Atoms and Quantum Numbers

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Atoms and Quantum Numbers

• GLY 4200 Lecture 5 Fall, 2009

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Atom

• Grossly oversimpliflied view of atom, but it does
  have a nucleus and electron cloud

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Nucleons

• Protons charge of 1
• Neutrons neutral, with a mass slightly greater
  than the proton
• Atomic number number of protons, often denoted
  z
• Atomic number is designated as a left subscript
  to the chemical symbol - 1H, 14Si

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Atomic Weight

• The atomic weight equals the number of protons
  plus neutrons
• Atomic weight is shown as a left superscript to
  the chemical symbol, such as 16O

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Isotopes

• One element may have one or more numbers of
  neutrons
• 11H is normal hydrogen, with one proton and no
  neutrons
• 12H is deuterium, or heavy hydrogen, with one
  proton and one neutron
• 13H is tritium, a radioactive form of hydrogen,
  with one proton and two neutrons
• Collectively, the different types of the atoms of
  one element are called isotopes

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Ions

• Cation - the atom has lost electrons, so there is
  a net positive charge
• Anion - the atom has gained electrons, so there
  is a net negative charge
• Cations are found toward the left side and center
  of the periodic table, while anions are found on
  the right side

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Planetary Model of the Atom

• Early models of the atom showed the electrons
  circling the nucleus like the planets orbit the
  sun
• Figure shows nitrogen represented this way

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Johann Balmer

• Discovered the spectral lines of hydrogen in 1885

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Neils Bohr

• Danish physicist
• 1885-1962
• Formulated the next model of the atom, now called
  the Bohr model
• Won the 1922 Nobel prize for physics

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Bohr Model of Nitrogen

• Electrons are in discrete orbitals
• Two of the electrons are in the first energy
  level
• The other five are in the second energy level

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Spectral lines of Elements
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De Broglie Waves

• An electron standing wave vibrating in an orbit
  around a nucleus of an atom
• Only integral numbers of wavelengths are allowed

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Standing Wave, One Loop

• One String Vibrating, 1/2 wavelength
• Two nodes
• Quantum number n 1

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Standing Wave, Two Loops

• One String Vibrating, 1 wavelength
• 3 nodes
• Quantum number n 2

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Standing Wave, Four Loops

• One String Vibrating, 2 wavelengths
• 5 nodes
• Quantum number n 4

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Schrodingers Equation
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Principal Quantum Number

• n has values 1,2,3.....
• The Principal Quantum Number refers to the
  angular momentum of the electron
• n determines which shell of electrons is being
  discussed
• May be referred to as n 1, n 2, etc.
• In X-ray terminology, shells are assigned
  letters, K,L,M,N,O,P,Q for n 1 to 7

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Azimuthal Quantum Number

• l may take values 0, 1, 2, 3, ... (n-1)
• The Azimuthal Quantum Number Indicates the
  symmetry of the orbital
• l determines the subshell to which an electron
  belongs
• s, p, d, f are used to designate l 0 to 3

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Magnetic Quantum Number

• m has allowed values are 0, 1, 2, 3, ..... l
• The Magnetic Quantum Number refers to the
  orientation of the orbital in space

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Spin Quantum Number

• s has allowed values are ½
• The Spin Quantum Number refers to the direction
  of rotation of the electron itself

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s Orbitals

• s orbitals are spherically symmetric
• The radius increases as n increases
• l 0
• One orbital, two electrons

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p Orbitals

• p orbitals are aligned along the three principal
  axes
• l 1
• Three orbitals, six electrons

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d Orbitals

• Four lobes, oriented as shown
• l 2
• Five orbitals, ten electrons

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f Orbitals

• Complex shapes
• l 3
• Seven orbitals, fourteen electrons

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Wolfgang Pauli

• Austrian physicist, 1900-1958
• Formulated the Exclusion Principle, which today
  bears his name
• Won the Noble Prize in Physics, 1945

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Pauli Exclusion Principle

• Proposed in 1925
• The Pauli Exclusion Principle States that no two
  electrons in an atom can have the same four
  quantum numbers
• Since any given orbital has n, l, and m the same,
  there can only be two electrons per orbital, with
  s ½