quantum model of the atom electrons in atoms. zschrödinger wave equation (1926) ydefines...
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Quantum Model of the Atom
Electrons in Atoms
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σ3/2 Zπ
11s 0
eΨ a
Schrödinger Wave Equation (1926)
defines probability of finding an e-
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Orbital
Orbital (“electron cloud”)
Region in space where there is 90% probability of finding an e-
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OrbitalOrbital
A 3-dimensional space around a nucleus in A 3-dimensional space around a nucleus in
which electrons are most likely to be foundwhich electrons are most likely to be found
Shape represents electron density (Shape represents electron density (not a not a
path the electron follows)path the electron follows)
Each orbital can hold up to 2 electronsEach orbital can hold up to 2 electrons
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Quantum Numbers
UPPER LEVEL
Four Quantum Numbers:
Specify the “address” of each electron in an atom
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Quantum MechanicsQuantum Mechanics
Describes the arrangement and space Describes the arrangement and space occupied by electrons in atomsoccupied by electrons in atoms
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Quantum MechanicsQuantum Mechanics
Describes the arrangement of electrons Describes the arrangement of electrons in atoms in terms of:in atoms in terms of:Main or principal energy levels or shells (n)Main or principal energy levels or shells (n)
(Oklahoma City)(Oklahoma City)Energy sublevels or subshellsEnergy sublevels or subshells
(Britton Road)(Britton Road)OrbitalsOrbitals
(house # 200)(house # 200)Electron spinElectron spin
(room # 4)(room # 4)
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Quantum Numbers
1. Principal Quantum Number ( n )
Energy level or shell
Size of the orbital
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Principal Quantum Number (Principal Quantum Number (nn))
Contain electrons that areContain electrons that are
Close in energyClose in energy
Similar distance from nucleusSimilar distance from nucleus
Have values of n = 1, 2, 3, 4, 5, 6…..Have values of n = 1, 2, 3, 4, 5, 6…..
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Energy Levels (Shells)Energy Levels (Shells)
The first shell (n = 1) is lowest in The first shell (n = 1) is lowest in energy, 2energy, 2ndnd level next and so on level next and so on 1<2<3<41<2<3<4
Low energy electrons are closest Low energy electrons are closest to the nucleusto the nucleus
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Quantum Numbers
s p d f
2. Angular Momentum Quantum # ( l )
Energy sublevel or subshell
Shape of the orbital
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SubshellsSubshells
Energy sublevels within energy levelEnergy sublevels within energy level
All electrons in a subshell have the All electrons in a subshell have the
same energysame energy
Designated Designated s, p, d, f .. s, p, d, f ..
Sublevel energy: s<p<d<fSublevel energy: s<p<d<f
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Main Main Energy Energy LevelsLevels SublevelsSublevels
n=4n=4 4s, 4p, 4d, 4f4s, 4p, 4d, 4f
n=3n=3 3s, 3p, 3d3s, 3p, 3d
n=2n=2 2s, 2p2s, 2p
n=1n=1 1s1s
nn == # of energy sublevels # of energy sublevels per energy levelper energy level
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Sublevels in n = 1,2, 3Sublevels in n = 1,2, 3
n = 3n = 3 3d3d
3p3p
3s3s
n = 2 n = 2 2p2p
2s2s
n = 1n = 1 1s1s
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Quantum Numbers
3. Magnetic Quantum Number ( ml )
Orientation of orbital
Specifies the exact orbital within each sublevel
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s subshell contains 1 s subshell contains 1 s orbitals orbital
1s 2s 3s
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p subshell contains 3 p p subshell contains 3 p orbitalsorbitals
px pz py
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d subshell contains 5 d orbitals
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f subshell contains 7 f orbitals
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Quantum Numbers
n = # of energy sublevels per energy level
n2 = # of orbitals per energy level
Sublevel sets: 1 s, 3 p, 5 d, 7 f
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Number of Electrons Number of Electrons
Each orbital can hold up to 2 Each orbital can hold up to 2 electronselectrons
Maximum number of electrons in any Maximum number of electrons in any energy level = 2nenergy level = 2n22
n =1n =1 2(2(11))22 = = 2 2
n =2n =2 2(2(22))22 == 8 8
n =3n =3 22(3(3))22 == 1818
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Electrons AllowedElectrons Allowed
All 2s electrons have the same energyAll 2s electrons have the same energy
All 2p electrons have the same energy which is All 2p electrons have the same energy which is
slightly higher than the energy of the 2s slightly higher than the energy of the 2s electronselectrons
s sublevel s sublevel 22 electrons electrons
p sublevel p sublevel 66 electrons electrons
d sublevel d sublevel 1010 electrons electrons
f sublevel f sublevel 1414 electrons electrons
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Quantum Numbers
Orbitals combine to form a spherical
shape.
2s
2pz2py
2px
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Quantum Numbers
4. Spin Quantum Number ( ms )
Electron spin +½ or -½
An orbital can hold 2 electrons that spin in opposite directions
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Quantum Numbers
1. Principal # 2. Ang. Mom. # 3. Magnetic # 4. Spin #
energy level
sublevel (s,p,d,f)
orbital
electron spin
Pauli Exclusion Principle
No two electrons in an atom can have the same 4 quantum numbers.
Each e- has a unique “address”
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Pauli Exclusion Principle
Each orbital can hold TWO electrons
with opposite spins.
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A. Number of electrons in a p orbital
1e or 2e
B. Number of orbitals in a p subshell
3
C. Number of orbitals in 4d subshell
5
D. Maximum number of electrons in a 3d subshell
10e
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ORBITAL DIAGRAM
Shows the electrons in each orbital
Circles, boxes, or lines are used to represent orbitals
Arrows or half-arrows represent electrons
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l = 0 s subshell
1 p
2 d
3 f
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ml 0
s orbital
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Ml -1 0 +1
p orbital
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Ml -2 -1 0 +1 +2
d orbital
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Ml -3 -2 -1 0 +1 +2 +3
f orbital
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electron spin
ms +1/2 -1/2
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Orbital diagram n l ml ms
7 0 0 +1/2
6 1 -1 +1/2
5 2 -2 -1/2
7s
6p
5d
-2 -1 0 +1 +2
-1 0 +1
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Orbital diagram n l ml ms
4 3 -3 +1/2
4 2 -1 -1/2
5 3 2 -1/2
4f
-3 -2 -1 0 +1 +2 +3
4d
-2 -1 0 +1 +2 5f
-3 -2 -1 0 +1 +2 +3
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Feeling overwhelmed?
Read Section 4-2!