prentice hall © 2003chapter 6 chapter 6 electronic structure of atoms david p. white

Prentice Hall © 2003 Chapter 6

Chapter 6Chapter 6Electronic Structure of AtomsElectronic Structure of Atoms

David P. White


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

• The frequency, f, 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:

c = fλ

c is the speed of light

The Wave Nature of LightThe Wave Nature of Light


• Modern atomic theory involves interaction of radiation with matter.

• Electromagnetic radiation moves through a vacuum with a speed of 3.00 108 m/s.

Electromagnetic spectrumElectromagnetic spectrum


Example 1: A laser produces radiation with a Example 1: A laser produces radiation with a wavelength of 640.0 nm. Calculate the wavelength of 640.0 nm. Calculate the frequency of this radiation.frequency of this radiation.

Example 2: The YFM radio station broadcasts Example 2: The YFM radio station broadcasts EM radiation at 99.2 MHz. Calculate the EM radiation at 99.2 MHz. Calculate the wavelength of this radiation (1 MHz = 10wavelength of this radiation (1 MHz = 1066 s s-1-1).).


• Planck: energy can only be absorbed or released from atoms in fixed amounts called quanta.

• For 1 photon (energy packet):

E = hf = hc/λ

where h is Planck’s constant (6.63 10-34 J.s).

Quantized Energy and Quantized Energy and PhotonsPhotons


• If light shines on the surface of a metal, there is a point (threshold frequency) at which electrons are ejected from the metal.

The Photoelectric Effect and Photons


Example 3: (a) A laser emits light with a frequency of Example 3: (a) A laser emits light with a frequency of 4.69 x 104.69 x 101414ss-1-1. What is the energy of one photon of the . What is the energy of one photon of the radiation from this laser? If the laser emits a pulse of radiation from this laser? If the laser emits a pulse of energy containing 5.0 x 10energy containing 5.0 x 101717 photons of this radiation, photons of this radiation, what is the total energy of that pulse?what is the total energy of that pulse?


Line Spectra• Monochromatic light – one λ.• Continuous light – different λs.• White light can be separated into a continuous spectrum

of colors.

Line Spectra and the Bohr Line Spectra and the Bohr ModelModel

A prism disperses light from a light bulb


• Balmer: discovered that the lines in the visible line spectrum of hydrogen fit a simple equation.

• Later Rydberg generalized Balmer’s equation to:

where RH is the Rydberg constant (1.096776 107 m-1), h is Planck’s constant, n1 and n2 are integers (n2 > n1).

22

21

111

nnhRH


• Rutherford assumed the electrons orbited the nucleus analogous to planets around the sun.

• However, a charged particle moving in a circular path should lose energy, ie, the atom is unstable

• Bohr noted the line spectra of certain elements and assumed the electrons were confined to specific energy states called orbits.

Bohr Model explains this equationBohr Model explains this equation


Colors from excited gases arise because

electrons move between energy states in the

atom.

Black regions show λs absent in the light


Bohr Model• Energy states are quantized, light emitted from excited

atoms is quantized and appear as line spectra.• Bohr showed that

where n is the principal quantum number (i.e., n = 1, 2, 3).

218 1

J 1018.2n

E


• The first orbit has n = 1, is closest to the nucleus, and has negative energy by convention.

• The furthest orbit 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

∆E = Efinal – Einitial = hf


• We can show that

• When ni > nf, energy is emitted.

• When nf > ni, energy is absorbed

2218 11

J 1018.2if nn

hchE f


Limitations of the Bohr Model• Can only explain the line spectrum of hydrogen

adequately.• Electrons are not completely described as small particles.


• Explores the wave-like and particle-like nature of matter.• Using Einstein’s and Planck’s equations, de Broglie

showed:

• The momentum, mv, is a particle property, whereas is a wave property.

The Wave Behavior of The Wave Behavior of MatterMatter

mvh


• Heisenberg’s Uncertainty Principle: on the mass scale of atomic particles, we cannot determine exactly the position, direction of motion, and speed simultaneously.

• For electrons: we cannot determine their momentum and position simultaneously.

• If x is the uncertainty in position and mv is the uncertainty in momentum, then

4·

hmvx

The Uncertainty Principle


• Schrödinger proposed an equation that contains both wave and particle terms.

• Solving the equation leads to wave functions, ψ (orbitals).

• ψ2 gives the probability of finding the electron• Orbital in the quantum model is different from Bohr’s

orbit

Quantum Mechanics and Quantum Mechanics and Atomic OrbitalsAtomic Orbitals


• Schrödinger’s 3 QNs:1. Principal Quantum Number, n. - same as Bohr’s n. As n

becomes larger, the atom becomes larger and the electron is further from the nucleus.


2. Azimuthal Quantum Number, l. - depends on the value of n. The values of l begin at 0 and increase to (n - 1). The 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.

3. Magnetic Quantum Number, ml. - depends on l. Has integral values between -l and +l. Gives the 3D orientation of each orbital. There are (2l +1) allowed values of ml and this gives the no. of orbitals.

Total no. of orbitals in a shell = n2


• Orbitals can be ranked in terms of energy to yield an Aufbau diagram.


Single electron atom – orbitals with Single electron atom – orbitals with the same value of n have the same the same value of n have the same energyenergy


The s-Orbitals• All s-orbitals are spherical.

• As n increases, the s-orbitals get larger & no. of nodes increase.

• A node is a region in space where the probability of finding an electron is zero, 2 = 0 .

• For an s-orbital, the number of nodes is (n - 1).

Representations of Representations of OrbitalsOrbitals


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

• The letters correspond to allowed values of ml of -1, 0, and +1.

• The orbitals are dumbbell shaped and have a node at the nucleus.

• As n increases, the p-orbitals get larger.


The d and f-Orbitals• There are five d and seven f-orbitals. • They differ in their orientation in the x, y,z plane


Orbitals and Their Energies• Orbitals 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 different for many-

electron systems.

Many-Electron Atoms Many-Electron Atoms

Many electron atoms – electrons Many electron atoms – electrons repel and thus orbitals are at repel and thus orbitals are at different energiesdifferent energies


Electron 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.

2 opposite directions of spin 2 opposite directions of spin produce oppositely directed produce oppositely directed magnetic fields leading to the magnetic fields leading to the splitting of spectral lines into splitting of spectral lines into closely spaced spectraclosely spaced spectra


• Since electron spin is quantized, we define ms = spin quantum number = + ½ and - ½ .

• Pauli’s Exclusion Principle:: no two electrons can have the same set of 4 quantum numbers.• Therefore, two electrons in the same orbital must have

opposite spins.


• In the presence of a magnetic field, we can lift the degeneracy of the electrons.


Hund’s Rule• Electron configurations - in which orbitals the electrons for an

element are located.

• For degenerate orbitals, electrons fill each orbital singly before any orbital gets a second electron.

Electron ConfigurationsElectron Configurations


Condensed Electron Configurations• Neon completes the 2p subshell.• Sodium marks the beginning of a new row.

Na: [Ne] 3s1

• Core electrons: electrons in [Noble Gas].• Valence electrons: electrons outside of [Noble Gas].


Transition Metals• After Ar the d orbitals begin to fill.• After the 3d orbitals are full, the 4p orbitals begin to fill.• Transition metals: elements in which the d electrons

are the valence electrons.


Lanthanides and Actinides• From Ce onwards the 4f orbitals begin to fill.• Note: La: [Xe]6s25d14f0

• Elements Ce - Lu have the 4f orbitals filled and are called lanthanides or rare earth elements.

• Elements Th - Lr have the 5f orbitals filled and are called actinides.

• Most actinides are not found in nature.


• The 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.• Groups 3A - 8A have the p-orbital filled.• Groups 3B - 2B have the d-orbital filled.• The lanthanides and actinides have the f-orbital filled.

Electron Configurations Electron Configurations and the Periodic Tableand the Periodic Table

prentice hall © 2003chapter 6 chapter 6 electronic structure of atoms david p. white

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