Transcript Atoms and Quantum Numbers

Atoms and Quantum Numbers
GLY 4200 – Lecture 5 –Fall, 2016
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Atom
• Grossly
oversimplified 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:

1H
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
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• 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 a formula
for 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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Schrődinger’s 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
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