Atomic Structure , Electron Configuration

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Atomic Structure , Electron Configuration
Periodicity

• Traveling Waves
• Electromagnetic Radiation
• The Photoelectric Effect
• Bohr Model of the Hydrogen Atom
• Wave Theory of the Electron
• Heisenberg Uncertainty Principle
• Quantum Model of the Atom
• Electron Configurations
• Atomic and Ionic Radii
• Ionization Energy
• Electron Affinity
• Chemical Properties and the Periodic Table
• Ways of Numbering Groups

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Traveling waves

• Much of what has been learned about atomic
  structure has come from observing the interaction
  of visible light and matter.
• An understanding of waves and electromagnetic
  radiation would be helpful at this point.
• Lets start with some basic definitions.

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Waves

• Some definitions
• Wavelength, l
• The distance for a wave to go through a complete
  cycle.
• Amplitude
• Half of the vertical distance from the top to
  the bottom of a wave.
• Frequency, n
• The number of cycles that pass a point each
  second.

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Travelling Waves
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Standing Waves

• Length of string ?/2
• ? 2 L
• Length of string ?
• Length of string 3/2 ?
• ? 2/3 L

Notes Nodes always occur at each end of the
string. The distance between nodes is always ½
?. Only certain wavelengths are allowed the
wavelengths of standing waves are quantized
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Electromagnetic radiation

• A form of energy that consists of perpendicular
  electrical and magnetic fields that change, at
  the same time and in phase, with time, and at
  right angles to each other
• The SI unit of frequency (n) is the hertz, Hz
• 1 Hz 1 s-1
• Wavelength and frequency are related
• ln c
• c is the speed of light, 2.998 x108 m/s

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Electromagnetic radiation
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Separation of light
White light is actually a blend of all visible
wavelengths. They can separated using a prism.
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Electromagnetic radiation

• Electromagnetic radiation (EM) and matter
• Transmission - EM will pass through matter -- no
  interaction.
• Absorption - EM is absorbed by an atom, ion or
  molecule, taking it to a higher energy state.
• Emission - the release of energy by an atom, ion
  or molecule as light, taking it to a lower energy
  state.

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Particle properties

• Although EM has definite wave properties, it also
  exhibits particle properties.
• Photoelectric effect.
• First observed by Hertz and then later explained
  by Einstein.
• When light falls on Group IA metals, electrons
  are emitted (photoelectrons).
• As the light gets brighter, more electrons are
  emitted.
• The energy of the emitted electrons depends on
  the frequency of the light.

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Photoelectric effect

• The cathode has a photoemissive surface.
• When light hits the cathode
• electrons are ejected.
• They are collected at the
• anode and can be
• measured.

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Plancks Equation

• Studies of this effect led to the discovery that
  light existed as small particles of
  electromagnetic radiation called photons.
• The energy of a photon is proportional to the
  frequency.
• Photon energy hn
• The energy is inversely proportional to the
  wavelength.
• Photon energy h (c/l)
• h - Planks constant, 6.626 x 10-34 J . s

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Photon energy example

• Determine the energy, in kJ/mol of a photon of
  blue-green light with a wavelength of 486 nm.
• energy of a photon
• 4.09 x 10-19 J / photon

h c l
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Photon energy example

• We now need to determine the energy for a mole of
  photons (6.022 x 1023)
• Energy for a mole of photons.
• (4.09 x 10-19 J / photon) (6.022 x 1023
  photons/mol)
• 246 000 J/mol
• Finally, convert to kJ
• ( 246 000 J/mol )
• 246 kJ / mol

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Energy Chemistry

• A roadmap for using Plancks equation
• ? (nm) ? ? (m) ? ? (s-1) ? Energy (J/photon)
  ? Energy (J/mol of e-)
• ?c/? Eh?
• As frequency increases, wavelength decreases, and
  energy of the EM radiation increases
• Plancks equation can be rewritten as
• To illustrate this relationship

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Bohr model of the atom

• Bohr studied the the spectra produced when atoms
  were excited in a gas discharge tube.

He observed that each element produced its own
set of characteristic lines.
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Bohr model of the atom

• Bohr proposed a model of how electrons moved
  around the nucleus.
• He wanted to explain why electrons did not fall
  in to the nucleus.
• He also wanted to account for spectral lines
  being observed.
• He proposed that the energy of the electron was
  quantized - only occurred as specific energy
  levels.

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Bohrs Mathematical Model

• Contradicted the laws of classical physics.
• Stated that electrons could only exist in certain
  energy levels around the nucleus, which were
  quantized

Where RRydberg constant, hPlancks constant,
cSpeed of light, nprinciple quantum number
Potential energy of an electron in the nth level
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Bohrs Model

• The energies of the ground and excited states of
  the hydrogen atom can be calculated using Bohrs
  equation
• The difference in energy between the excited and
  ground states is equivalent to the amount of
  energy which must be absorbed to jump to the
  excited state and the amount of energy emitted in
  the form of a photon of EM radiation when the
  electron returns to the ground state

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Bohr model of the atom

• In the Bohr model, electrons can only exist at
  specific energy levels (orbit).
• Each energy level was assigned a principal
  quantum number, n.

Energy
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The Hydrogen Spectrum

• Lyman series Spectral lines in the UV
• Balmer series Spectral lines in the visible
  spectrum
• Paschen series Spectral lines in the infrared

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Bohr model of the atom

• The Bohr model is a planetary type model.
• Each principal quantum represents a new orbit
  or layer.
• The nucleus is at the center of the model.

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Bohr model of the atom

• Bohr was able to use his model hydrogen to
• Account for the observed spectral lines.
• Calculate the radius for hydrogen atoms.
• His model did not account for
• Atoms other than hydrogen.
• Why energy was quantized.
• His concept of electrons moving in fixed orbits
  was later abandoned.

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Wave theory of the electron

• 1924 De Broglie suggested that electrons have
  wave properties to account for why their energy
  was quantized.
• He reasoned that the electron in the hydrogen
  atom was fixed in the space around the nucleus.
• He felt that the electron would best be
  represented as a standing wave.
• As a standing wave, each electrons path must
  equal a whole number times the wavelength.

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De Broglie waves

• De Broglie proposed that all particles have a
  wavelength as related by
• l wavelength, meters
• h Planks constant
• m mass, kg
• v frequency, m/s

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De Broglie waves

• Using De Broglies equation, we can calculate the
  wavelength of an electron.

l
3.3 x 10-10 m
The speed of an electron had already been
reported by Bohr as 2.2 x 106 m s-1. You can
calculate the wavelength of any particle. Suppose
you wanted to calculate the wavelength of a
baseball (mass of approximately 145 g) traveling
at 100 mph (44.7 m/s)? Its silly, but it
illustrates the point!
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Heisenberg uncertainty principle

• According to Heisenberg, it is impossible to know
  both the position and the speed of an object
  precisely.
• He developed the following relationship
• Dx Dv
• Where ?x is the error in measuring position, ?p
  is the error in measuring velocity, h is Plancks
  constant, and m is mass
• As the mass of an object gets smaller, the
  product of the uncertainty of its position and
  speed increase.

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Quantum model of the atom

• Schrödinger developed an equation to describe the
  behavior and energies of electrons in atoms.
• His equation is similar to one used to describe
  electromagnetic waves. Electrons are best
  described as standing waves. (Remember that only
  certain wavelengths are allowed for standing
  waves.)
• Each wave function corresponds to an allowed
  amount of energy for the electron.
• Therefore, the energy of an electron is quantized
• While the equation is too complicated to write
  here, we can still use the results.
• The square of a wave function can be related to
  the probability of finding an electron in a
  particular region of space.
• This is called electron density
• Electron density plots can be used to
  characterize the shapes of orbitals
• An orbital corresponds to a region where the
  electron can be found 90 of the time

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Quantum numbers

• Each electron can be described in terms of its
  quantum numbers.
• Only certain combinations are allowed somewhat
  like an address.
• Principal quantum number, n
• Largely determines the energy of the electron
• Also describes the size of the orbital the
  larger the n the larger the orbital is
• n 1, 2, 3,
• Angular momentum, l
• Refers to the number of subshells that a
  principal level contains. Each value of l
  corresponds to a different type of orbital and
  indicates the number of nodal surfaces (planes).
• A nodal surface is a surface that slices through
  the nucleus and along which there is a zero
  probability of finding an electron.
• l 0 to n 1

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Quantum numbers

• Magnetic quantum number, ml
• Describes the direction that the orbital
  projects in space.
• ml -l to l (all integers, including zero)
• For example, if l 2, then ml would have values
  of -2, -1, 0, 1 and 2.
• Knowing all three numbers provide us with a
  picture of all of the orbitals.

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Allowed Combinations of Quantum Numbers

• subshell of
• n l ml label orbitals
• 1 0 0 1s 1
• 2 0 0 2s 1
• 1 -1, 0, 1 2p 3
• 3 0 0 3s 1
• 1 -1, 0, 1 3p 3
• 2 -2, -1, 0, 1, 2 3d 5
• 4 0 0 4s 1
• 1 -1, 0, 1 4p 3
• 2 -2, -1, 0, 1, 2 4d 5
• 3 -3, -2, -1, 0, 1, 2, 3 4f 7

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The s orbital
The s orbital is a sphere. Every level has one s
orbital.
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p orbitals
There are three p orbitals px, py and pz
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Representative d orbitals
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Representative f orbitals
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Combined orbitals - n2
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Combined orbitals - n3
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Electron spin

• Pauli added one additional quantum number that
  would allow only two electrons to be in an
  orbital.
• Spin quantum number, ms.
• It can have values of 1/2 and -1/2
• Pauli also proposed that no two electrons in an
  atom can have the same set of four quantum
  numbers --
• Pauli exclusion principle.

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Paramagnetism Diamagnetism

• Substances that are attracted to a magnetic field
  are called paramagnetic
• Most substances are very slightly repelled by
  magnetic fields. This is called diamagnetism.
• When electrons spin in opposite directions their
  magnetic fields cancel each other out
• Substances in which there are unpaired electrons
  are paramagnetic
• Each electron behaves like a tiny magnet
• When an external magnetic field is applied, the
  electron spins align with the magnetic field

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Orbital Box Diagrams

• Orbital box diagrams show the arrangement of
  electrons in an atom
• Each box represents an individual orbital
• Each arrow represents an electron
• Therefore, each box can contain a maximum of two
  electrons
• The orientation of the arrow (pointing up or
  down) represents the spin of the electron
• If there are two arrows in a box, they must
  point in opposite direction to represent their
  paired spins
• This is another way of depicting electron
  configuration

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Sample Orbital Box Diagrams
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Electron configuration

• For the hydrogen atom, the principal quantum
  number determines the energy of the orbital.
• All sublevels have
• the same energy.
• If more than 1312 kJ/mol
• of energy is added, the
• electron is completely removed.

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Electron configuration

• Things get a bit more complex where more than one
  electron is involved.
• Effective nuclear charge
• Inner electrons act to shield outer electrons
  from the positive charge of the nucleus.
• Some orbitals penetrate to the nucleus more
  than others s gt p gt d gt f
• As a result, we see different energy levels for
  the different sublevels for any given principal
  quantum number.

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Effective Nuclear Charge

• Abbreviated Z
• Describes the pull of the nucleus on a particular
  electron in an atom that has more than one
  electron
• Indicates that the presence of other electrons
  affects the nuclear charge experienced by
  valence electrons
• Valence electrons are shielded by core electrons

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Aufbau approach

• We can use this approach to build atoms and
  describe their electron configurations.
• For any element, you know the number of
  electrons in the neutral atom equals the atomic
  number.
• Start filling orbitals, from lowest energy to
  highest.
• If two or more orbitals exist at the same energy
  level, they are degenerate. Do not pair the
  electrons until you have to.

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Hunds Rule

• When putting electrons into orbitals with the
  same energy, place one electron in each orbital
  before putting two in any one.
• The existence of unpaired electrons can be
  tested for since each acts like a tiny
  electromagnet.
• This is how we end up with the unpaired electrons
  that make substances paramagnetic.

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5d
4f
Major trends in electron filling
6s
5p
4d
5s
4p
4s
1s
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Using Quantum Numbers to Explain Filling Order

• Electrons are placed in subshells in order of
  energy
• The pattern can be shown by adding the values
  for the quantum numbers n l
• The 4s subshell fills before the 3d
• In the 4s
• n4
• l0
• In the 3d
• n3
• l2

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Classification by sublevels
s
p
H
He
d
Li
Be
B
Ne
F
O
N
C
Na
Mg
Al
Ar
Cl
S
P
Si
K
Ca
Zn
Cu
Sc
Ni
Co
Fe
Mn
Cr
V
Ga
Kr
Br
Se
As
Ge
Rb
Sr
Cd
Ag
Y
Pd
Rh
Ru
Tc
Mo
Nb
In
Xe
I
Te
Sb
Sn
Cs
Tl
Hg
Au
Lu
Ba
Pt
Ir
Os
Re
W
Ta
Rn
At
Po
Bi
Pb
Fr
Lr
Ra
Gd
Tb
Sm
Eu
Nd
Pm
Ce
Pr
Yb
La
Er
Tm
Dy
Ho
f
Cm
Bk
Pu
Am
U
Np
Th
Pa
No
Ac
Fm
Md
Cf
Es
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Using the periodic table

• To write the ground-state electron configuration
  of an element
• Starting with hydrogen, go through the elements
  in order of increasing atomic number
• As you move across a period
• Add electrons to the ns orbital as you pass
  through groups IA (1) and IIA (2).
• Add electrons to the np orbital as you pass
  through Groups IIIA (13) to 0 (18).
• Add electrons to (n-1) d orbitals as you pass
  through IIIB (3) to IIB(12) and add electrons to
  (n-2) f orbitals as you pass through the f-block.

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Writing electron configurations

• Examples
• O 1s2 2s2 2p4
• Ti 1s2 2s2 2p6 3s2 3p6 3d2 4s2
• Br 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p5
• Core format
• O He 2s2 2p4
• Ti Ar 3d2 4s2
• Br Ar 3d10 4s2 4p5

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Writing electron configurations

• Electron configurations can also be written for
  ions.
• Start with the ground-state configuration for the
  atom.
• In the s- and p-blocks
• For cations, remove a number of the outermost
  electrons equal to the charge.
• For anions, add a number of outermost electrons
  equal to the charge.
• In the d-block explaining the charge(s) on
  cations is a bit more complex

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Writing electron configurations

• Example - Cl-
• First, write the electron configuration for
  chlorine
• Cl Ne 3s2 3p5
• Because the charge is 1-, add one electron.
• Cl- Ne 3s2 3p6 or Ar

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Writing electron configurations

• Example - Ba2
• First, write the electron configuration for
  barium.
• Ba Xe 6s2
• Because the charge is 2, remove two electrons.
• Ba2 Xe or Kr 3d10 4s2 4p6

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Periodic trends

• Many trends in physical and chemical properties
  can be explained by electron configuration and
  the phenomenon of effective nuclear
  charge/shielding.
• Well look at some of the more important
  examples.
• Atomic radii
• Ionic radii
• First ionization energies
• Electron affinities
• Electronegativity

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Atomic radii
Radus (pm)
Atomic number (noble gases are not included)
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Atomic radii for themain group elements
H
Li
Be
B
C
N
O
F
Na
Mg
Al
Si
P
S
Cl
K
Ca
Ga
Ge
As
Se
Br
Rb
Sr
In
Sn
Sb
Te
I
Cs
Ba
Tl
Pb
Bi
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Atomic radii of themain group elements

• Atoms get larger as you go down a group.
• A new shell is being added.
• Atoms get smaller as you go across a period.
• The nucleus contains more protons.
• The higher charge attracts the electrons more
  strongly, making the atom smaller.
• Notice the absence of the noble gases on the
  graphic on the previous slide

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Ionic radii (pm)

• Li Li Be Be2 O O2- F F-
• 152 74 111 35 74 140 71 133
• Na Na Mg Mg2 S S2- Cl Cl-
• 186 102 160 72 103 184 99 181
• K K Ca Ca2 Br Br-
• 227 138 197 100 114 195
• Rb Rb Sr Sr2 I I-
• 248 149 215 116 133 216
• Cs Cs Ba Ba2
• 265 170 217 136

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Ionic radii

• Cations
• These are smaller than the atoms from which they
  are formed.
• For main group elements, the outer shell of
  electrons is removed.
• The positively charged ion can also do a better
  job of holding on to the electrons that remain.

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Ionic radii

• Anions
• These are larger than the atoms from which there
  are formed..
• Adding electrons increases the repulsion between
  electrons.
• The ion has a harder time holding on to the
  electrons.

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Isoelectronic configurations

• Species that have the same electron
  configurations.
• Example
• Each of the following has an electron
  configuration of 1s2 2s2 2p6
• O2- F- Ne
• Na Mg2 Al3

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Ionization energy

• First ionization energy
• The energy to remove one electron from a neutral
  atom in the gas phase.
• A(g) first ionization energy A(g)
  e-
• This indicates how easy it is to form a cation.
  
• Metals tend to have lower first ionization
  energies than nonmetals.
• They prefer to become cations.

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First ionization energy
He
Ne
Ar
Kr
Xe
First ionization energy (kJ/mol)
Rn
Atomic number
66
First ionization energy

• The energy required to remove the first e- from a
  neutral atom in the gas state.

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Electron affinity

• A measure of an atoms tendency to gain electrons
  in the gas phase.
• A(g) e- A-(g) thermal
  energy
• Electron affinity is an irregular periodic
  function of atomic number. In general, it
  increases from left to right.
• Noble gases are not included since they have
  little or no tendency to gain electrons.

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Electron affinity
Cl
F
Br
I
Electron affinity (kJ/mol)
Atomic number
69
Electron affinity

• Energy released when an atom gains an e-.

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Chemical properties and the periodic table

• Electron configurations help us understand
  changes in atomic radii, ionization energies, and
  electron affinities.
• Various trends in reactivity can be observed.
• Main group metals become more reactive as you go
  down a group.
• Reactivity of nonmetals decreases as you go down
  a group.
• Transition metals become less reactive as you go
  down a group.

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Hydrogen

• Hydrogen is a nonmetal under normal conditions.
• While it may lose an electron to form H, it
  also can gain an electron to form H-.
• 2 Na(l) H2 (g) 2 NaH (s)
• Hydrogen is commonly placed either in the group
  IA (1) or in the IA (1) and VIIA (17) or not in
  any group.

gt 200oC
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Noble Gases

• Each of these has filled s and p sublevels except
  for helium (s only)
• All are very unreactive.
• A limited number of compounds have been produced
  using xenon and krypton.
• Xe (g) F2 (g) XeF2 (g)

gt250oC
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Alkali metals

• The group IA (1) metals all have an outer
  electron configuration of ns1.
• Loss of an electron to form a 1 ion is the
  basis of almost all reactions of the alkali
  metals.
• M M e-
• The reactivity of the elements increases from
  top to bottom of the group.

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Alkaline earth metals

• The group IIA (2) metals are not as reactive as
  the alkali metals.
• They need to lose two electrons in order to
  achieve a noble gas configuration.
• M M2 2 e-
• Reactivity increases as you go from the top to
  the bottom of the group

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Halogens

• The common group VIIA (17) elements are all
  nonmetals. Each only needs a single electron to
  achieve a noble gas configuration.
• When reacting with metals, they form 1- ions.
• 2 Na (s) Cl2 (g) 2 NaCl (s)
• When reacting with nonmetals, they share
  electrons.
• O2 (g) 2 F2 (g) 2 OF2 (g)

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Other ways of numbering groups

• Several methods are used for numbering periodic
  table groups
• American chemists preferred method.
• The IUPAC old system.
• The IUPAC current system.
• The American Chemical Society (ACS) has also
  adopted the current IUPAC system.

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Other numbering systems
Previous IUPAC Current IUPAC and ACS Preferred
US Mrs. Hodges Preferred ?