spherical.As n increases, the s-orbitals get larger.As n increases, the number of nodes increase.

Representations of Orbitals

A node is a region in space where the probability of finding an electron is zero.At a node, 2 = 0 For an s-orbital, the number of nodes is (n - 1).

Representations of Orbitals

The s-OrbitalsRepresentations of Orbitals

Representations of OrbitalsThe p-OrbitalsThere are three p-orbitals px, py, and pz. The three p-orbitals lie along the x-, y- and z- axes of a Cartesian system. The letters correspond to allowed values of ml of -1, 0, and +1.

Representations of OrbitalsThe p-OrbitalsThe orbitals are dumbbell shaped.As n increases, the p-orbitals get larger.All p-orbitals have a node at the nucleus.

The p-Orbitals

Representations of Orbitals

Representations of OrbitalsThe d and f-OrbitalsThere are five d and seven f-orbitals. Three of the d-orbitals lie in a plane bisecting the x-, y- and z-axes.Two of the d-orbitals lie in a plane aligned along the x-, y- and z-axes.

Many-Electron Atoms

Orbitals and Their EnergiesOrbitals of the same energy are said to be degenerate.For n 2, the s- and p-orbitals are no longer degenerate because the electrons interact with each other.Therefore, the Aufbau diagram looks slightly different for many-electron systems.

Many-Electron Atoms Orbitals and Their Energies

Many-Electron AtomsElectron Spin and the Pauli Exclusion PrincipleLine spectra of many electron atoms show each line as a closely spaced pair of lines.Stern and Gerlach designed an experiment to determine why.

Many-Electron AtomsA beam of atoms was passed through a slit and into a magnetic field and the atoms were then detected.Two spots were found: one with the electrons spinning in one direction and one with the electrons spinning in the opposite direction.

Electron Spin and the Pauli Exclusion PrincipleMany-Electron Atoms

Many-Electron AtomsElectron Spin and the Pauli Exclusion PrincipleSince electron spin is quantized, we define ms = spin quantum number = .Paulis Exclusions Principle: no two electrons can have the same set of 4 quantum numbers.Therefore, two electrons in the same orbital must have opposite spins.

Electron ConfigurationsHunds RuleElectron configurations tells us in which orbitals the electrons for an element are located.

Electron ConfigurationsThree rules:electrons fill orbitals starting with lowest n and moving upwards;no two electrons can fill one orbital with the same spin (Pauli);for degenerate orbitals, electrons fill each orbital singly before any orbital gets a second electron (Hunds rule).

Electron ConfigurationsCondensed Electron ConfigurationsNeon completes the 2p subshell.Sodium marks the beginning of a new row.So, we write the condensed electron configuration for sodium asNa: [Ne] 3s1

Electron ConfigurationsCondensed Electron Configurations[Ne] represents the electron configuration of neon.Core electrons: electrons in [Noble Gas].Valence electrons: electrons outside of [Noble Gas].

Electron Configurations Transition MetalsAfter Ar the d orbitals begin to fill.After the 3d orbitals are full, the 4p orbitals being to fill.Transition metals: elements in which the d electrons are the valence electrons.

Electron Configurations

Lanthanides and ActinidesFrom Ce onwards the 4f orbitals begin to fill.Note: La: [Xe]6s25d14f0Elements Ce - Lu have the 4f orbitals filled and are called lanthanides or rare earth elements.

Electron Configurations

Lanthanides and ActinidesElements Th - Lr have the 5f orbitals filled and are called actinides.Most actinides are not found in nature.

Electron Configurations and the Periodic TableThe periodic table can be used as a guide for electron configurations.The period number is the value of n.Groups 1A and 2A have the s-orbital filled.

Electron Configurations and the Periodic TableGroups 3A - 8A have the p-orbital filled.Groups 3B - 2B have the d-orbital filled.The lanthanides and actinides have the f-orbital filled.

End of Chapter 6:Electronic Structure of Atoms

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