Arrangement of Electrons in Atoms (Chapter 4) Notes

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Arrangement of Electrons in Atoms (Chapter 4)
Notes

• Part 1 Properties of Electrons

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• I. Properties of Light-Different types of
  electromagnetic radiation (x-rays, radio waves,
  microwaves, etc) SEEM to be very different from
  one another. Yet they share certain fundamental
  characteristics. All types of electromagnetic
  radiation, also called radiant energy, move
  through a vacuum at a speed of 3.00 x l08 meters
  per second.

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• A. Wavelength distance between identical points
  on successive waves may be measured in any
  length unit but is usually dependent on how long
  the wave is (X-rays are usually measured in
  nanometers or Angstroms while the very long radio
  waves might be measured in meter. The Greek
  letter, ?, is used to depict wavelength (pg 92)

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• B. Frequency the number of complete wave cycles
  that pass a given point in one second the unit
  is cycles/second but is written as sec-1, or
  Hertz. The Greek letter ?, is used to depict
  frequency.
• Wavelength and frequency vary inversely and are
  thus related as the product of frequency and
  wavelength equals the speed of light, c.
  
• c ??
• c 3.00 X 108m/s

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• What is the wavelength of radiation whose
  frequency is 6.24 x l013 sec-1?
• A 4.81X10-6 m
• what is the frequency of radiation whose
  wavelength is 2.20 x l0-6 nm? (2.20 X 10-15 m)
  
• A 1.36X1023 s-1 or Hz
• The range of visible light is generally
  considered to be from 350 to 700 nm (3.50 X 10-7m
  to 7.00 X 10-7 m. What is the range of frequency
  of visible light?
• A 8.6X1014 s-1or Hz to 4X1014 s-1or Hz

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Violet   400 - 420 nm Indigo   420 - 440
nm Blue   440 - 490 nm Green   490 - 570 nm
Yellow   570 - 585 nm Orange   585 - 620 nm
Red   620 - 780 nm
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When white light passes through or is reflected
by a colored substance, a characteristic portion
of the mixed wavelengths is absorbed. The
remaining light will then assume the
complementary color to the wavelength(s)
absorbed. This relationship is demonstrated by
the color wheel shown on the right. Here,
complementary colors are diametrically opposite
each other. Thus, absorption of 420-430 nm light
renders a substance yellow, and absorption of
500-520 nm light makes it red
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• II. The Photoelectric Effect (pg 93) refers to
  the emission of electrons from a metal when light
  shines on the metal. The wave theory of light
  (early 1900) could not explain this phenomenon.
  The mystery of the photoelectric effect involved
  the frequency of the light striking the metal.
  For a given metal, no electrons were emitted if
  the lights frequency was below a certain minimum
  regardless of how long the light was shone.
  Light was known to be a form of energy, capable
  of knocking loose an electron from a metal. But
  the wave theory of light predicted that light of
  any frequency could supply enough energy to eject
  an electron. Scientists couldnt explain why the
  light had to be of a minimum FREQUENCY in order
  for the photoelectric effect to occur.

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• Energy Information Radiation of different
  wavelengths affect matter differently certain
  wavelengths (near infrared) may burn your skin
  with a heat burn, overexposure to X radiation
  causes tissue damage. These diverse effects are
  due to differences in the energy of the
  radiation. Radiation of high frequency and short
  wavelength are more energetic than radiation of
  lower frequency and longer wavelength. THE
  QUANTITATIVE RELATIONSHIP BETWEEN FREQUENCY AND
  ENERGY WAS DEVELOPED THROUGH THE QUANTUM THEORY
  OF MAX PLANCK.

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• The explanation of the photoelectric effect dates
  back to 1900 when Max Planck revised classical
  ideas of light by proposing that light, which
  before was thought of as a collection of waves,
  consisted of BUNDLES OF ENERGY called QUANTA. A
  quantum is the minimum quantity of energy that
  can be lost or gained by an atom. Planck
  proposed the following relationship between a
  quantum of energy and the frequency of radiation
  
• E hv
• Plancks constant, h, is 6.63 x l0-34 Joules ?
  sec
• Many times, you will use this formula AND the
  formula, c ??, together.

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• If a certain light has 7.18 x l0-19 J of energy,
  what is the frequency of this light?
• A 1.08X1015 s-1or Hz
• what is the wavelength of this light?
• A 2.75X10-7 m
• If the frequency of a certain light is 3.8 x l014
  Hz, what is the energy of this light?
• A 2.5X10-19 J
• The energy of a certain light is 3.9 x l0-19 J.
  What is the wavelength of this light? Is it
  visible?
• A 510 nm Yes visible light.
• Calculate the smallest increment of energy that
  an object can absorb from yellow light, the color
  given off when sodium atoms are heated in a
  flame. The wavelength of this light is 589 nm.
• A 3.36X10-19 J

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• Albert Einstein expanded on Plancks theory by
  explaining that electromagnetic radiation has a
  dual wave-particle nature. While light exhibits
  many wavelike properties, it can also be thought
  of as a stream of particles. Each particle of
  light carries a quantum of energy. Einstein
  called these particles PHOTONS. A photon is a
  particle of electromagnetic radiation having zero
  mass and carrying a quantum of energy.

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• Einstein explained the photoelectric effect by
  proposing that electromagnetic radiation is
  absorbed by matter only in whole numbers of
  photons. In order for an electron to be ejected
  from a metal surface, the electron must be struck
  by a single photon possessing at least the
  minimum energy (Ephoton hv) required to knock
  the electron loose, this minimum energy
  corresponds to a minimum frequency. If a
  photons frequency is below the minimum, then the
  electron remains bound to the metal surface.
  Electrons in different metals are bound more or
  less tightly, so different metals require
  different minimum frequencies to exhibit the
  photoelectric effect.

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•  
• Example from problem 4 An atom or molecule
  emitting or absorbing radiation whose wavelength
  is 589 nm cannot lose or gain energy by radiation
  except in MULTIPLES OF 3.37x l0-19 J. It cannot,
  for example, gain 5.00 x l0-19 J from this
  radiation because this amount is not a multiple
  of 3.37 x l0-19.

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• In astronomy, it is often necessary to be able to
  detect just a few photons because the light
  signals from distant stars are so weak. A photon
  detector receives a signal of total energy 4.05 x
  l0-18 J from radiation of 540 nm wavelength. How
  many photons have been detected? 
• A 11 photons
• Excited chromium atoms strongly emit radiation of
  427 nm. What is the energy in kilojoules per
  photon?
• A 4.66X10-22 kJ
• 7. Light hitting certain chemical substances may
  cause rupture of a chemical bond. If a minimum
  energy of 332 kJ is required to break a
  carbon-chlorine bond in a plastic material, what
  is the longest wavelength of radiation that
  possesses the necessary energy? A 5.99X10-31 m
•  

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• III. The Hydrogen-Atom Line-Emission Spectrum
• When investigators passed electric current
  through a vacuum tube containing hydrogen gas at
  low pressure, they observed the emission of a
  characteristic pinkish glow. When a narrow beam
  of the emitted light was shined through a prism,
  it was separated into a series of specific
  frequencies (and therefore specific wavelengths,
  c ??) of visible light. The bands of light were
  part of what is known as hydrogens LINE-EMISSION
  SPECTRUM. (page 95)

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• The lowest energy state of an atom is its ground
  state.
• A state in which an atom has a higher amount of
  energy is an excited state. When an excited atom
  returns to its ground state, it gives off energy.

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• IV. Bohrs Model of Hydrogen Neils Bohr
  incorporated Plancks quantum theory to explain
  line-emission spectra. Bohr said the absorptions
  and emissions of light by hydrogen corresponded
  to energy changes within the atom. The fact that
  only certain frequencies are absorbed or emitted
  by an atom tells us that only certain energy
  changes are possible.
•  
• Bohrs model incorporated (l) Rutherfords
  Experiment, which established a nucleus and (2)
  Einsteins theory that used Plancks quantum
  theory to determine that light is discrete
  bundles of energy.

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• V. Bohrs Theory of the Atom
• Electrons cannot have just any energy only
  orbits of certain radii having CERTAIN energies
  are permitted.
• Thus, when an electron absorbs quanta of energy,
  it will cause them to jump away from the nucleus
  to a higher orbit (energy level or n) and when
  the electron falls from a high orbit to a lower
  one, a photon of a particular wavelength is
  released, and a particular color will be given
  off. Bohr was able to calculate a set of allowed
  energies. Each of these allowed energies
  corresponds to a circular path of a different
  radius.

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• Thus the larger the value of n, the farther the
  electron is from the nucleus and the higher
  energy it possesses.
•  
• The success of Bohrs model of the hydrogen atom
  is explaining observed spectral lines led many
  scientist to conclude that a similar model could
  be applied to all atoms. It was soon recognized,
  however, that Bohrs approach did not explain the
  spectra of atoms with more than one electron.
  Nor did Bohrs theory explain the chemical
  behavior of atoms.

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Part 2 Quantum Model of the Atom
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• So, where are the electrons of an atom located?
• A. Various Models of the Atom
• Daltons Model
• Thompsons Plum Pudding Model
• Rutherfords Model
• Bohrs Solar System Model electrons rotate
  around the nucleus
• Quantum Mechanics Model modern description of
  the electron in atoms, derived from a
  mathematical equation (Schrodingers wave
  equation)

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• B. In 1926, the Austrian physicist Erwin
  Schrodinger used the hypothesis that electrons
  have a dual wave/particle nature to develop an
  equation that treated electrons in atoms as
  waves.
• Schrodingers equation results in a series of so
  called wave functions, represented by the letter
  ? (psi). Although ? has no actual physical
  meaning, the value of ?2 describes the
  probability distribution of an electron. (Same
  concept you learned in Algebra II when you were
  doing linear regressions and finding the best fit
  line.)

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• We cannot know both the location and velocity of
  an electron (Heisenbergs uncertainty principle),
  thus Schrodingers equation does not tell us the
  exact location of the electron, rather it
  describes the probability that an electron will
  be at a certain location in the atom.

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• 1.      Waves are confined to a space and can
  only have certain frequencies.
• 2.      Electrons are considered to be waves
  confined to the space around an atomic nucleus.
  Electrons can only exist at specific frequencies.
  And according to Ehv (Plancks hypothesis),
  these frequencies correspond to specific energies
  (or quantified amounts of energy.)
• 3.      Electrons, like light waves, can be bent
  or diffracted.

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• Heisenbergs Uncertainty Principle says that
  there is a fundamental limitation on just how
  precisely we can hope to know both the location
  and the momentum of a particle. It turns out
  that when the radiation used to locate a particle
  hits that particle, it changes its momentum.
  Therefore, the position and momentum cannot both
  be measure exactly. As one is measured more
  precisely, the other is known less precisely.
• Today we say that the electrons are located in a
  region outside the nucleus called the electron
  cloud.

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• Electron Cloud Energy Levels
• Electrons are found in various energy levels
  around the nucleus. The energy levels are
  analogous to the rungs of a ladder. The lowest
  rung of the ladder corresponds to the lowest
  energy level. A person can climb up or down a
  ladder by going from rung to rung. Similarly, an
  electron can jump from one energy level to
  another. A person on a ladder cannot stand
  between the rungs, similarly, the electrons in an
  atom cannot exist between energy levels.

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• A. Quantum To move from one rung to another, a
  person climbing a ladder must move just the right
  distance. To move from one energy level to
  another, an electron must gain or lose just the
  right amount of energy. The exact amount of
  energy required to move from one energy level to
  another is called a quantum of energy.

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• B. Photon When electrons move from one energy
  level to another energy level we see light
  going from one energy level to another energy
  level gives off an exact amount of light (called
  a photon).

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• II. Quantum Mechanics Model of the Atom and
  Quantum Numbers
• Quantum Numbers a series of numbers which
  describe several properties of an energy level
  (or orbit)
• A. Principal Quantum Number, n (Energy
  Levels) energy levels (represented by the
  letter n) are assigned values in order of
  increasing energy n1,2,3,4, and so forth.
  which correspond to the periods in the periodic
  table. The principle q. n. is related to the
  size and energy of the orbital. n1, n2, n3,
  n4, n5, etc Which energy level is furthest
  away from the nucleus and has electrons with the
  highest energy - 1, 2,3, or 4?

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• B. Angular Momentum or Azimuthal Quantum Number,
  l (Sublevels) Within each energy level, the
  electrons are located in various sublevels
  there are 4 different sublevels s, p, d, and f.
  l defines the shape of the orbital (s, p, d,
  f). The possible values of l are limited by
  the value for n. If n 3, l can be 0, 1, or
  2, but not 3 or higher. This q.n. is related to
  the shape of the orbital.

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• l 0, is referring to the s sublevel
• l 1, is referring to p sublevel
• l 2, is referring to d sublevel
• l 3, is referring to f sublevel

1s
3p
2p
2s
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• C. Orbitals Where are the electrons in the
  various sublevels located in relation to the
  nucleus? Electrons are NOT confined to a fixed
  circular path, they are, however, found in
  definite regions of the atoms these regions are
  called atomic orbitals! Each orbital can only
  hold 2 electrons at a time (Pauli exclusion
  principle).

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• Within the s sublevel (l0) there is only 1
  orbital (which is spherical) it is called the s
  orbital.http//www.shef.ac.uk/chemistry/orbitron/A
  Os/1s/index.html
• Within the p sublevel (l1) there are 3 orbitals
  (which are dumbbell shaped) called the px, py, pz
  orbitals.
• Within the d sublevel (l2) there are 5 orbitals
  (4 of which are cloverleaf shaped) called the
  dxy, dxz, dyz, dx2-y2, dz2 orbitals.
• Within the f sublevel (l3) there are 7 orbitals
  - which are too complex to draw

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• The magnetic quantum number, ml, refers to the
  position of the orbital (plane) in space relative
  to other orbitals. It may have integral numbers
  ranging from 0 in the s sublevel, 1 to 1 in the
  p sublevel, 2 to 2 in the d sublevel and 3 to 3
  in the f sublevel.

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• ml 0, is referring to the s orbital
• ml -1, 0, 1, are referring to the three p
  orbitals (px, py, and pz)
• ml -2, -1, 0, 1, 2, are referring to the five
  d orbitals
• ml -3, -2, -1, 0, 1, 2, 3, are referring to
  the seven f orbitals

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Examples

• What are the values of n, l, and ml for the
  orbitals in the 3 d sublevel?
• 2. What are all possible values of n, l, and ml
  in the n 3 energy level?
• 3. Which of the following sets of quantum
  numbers are NOT allowed in an atom? For each
  incorrect set, state why it is incorrect.
• A. n l, l 0, ml l
• B. n 2, l 2, ml l
• C. n 5, l 3, ml 2
• D. n 6, l -2, ml 2
• E. n 6, l 2, ml -2

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• D. How many electrons can go into each energy
  level?
• Each orbital can hold two electrons. (2n2
  number of electrons per energy level)
• The 1st energy level (n1) only has 1 sublevel
  called 1s. s only has 1 orbital called the s
  orbital, so only 2 electrons will be found in the
  1st energy level. (2n2 2)

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• The 2nd energy level (n2) has 2 sublevels called
  2s and 2p. s only has 1 orbital called the s
  orbital, p has 3 orbitals called px, py, and pz
  orbitals, so 8 electrons will be found in the
  2nd energy level. (2n2 8)

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• The 3rd energy level (n3) has 3 sublevels called
  3s, 3p, and 3d. s only has 1 orbital called the
  s orbital, p has 3 orbitals called px, py, and
  pz orbitals, and d has 5 orbitals, so 18
  electrons will be found in the 3rd energy level.
  (2n2 18)

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• How about the 4th energy level?
• It has 4 sublevels called 4s, 4p, 4d, and 4f. s
  only has 1 orbital, p has 3 orbitals, d has 5
  orbitals, and f has 7 orbitals, so 32 electrons
  will be found in the 4th energy level. (2n2 32)

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• E. Lets put it all together
• Example of neon atom

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• Fourth Quantum Number, ms, refers to the magnetic
  spin of an electron within an orbital. Each
  orbital can hold two electrons, both with
  different spins. Clockwise spin is represented
  with a value of 1/2 and counterclockwise spin
  is represented with a value of 1/2. Electrons
  fill the orbitals one at a time with the same
  spin (1/2), then fill up the orbital(s) with
  electrons of the opposite spin (-1/2).
• ms 1/2 or 1/2

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• Example Which of the following sets of quantum
  numbers are not allowed? For each incorrect set
  state why it is incorrect.
• A. n 3, l 3, ml 0 ms -1/2
• B. n 4, l 3, ml 2, ms -1/2
• C. n 4, l l, ml l, ms 1/2
• D. n 2, l 1, ml -l, ms -1
• E. n 3, l 1, ml -2, ms -1/2

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• Quantum Numbers Analogy
• Energy Levels (n) or Principal Q.N.
• n1 (Georgetown) n2 (Austin)
  n3 (San Antonio) n4 (Laredo)
• Sublevels (l) or Azimuthal Q.N.
• l0 s shape 1 bedroom
• l1 p shape 3 bedroom
• l2 d shape 5 bedroom
• l3 f shape 7 bedroom
• Orbitals (ml) or Magnetic Q.N.
• If l0 then ml0 (Represents the 1 bed/orbital
  in the s sublevel)
• If l1 then ml -1, 0, 1 (Represents the 3
  beds/orbitals in the p sublevel)
• If l2 then ml -2, -1, 0, 1, 2 (Represents
  the 5 beds/orbitals in the p sublevel)
• If l3 then ml -3, -2, -1, 0, 1, 2, 3
  (Represents the 7 beds/orbitals in the
  p sublevel)
• Magnetic Spin Fourth Q.N. (ms)
• ms 1/2 - 1st electron in orbital
• ms -1/2 2nd electron in orbital

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Part III Electron Configurations
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• I. Electron Configuration
• Definition of electron configuration An
  electron configuration is a written
  representation of the arrangement of electrons in
  an atom.

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• Rules for writing Electron Configurations
• Aufbau Principle electrons fill in order from
  lowest to highest energy.

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Aufbau Diagram
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• The Pauli Exclusion Principle An orbital can
  only hold two electrons.
• Two electrons in the same orbital must have
  opposite spins.
• How many electrons can occupy each sublevel (s,
  p, d, f)?
• s 1 x 2 2 e-
• p 3 x 2 6 e-
• d 5 x 2 10 e-
• f 7 x 2 14 e-

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• Hunds rule the lowest energy configuration for
  an atom is the one having the maximum number of
  unpaired electrons for a set of degenerate
  orbitals. By convention, all unpaired electrons
  are represented as having parallel spins with
  spin up.

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Hunds Rule

• One electron enters each orbital until all the
  orbitals contain one electron with spins
  parallel.
• Ex. Nitrogen

1s
2s
2p
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• What? How do we write an electron configuration?
• 1st rule - electrons occupy orbitals that
  require the least amount of energy for the
  electron to stay there. So always follow the
  vertical rule (Aufbau Principle)
• You notice, for example, that the 4s sublevel
  requires less energy than the 3d sublevel
  therefore, the 4s orbital is filled with
  electrons before any electrons enter the 3d
  orbital!!!! So just follow the above chart and
  you cant go wrong!!!!)

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Diagonal Rule
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• B. 2nd rule only 2 electrons can go into any
  orbital, however, you must place one electron
  into each orbital in a sublevel before a 2nd
  electron can occupy an orbital. Orbitals with
  only 1 electron in the orbital are said to have
  an unpaired electron in them.

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III. Writing Electron Configurations (3 ways)

• A. Orbital Notation an unoccupied orbital is
  represented by a line______, with the orbitals
  name written underneath the line. An orbital
  containing one electron is written as __?___, an
  orbital with two electrons is written as __??__.
  The lines are labeled with the principal quantum
  number and the sublevel letter.

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Examples (Remember that you must place one
electron into each orbital before a second
electron in placed into an orbital.)

• Hydrogen _?___ Helium _??_
• 1s 1s
• Lithium _??__ _?___
• 1s 2s
• Carbon __??__ __??__ __?__ __?__ _____
• 1s 2s 2p
  2p 2p
• You try to write the notation for Titanium

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• B. Electron Configuration Notation eliminates
  the lines and arrows of orbital notation.
  Instead, the number of electrons in a sublevel is
  shown by adding a superscript to the sublevel
  designation. The superscript indicates the
  number of electrons present in that sublevel.

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Examples

• Hydrogen 1s1 Helium 1s2
• Lithium 1s22s1
• Carbon 1s22s22p2
• You try to write the notation for Titanium

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1. Short Hand or Noble Gas Notation Use the noble
   gases that have complete inner energy levels and
   an outer energy level with complete s and p
   orbitals. Use the noble gas that just precedes
   the element you are working with.

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• Boron is ls22s22p1
• The noble gas preceding Boron is He, so the short
  way is He2s22p1.
• Sulfur is ls22s22p63s23p4
• Short way Ne3s23p4
• Example Titanium

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Using the Periodic Table
               
               
               
                                   
                                   
                                   
                                   
                       
                           
                           
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• More Practice Problems
• Write electron configurations for each of the
  following atoms
• 1. boron
• 2. sulfur
• 3. vanadium
• 4. iodine
• Draw orbital diagrams for these
• 5. sodium
• 6. phosphorus
• 7. chlorine
• Write shorthand electron configuration for the
  following
• 8. Sr
• 9. Mo
• 10. Ge

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• Electron Configurations and Quantum Numbers
  When writing the quantum numbers for a given
  element, keep the following in mind
• 1. The highest energy electron is the LAST one
  you write in the electron configuration.
• 1s22s22p63s23p5 -- the 3p5
  electron is the last written. Remembering
  Aufbaus Principle, electrons fill from the
  lowest to the highest energy.
• 2. The outermost electron is the one with the
  LARGEST principle quantum number. It may be the
  last one you write 1s22s22p63s23p64s23d104p2.
  The 4 p2 is the farthest from the nucleus. OR
• (2) 1s22s22p63s23p64s23d10. Here, it is the 4s2
  electron, because it has the largest principle
  q.n.

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• To write the quantum numbers for the first
  example above, the 3p5 electron
• n 3, l 1, ml 0, ms -1/2
• For the second example, the 4p2 electron
• n 4, l 1, ml 0, ms 1/2
• For the third example, the 4s2 electron is the
  outermost electron (but not the one with the
  highest energy) so the q.n.s for the outermost
  electron would be
• n 4, l 0, ml 0, ms -1/2

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• You try it Write the electron configuration and
  the quantum numbers for the following
• 1. outermost electron in bromine
• 2. outermost electron in copper
• 3. highest energy electron in vanadium
• 4. Write the electron configuration and the
  quantum numbers for the 35th electron in rubidium
  

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• Irregular Electron configurations sometimes the
  electron configuration is NOT what we would
  predict it to be. Sometimes electrons are moved
  because (l) it will result in greater stability
  for that atom or (2) for some unknown reason??

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• It is very important to define stable here.
  STABLE means
• 1. all degenerate (equal energy) orbitals are
  FULL
• 2. all degenerate orbitals are half-full
• 3. all degenerate orbitals are totally empty.

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• Examples draw the orbitals (lines or boxes)
  and fill each orbital with the predicted number
  of electrons. Predict the electron configuration
  for Cr 24 Ar4s23d6
• However, the real E. C. is Ar4s13d5. The 4s1
  electron has been moved to achieve greater
  stability.
• ALWAYS USE THE ACTUAL E. C. AND NOT THE PREDICTED
  ONE. YOU WILL HAVE THESE ATOMS WITH IRREGULAR
  E. C. HIGHLIGHTED OR MARKED ON YOUR PERIODIC
  TABLE.

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• Electron configurations for Ions-First, determine
  if the element will lose or gain electrons.
  Secondly, what number of electrons will be gained
  or lost? It is recommended that you write the
  e.c. for the atom and then determine what will
  happen.

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• For cations (positive ions) look at the element
  and decide how many electrons will be lost when
  it ionizes and keep that in mind when writing the
  E. C. The last number in the E. C. will now be
  LESS than what is written on your periodic table.
• Ex. Write the electron configuration for
  magnesium ion Ne3s2 is for the atom. Mg is
  a metal and will lose its valence (outer)
  electrons, so the e.c. for Mg2 is 1s22s22p6
• Practice
• 1. 3
• 2. 12
• 3. 19
• 4. 13

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• For anions (negative ions) look at the element
  and decide how many electrons that element will
  GAIN when it ionizes. The last number in the E.
  C. will be MORE than what is written on the
  periodic table.
• Ex. Sulfide ion Sulfur atom is 1s22s22p4.
  Sulfur is a nonmetal with 6 valence electrons
  (2s2 and 2p4) and will gain 2 electrons
  1s22s22p6 is for the sulfide ion.
• Practice
• 17
• 7
• 16
• 30