Estructura electronica atomica

Prentice Hall © 2003 Chapter 6

Chapter 6Chapter 6Electronic Structure of AtomsElectronic Structure of Atoms

CHEMISTRY The Central Science

9th Edition

David P. White


• 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.

The Wave Nature of LightThe Wave Nature of Light

v


The Wave The Wave Nature of Nature of

LightLight



• Modern 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 10-8 m/s.

• Electromagnetic waves have characteristic wavelengths and frequencies.

• Example: visible radiation has wavelengths between 400 nm (violet) and 750 nm (red).








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

• The relationship between energy and frequency is

where h is Planck’s 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 Quantized Energy and PhotonsPhotons

hE


The Photoelectric Effect and Photons• 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.• Above the threshold frequency, the number of electrons

ejected depend on the intensity of the light.



The Photoelectric Effect and Photons• Einstein assumed that light traveled in energy packets

called photons.• The energy of one photon:


hE





• 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.

Line Spectra and the Bohr Line Spectra and the Bohr ModelModel




Line Spectra• 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 (6.626 10-34 J·s), n1 and n2 are integers (n2 > n1).


22

21

111

nnhRH


Bohr Model• 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.• This means that the atom should be unstable according to

Rutherford’s theory.• Bohr noted the line spectra of certain elements and

assumed the electrons were confined to specific energy states. These were called orbits.



Bohr Model• Colors from excited gases arise because electrons move

between energy states in the atom.



Bohr Model• Since 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

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


218 1

J 1018.2n

E


Bohr Model• The 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




Bohr Model• We can show that

• When ni > nf, energy is emitted.

• When nf > ni, energy is absorbed


2218 11

J 1018.2if nn

hchE

Bohr Model

Line Spectra and Line Spectra and the Bohr Modelthe Bohr Model




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

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



• Knowing that light has a particle nature, it seems reasonable to ask if matter has a wave nature.

• Using Einstein’s and Planck’s equations, de Broglie showed:

• The momentum, 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 The Wave Behavior of MatterMatter

mvh





The Uncertainty Principle• 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

The Wave Behavior of The Wave Behavior of MatterMatter

4·

hmvx


H= x


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

• 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.

Quantum Mechanics and Quantum Mechanics and Atomic OrbitalsAtomic Orbitals




Orbitals and Quantum Numbers• If we solve the Schrödinger equation, we get wave

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

1. 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.



Orbitals and Quantum Numbers2. Azimuthal 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.

3. Magnetic 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



Orbitals and Quantum Numbers• 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 Numbers

Quantum Quantum Mechanics and Mechanics and

Atomic Atomic OrbitalsOrbitals


The s-Orbitals• All 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).

Representations of Representations of OrbitalsOrbitals



The s-Orbitals



The p-Orbitals

• There 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.

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



The p-Orbitals



The d and f-Orbitals• There 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.• Four of the d-orbitals have four lobes each.• One d-orbital has two lobes and a collar.



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.

• 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.




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

• 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.



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


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 slightly different

for many-electron systems.




Many-Electron Atoms Many-Electron Atoms

Orbitals and Their Energies




Hund’s Rule• 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).

Electron ConfigurationsElectron Configurations


Condensed Electron Configurations• Neon completes the 2p subshell.• Sodium marks the beginning of a new row.• So, we write the condensed electron configuration for

sodium as

Na: [Ne] 3s1

• [Ne] represents the electron configuration of neon.• 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 being 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


End of Chapter 6:End of Chapter 6:Electronic Structure of AtomsElectronic Structure of Atoms

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Estructura electronica atomica