Chapter 6 Electronic Structure of Atoms

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Chapter 6Electronic Structureof Atoms
Chemistry, The Central Science, 10th
edition Theodore L. Brown H. Eugene LeMay, Jr.
and Bruce E. Bursten
John D. Bookstaver St. Charles Community
College St. Peters, MO ? 2006, Prentice Hall, Inc.
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Next test unit 6 and 7 together

• The nature of waves
• 6.9 to and 6.17 ODD 6.12
• Photoelectric Effect
• Line Spectra
• Bohr Model
• Quantum Model
• Hw for the whole chapter 6
• 21to 37 odd only and 43
• 47 to 53 odd only
• 63,66,67,68,71,72,73,75

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Waves

• To understand the electronic structure of atoms,
  one must understand the nature of electromagnetic
  radiation.
• The distance between corresponding points on
  adjacent waves is the wavelength (?).

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Waves

• The number of waves passing a given point per
  unit of time is the frequency (?).
• For waves traveling at the same velocity, the
  longer the wavelength, the smaller the frequency.

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Waves

• Long Wavelength
• Low Frequency
• Low energy

• Short Wavelength
• High Frequency
• High energy

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• Light and Waves
• All waves have a characteristic wavelength, l
  (lambda) and amplitude, A.
• The frequency, n (nu) 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.

ms-1 Hz (s-1) m
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Electromagnetic Radiation

• All electromagnetic radiation travels at the same
  velocity the speed of light (c)
• 3.00 ? 108 m/s.
• Therefore,
• c ??

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• Modern atomic theory arose out of studies of the
  interaction of radiation (light) with matter.
• Electromagnetic radiation moves through a vacuum
  with a speed of 2.99792458 ? 108 m/s.
• Electromagnetic waves have characteristic
  wavelengths and frequencies.
• Example visible radiation has wavelengths
  between 400 nm (violet) and 750 nm (red).

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The Wave Nature of Light
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• Examples
• Calculate the frequency of light with a
  wavelength of 585 nm.
• Calculate the wavelength of light with a
  frequency of 1.89 x 1018 Hz.

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The Nature of Energy

• The wave nature of light does not explain how an
  object can glow when its temperature increases.
• Max Planck explained it by assuming that energy
  comes in packets called quanta.

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• Plank proposed quantization of energy
• Einstein proposed and explanation for the
  photoelectric effect. Light behave like a
  particle- Photon-
• BOHR THEORY AND THE SPECTRA OF EXCITED ATOMS
• BALMER SERIES AND LYMAN SERIES

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Quantized Energy and Photons

• 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 Plancks constant (6.626 ? 10-34 Js).
• 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.

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The Nature of Energy

• If one knows the wavelength of light, one can
  calculate the energy in one photon, or packet, of
  that light
• c ??
• E h?

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• 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 (work function-
  energy needed for an electron to overcame the
  attractive forces that hold it in a metal.
• Below the threshold frequency, no electrons are
  ejected.
• Above the threshold frequency, the number of
  electrons ejected depend on the intensity of the
  light.

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The Nature of Energy

• Einstein used this assumption to explain the
  photoelectric effect.
• He concluded that energy is proportional to
  frequency
• E h?
• where h is Plancks constant, 6.63 ? 10-34 J-s.

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• Einstein assumed that light traveled in energy
  packets called photons.
• The energy of one photon

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Einstein

• Said electromagnetic radiation is quantized in
  particles called photons.
• Each photon has energy hn hc/l
• Combine this with E mc2
• You get the apparent mass of a photon.

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• Examples
• Calculate the energy of a photon of light with a
  frequency of 7.30 x 1015 Hz.
• Calculate the energy of red light with a
  wavelength of 720 nm.
• Calculate the energy of a mole of photons of
  that red light.
• Calculate the wavelength of a photon with an
  energy value of 4.93 x 10-19 J.

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• Examples
• Calculate the energy of a photon of light with a
  frequency of 7.30 x 1015 Hz.
• 4.84 x 10-18 J
• Calculate the energy of red light with a
  wavelength of 720 nm.
• 2.76 x 10-19 J
• Calculate the wavelength of a photon with an
  energy value of 4.93 x 10-19 J.
• 403 nm (4.03 x 10-7 m)

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NOVEMBER

• 6.3 Line Spectra and Bohr Model
• Hydrogen Spectra
• Balmer series
• Lyman Series
• Paschem Series
• 6.4 The wave behavior of matter

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The Nature of Energy

• Another mystery involved the emission spectra
  observed from energy emitted by atoms and
  molecules.
• When gases at low pressure were placed in a tube
  and were subjected to high voltage, light of
  different colors appeared

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Line Spectra and the Bohr Model

• Continuous 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 Spectra

• If high voltage is applied to atoms in gas phase
  at low pressure light is emitted from the gas.
• If the light is analyzed the spectrum obtained is
  not continuous.
• SPECTROSCOPE

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Line Spectra. When the light from a discharge
tube is analyzed only some bright lines appeared.
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Bohrs Model

• Niels Bohr adopted Plancks assumption about
  energy and explained the hydrogen spectrum this
  way
• 1. Only orbits of certain radii corresponding to
  certain definite energies are permitted for the
  electron in the hydrogen atom.

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Bohr Model

• 2 An electron in a permitted orbit has a
  specific energy an is in an allowed energy
  state. It will not spiral into the nucleus
• 3 Energy is emitted or absorbed by the electron
  only as the electron changes from one allowed
  state to other

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To calculate the energy of an electron in a given
energy level use this formula

• En - 2.18 ? 10-18 J/ n2
• The higher the energy level the lowest the value
  needed to remove the electron.

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Hydrogen Line Spectrum

• The line spectrum for H has 4 lines in the
  visible region.
• Johan Balmer in 1885 showed that the wavelengths
  of these lines fit a simple formula. Later on
  additional lines were
• found in the ultraviolet (Lyman series) and
  infrared (Pashem series)region. The equation was
  extended to a more general one that allowed the
  calculation of the wavelength for all lines of
  Hydrogen

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Energy states of the Hydrogen Atom

• The energy absorbed or emitted from the process
  of electron promotion or demotion can be
  calculated by the equation

where RH is the Rydberg constant, 2.18 ? 10-18 J,
and ni and nf are the initial and final energy
levels of the electron.
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Balmer series

• If n3 the wavelength of the red light in the
  Hydrogen Spectrum is obtained (656 nm)
• If n4 the wavelength of the green line is
  calculated
• If n5 and n6 the equation give the wavelength
  for the blue lines

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Balmer series. Visible range

• Electrons moving from states with ngt2 to the n2
  state

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Lyman Series

• Emission lines in the ultraviolet region.
• Electrons moving from states with ngt1 to state1

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Paschem Series

• In the infrared area of the spectrum.
• From other energy levels to n 1
• The largest jump, high energy, ultraviolet
  region.

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Limitations of Bohrs Model

• It does offer an explanation for the line
  spectrum of hydrogen, but it cannot explain other
  atoms.
• The two main contributions are that
• a) Electrons exist only in certain energy levels.
• b) If electrons move to another permitted energy
  level it must absorbed or emit energy as light.

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• OBJECTIVE QUANTUM THEORY
• THE MODERN ATOMIC MODEL

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Which is it?

• Is energy a wave like light, or a particle?
• Both! Concept is called the Wave -Particle
  duality.
• What about the other way, is matter a wave?
• Yes

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The Wave Nature of Matter

• Louis de Broglie suggested that if light can have
  material properties, matter should exhibit wave
  properties.
• He demonstrated that the relationship between
  mass and wavelength was

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Flame Test

• The flame test is used to visually determine the
  identity of an unknown metal or metalloid ion
  based on the characteristic color the salt turns
  the flame of a bunsen burner. The heat of the
  flame converts the metal ions into atoms which
  become excited and emit visible light. The
  characteristic emission spectra can be used to
  differentiate between some elements.

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Flame Test Colors

• Li                                       Deep
  red (crimson)
• Na                                      
  Yellow-orange
• K                                       Violet -
  lilac
• Ca2                                    Orange-red
  
• Sr2                                     Red
• Ba2                                    Pale
  Green
• Cu2                                    Green

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Matter waves

• De Broglie described the wave characteristics of
  material particles.
• mv is the momentum
• His equation is applicable to all matter, however
  the wavelength associated with objects of
  ordinary size would be so tiny that could not be
  observed.
• Only for objects of the size of the electrons
  could be detected

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The Uncertainty Principle

• Heisenberg showed that the more precisely the
  momentum of a particle is known, the less
  precisely is its position known
• In many cases, our uncertainty of the whereabouts
  of an electron is greater than the size of the
  atom itself!

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• The Uncertainty Principle
• Heisenbergs 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 Dx is the uncertainty in position and Dmv is
  the uncertainty in momentum, then

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5th Solvay Conference of Electrons and Photons -
1927
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Quantum Mechanics

• Erwin Schrödinger developed a mathematical
  treatment into which both the wave and particle
  nature of matter could be incorporated.
• It is known as quantum mechanics.

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Quantum Mechanics

• The wave equation is designated with a lower case
  Greek psi (?).
• The square of the wave equation, ?2, gives a
  probability density map of where an electron has
  a certain statistical likelihood of being at any
  given instant in time.

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• QUANTUM MECHANICS AND ATOMIC ORBITALS
• ELECTRON CONFIGURATION.

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Quantum Numbers

• Solving the wave equation gives a set of wave
  functions, or orbitals, and their corresponding
  energies.
• Each orbital describes a spatial distribution of
  electron density.
• An orbital is described by a set of three quantum
  numbers.

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Principal Quantum Number, n

• The principal quantum number, n, describes the
  energy level on which the orbital resides.
• The values of n are integers 0.
• As n becomes larger, the electron is further from
  the nucleus.

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Azimuthal Quantum Number, l(Angular momentum
quantum )SUBSHELLS

• This quantum number defines the shape of the
  orbital.
• Allowed values of l are integers ranging from 0
  to n - 1.
• We use letter designations to communicate the
  different values of l and, therefore, the shapes
  and types of orbitals.

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Azimuthal or angular momentum Quantum Number,
lrelated to the type of orbitals
Value of l 0 1 2 3
Type of orbital s p d f
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Magnetic Quantum Number, ml

• Describes the three-dimensional orientation of
  the orbital.
• Values are integers ranging from -l to l
• -l ml l.
• Therefore, on any given energy level, there can
  be up to 1 s orbital, 3 p orbitals, 5 d orbitals,
  7 f orbitals, etc.

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Magnetic Quantum Number, ml

• Orbitals with the same value of n form a shell.
• Different orbital types within a shell are
  subshells.

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s Orbitals

• Value of l 0.
• Spherical in shape.
• Radius of sphere increases with increasing value
  of n.

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• 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).

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s Orbitals

• Observing a graph of probabilities of finding an
  electron versus distance from the nucleus, we see
  that s orbitals possess n-1 nodes, or regions
  where there is 0 probability of finding an
  electron.

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p Orbitals

• Value of l 1.
• Have two lobes with a node between them.

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• 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.

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d Orbitals

• Value of l is 2.
• Four of the five orbitals have 4 lobes the other
  resembles a p orbital with a doughnut around the
  center.

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• Objective Electron configuration and the
  periodic table
• Review of building up principle.
• Pauli exclusion principle, Hunds rule.
• Exceptions to the Building up principle.
• Paramagnetism vs diagmanetism.

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Quantum numbers (4 numbers that determine the
energy of an electron)

• Principal quantum number (n) positive whole
  number
• Azimuthal or angular momentum quantum number (l)
  cannot be greater than n integer from 0 to n-1
• Magnetic quantum number (ml) integer from l to
  l
• Spin quantum number (ms) 1/2 or 1/2

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Building up principle (Aufbau Principle)

• Electrons will fill the lowest available energy
  levels first.
• Same energy is said to be degenerate so sublevel
  p has 3 degenerate orbitals (same energy)

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Electron Configuration of Excited Atoms

• They do not follow the proper fill out order. One
  or more electrons are at a higher energy level
  that what they are supposed to be.
• You need to spot the electron out of sequence to
  realize that the atom is in an excited state.

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Energies of OrbitalsAUFBAU diagram

• As the number of electrons increases, though, so
  does the repulsion between them.
• Therefore, in many-electron atoms, orbitals on
  the same energy level are no longer degenerate.

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• http//intro.chem.okstate.edu/WorkshopFolder/Elect
  ronconfnew.html

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Spin Quantum Number, ms

• In the 1920s, it was discovered that two
  electrons in the same orbital do not have exactly
  the same energy.
• The spin of an electron describes its magnetic
  field, which affects its energy.

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Spin Quantum Number, ms

• This led to a fourth quantum number, the spin
  quantum number, ms.
• The spin quantum number has only 2 allowed
  values 1/2 and -1/2.

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Pauli Exclusion Principle

• No two electrons in the same atom can have
  exactly the same energy.
• For example, no two electrons in the same atom
  can have identical sets of quantum numbers.

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Electron Configurations

• Distribution of all electrons in an atom
• Consist of
• Number denoting the energy level

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Electron Configurations

• Distribution of all electrons in an atom
• Consist of
• Number denoting the energy level
• Letter denoting the type of orbital

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Electron Configurations

• Distribution of all electrons in an atom.
• Consist of
• Number denoting the energy level.
• Letter denoting the type of orbital.
• Superscript denoting the number of electrons in
  those orbitals.

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Orbital Diagrams

• Each box represents one orbital.
• Half-arrows represent the electrons.
• The direction of the arrow represents the spin of
  the electron.

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Hunds Rule

• For degenerate orbitals, the lowest energy is
  attained when the number of electrons with the
  same spin is maximized.

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HUNDS RULE

• Lowest energy arrangement of electrons in a
  subshell is obtained by putting electrons into
  separate orbitals of the subshell with the same
  spin before pairing electrons.

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Electron configuration vs orbital diagrams

• Electron configurations give the distribution of
  electrons in the available subshells

• Show how the orbitals of a subshell are occupied
  by electrons.

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• Building up principle
• 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 (Hunds rule).

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• 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.

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Periodic Table

• We fill orbitals in increasing order of energy.
• Different blocks on the periodic table, then
  correspond to different types of orbitals.

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Some Anomalies

• Some irregularities occur when there are enough
  electrons to half-fill s and d orbitals on a
  given row.

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Some Anomalies

• For instance, the electron configuration for
  chromium is
• Ar 4s1 3d5
• rather than the expected
• Ar 4s2 3d4.

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Some Anomalies

• This occurs because the 4s and 3d orbitals are
  very close in energy.
• These anomalies occur in f-block atoms, as well.

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Anomalies

• Cr 3d5 4s1
• Mo
• Cu
• Ag
• Au
• The energies between 3d and 4s are close, and to
  have a sublevel half filled or completely filled
  gives stability to the atom.

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Electron Configurations

• 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 last electrons to fill.

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• Examples Write electron configurations for the
  following
• Mg
• N
• Br
• Cu
• O

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• Lanthanides and Actinides
• From Ce onwards the 4f orbitals begin to fill.
• Note La Xe6s25d14f0
• 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.

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Electron Configurations and the Periodic Table

• The periodic table can be used as a guide for
  electron configurations.
• The period number is the value of n.
• Groups 1 and 2 have the s-orbital filled.
• Groups 13 - 18 have the p-orbitals filled.
• Groups 3 - 12 have the d-orbitals filled.
• The lanthanides and actinides have the f-orbital
  filled.

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Electron Configurations

• 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 last electrons to fill.

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• Lanthanides and Actinides
• From Ce onwards the 4f orbitals begin to fill.
• Note La Xe6s25d14f0
• 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.

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Magnetic properties of atoms

• An electron in an atom behaves like a small
  magnet, the magnetic attraction from two
  electrons that are opposite in spin cancel each
  other.
• PARAMAGNETIC SUBSTANCES
• Atoms with unpaired electrons exhibit a net
  magnetism and is weakly attracted by a magnetic
  field.

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Paramagnetism

• Elements and compounds that have unpaired
  electrons are attracted to a magnet. The effect
  is weak but it can be observed.
• Liquid O2 attracted to a magnet.

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Diagmagnetism

• Substances with no unpaired electrons experiment
  a slight repulsion when subjected to a magnetic
  field.

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