1 electronic structure of atoms chapter 6 2 the wave nature of light all waves have a characteristic...

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Electronic Structure of Electronic Structure of AtomsAtoms

Chapter 6Chapter 6

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The Wave Nature of LightThe Wave Nature of Light

• All waves have a characteristic wavelength, , and amplitude, A.

• The frequency, , of a wave is the number of cycles which pass a point in one second.

• The speed of a wave, v, is given by its frequency multiplied by its wavelength: For light, speed = c.

c =

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The Wave Nature of LightThe Wave Nature of Light

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Quantized Energy and PhotonsQuantized Energy and PhotonsPlanckPlanck: energy can only be absorbed or released from atoms in certain amounts called quantaquanta.The relationship between energy and frequency is

E = hwhere h is Planck’s constant (6.626 10-34 J.s).

To understand quantization consider the notes produced by a violin (continuous) and a piano (quantized):

a violin can produce any note by placing the fingers at an appropriate spot on the bridge. A piano can only produce notes corresponding to the keys on the keyboard.

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Quantized Energy and PhotonsQuantized Energy and Photons

The Photoelectric EffectThe Photoelectric Effect•The 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.•The electrons will only be ejected once the threshold frequency is reached.•Below the threshold frequency, no electrons are ejected.

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The Photoelectric EffectThe Photoelectric Effect•Above the threshold frequency, the number of electrons ejected depend on the intensity of the light.•Einstein assumed that light traveled in energy packets called photons.•The energy of one photon, E = h.

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The Photoelectric EffectThe Photoelectric Effect

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Bohr’s Model of the Hydrogen Atom Bohr’s Model of the Hydrogen Atom

Line SpectraLine Spectra•Radiation composed of only one wavelength is called monochromatic.•Radiation that spans a whole array of different wavelengths is called continuous.•White 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.

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Line SpectraLine Spectra

Shows that visible light contains many wavelengths

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

Only a few wavelengths emitted from elements

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Bohr’s ModelBohr’s ModelSince the energy states are quantized, the light emitted from excited atoms must be quantized and appear as line spectra.After lots of math, Bohr showed that

E = (-2.18 x 10-18 J)(1/n2)

where n is the principal quantum number (i.e., n = 1, 2, 3, …. and nothing else)

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Bohr’s Model of the Hydrogen Atom Bohr’s Model of the Hydrogen Atom Bohr’s ModelBohr’s 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.Electrons in the Bohr model can only move between orbits by absorbing and emitting energy in quanta (h).The amount of energy absorbed or emitted on movement between states is given by

hEEE if

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Bohr’s ModelBohr’s ModelWe can show that

E = (-2.18 x 10-18 J)(1/nf2 - 1/ni

2 )

When ni > nf, energy is emitted.When nf > ni, energy is absorbed.

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The Wave Behavior of MatterThe Wave Behavior of MatterUsing Einstein’s and Planck’s equations, de Broglie supposed:

mv = momentum

vm

h

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The Uncertainty PrincipleThe Uncertainty PrincipleHeisenberg’s Uncertainty PrincipleHeisenberg’s Uncertainty Principle: on the mass scale of atomic particles, we cannot determine the exactly the position, direction of motion, and speed simultaneously.For electrons: we cannot determine their momentum and position simultaneously.

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Quantum Mechanics and Atomic Quantum Mechanics and Atomic OrbitalsOrbitals

•Schrödinger proposed an equation that contains both wave and particle terms.•Solving the equation leads to wave functions. •The 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.

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Orbitals and Quantum NumbersOrbitals and Quantum NumbersIf we solve the Schrödinger equation, we get wave

functions and energies for the wave functions.We call wave functions orbitalsorbitals.Schrödinger’s equation requires 3 quantum numbers:

Principal Quantum Number, n. This is the same as Bohr’s n.

As n becomes larger, the atom becomes larger and the

electron is further from the nucleus.

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Orbitals and Quantum NumbersOrbitals and Quantum NumbersAzimuthal Quantum Number, l. Shape 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.

Magnetic Quantum Number, ml direction 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.

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Orbitals and Quantum NumbersOrbitals and Quantum Numbers

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Orbitals and Quantum NumbersOrbitals and Quantum NumbersOrbitals 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.

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Representation of OrbitalsRepresentation of Orbitals

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

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The The ss Orbitals Orbitals

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The The pp Orbitals Orbitals

There are three p-orbitals px, py, and pz. (The three p-

orbitals lie along the x-, y- and z- axes. The letters

correspond to allowed values of ml of -1, 0, and +1.)

The orbitals are dumbbell shaped.

As n increases, the p-orbitals get larger.

All p-orbitals have a node at the nucleus.

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The The pp Orbitals Orbitals

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The The dd and and ff Orbitals OrbitalsThere are 5 d- and 7 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.Four of the d-orbitals have four lobes each.One d-orbital has two lobes and a collar.

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Representation of OrbitalsRepresentation of OrbitalsThe The dd Orbitals Orbitals

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Orbitals in Many Electron AtomsOrbitals in Many Electron Atoms

Orbitals of the same energy are said to be degenerate.

All orbitals of a given subshell have the same energy (are degenerate)

For example the three 4p orbitals are degenerate

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Energies of OrbitalsEnergies of Orbitals

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Electron Spin and the Pauli Exclusion PrincipleElectron Spin and the Pauli Exclusion Principle •Line spectra of many electron atoms show each line as a closely spaced pair of lines.•Stern and Gerlach designed an experiment to determine why.•A 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.

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Electron Spin and the Pauli Exclusion PrincipleElectron Spin and the Pauli Exclusion Principle

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Orbitals in Many Electron AtomsOrbitals in Many Electron AtomsElectron Spin and the Pauli Exclusion PrincipleElectron Spin and the Pauli Exclusion Principle

Since electron spin is quantized, we define ms = spin

quantum number = ½.

Pauli’s Exclusions Principle:Pauli’s 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.

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

Three 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 (Hund’s rule).

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Electron Configurations and the Periodic Electron Configurations and the Periodic TableTable

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Electron Configurations and the Periodic Electron Configurations and the Periodic TableTable

There is a shorthand way of writing electron configurationsWrite the core electrons corresponding to the filled Noble gas in square brackets.Write the valence electrons explicitly.Example, P: 1s22s22p63s23p3

but Ne is 1s22s22p6

Therefore, P: [Ne]3s23p3.

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End of Chapter 6End of Chapter 6

Electronic Structure of Electronic Structure of AtomsAtoms

1 electronic structure of atoms chapter 6 2 the wave nature of light all waves have a characteristic...

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