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04/18/23
Descriptive Chemistry
Besides assigned readings on orbital shapes and electron probability, there are readings on descriptive chemistry.
This week• Group III (Boron family)• Group IV (Carbon family)
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Orbitals
The region around a nucleus in which an electron has a probability of being located is called an orbital.
Orbitals can vary in• distance from the nucleus (radial function)• direction (angular function)
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Wave Function
(2
x2
2
y2
2
z2 + V2m
E= h2
The shape of the orbital and the energy of the electronis related to the wave function ().
The electron is mathematically describedby the wave function,
the Schrödinger Equation is used to calculatethe energy of that electron.
The wave function is composed of radialand angular functions (in three dimensions).
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Spherical Coordinates
z
x
y
r
r = distance of electron from nucleus = angle of declination (angle from z-axis)
= angle of rotation (angle from x-axis in xy plane)
coordinates (r,,)
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Orbital Shapes
The shape of the orbital is determined by the wave function.
The shape of the orbital can be determined from the nodes of the wave function.
ao = Bohr radius (0.529 Å) Z = nuclear charge
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Orbital Wave Functions
Wave FunctionRadialNodes
AngularNodes
1s=
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Zao
e
Zrao
no radialnodes
no angulardependence
2s=
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Zao
2Zrao
e
Zrao
whenZr/ao=2
no angulardependence
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Orbitals WithNo Angular Dependence
1s
2ss orbitals have a spherical shape
isotropic orbitals
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Orbital Wave Functions
2pz =
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Zao
Zrao
e
Zr2ao cos
noradialnodes
= 90°
z
x
y
RadialNodes
AngularNodesWave Function
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Orbital Wave Functions
z
x
y
RadialNodes
AngularNodesWave Function
2px =
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Zao
Zrao
e
Zr2ao (sin cos
noradialnodes
= 0°or
= 90°
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Orbital Wave Functions
z
x
y
RadialNodes
AngularNodesWave Function
2py =
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Zao
Zrao
e
Zr2ao (sin sin
= 0°or
= 0°
noradialnodes
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Orbitals WithAngular Dependence
p orbitals have a propeller shape
2px
x
y
z
x
y
z
2py
x
y
z
2pz
How can you distinguish px from py or pz?
Anisotropic orbitalsthe angular probability function isnot the same in all directions
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Higher Energy Orbitals
Higher energy levels correspond to higher wave functions including 3s, 3px, 3py, 3pz and d orbitals.
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Orbital Sets
Other orbitals are anisotropic, however when they are combined as a set the result is "spherically symmetric" (i.e., isotropic).
s orbitals are spherical in shape and therefore spherically symmetric.
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Orbital Sets
+ + =
no angulardependence
spherically symmetricisotropic
p orbitals are individually anisotropic,but as a set are isotropic.
px py pz
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Orbital Sets
++
++
=
d orbitals are individually anisotropic,but as a dxy, dxz, dyz, dx
2-y
2, dz2 set are isotropic.
electrons inspherically symmetric
orbitalsare slightly
more stable
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Quantum Numbers
Each electron in the orbital of the atom can be described by an unique combination of values known as quantum numbers.
There are four different quantum numbers
n , , m, ms
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Principal Quantum Number
n=1n=2n=3n=4n=5n=6n=7
principalquantumnumber
Larger valuesof n refer tohigher energyorbitals(further fromthe nucleus)
range: n = 1, 2, 3, …,
The principal quantum numberis related to the rows of
the periodic table.
Angular Quantum Number
= 0s orbital
(no angulardependence)
= 1p orbital
= 2d orbital
= 3f orbital
range: = 0, … , n-1
Is it possible to have a 2f orbital?
Is it possible to have a 3p orbital?
This is the principal quantum number
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Magnetic Quantum Number
What would be the names of these orbitals?
m = -, … , 0, … , +
Differentiates betweenorbitals with the samen and quantum numbers
In a magnetic field alignedalong the z-axis,
an electron in the 2pz orbitalwill behave differently
than an electron in the 2px or 2py orbitals.
p-1 p0 p+1
How many f-orbitals are there in an f-orbital set?
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Spin Quantum Numberms = -1/2, +1/2
Each orbital can contain up to two electrons
one aligned withan external field
one aligned againstan external field
Which electron has lower energy?
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Quantum Numbersand the Periodic Table
Identify the regions of the periodic table thatcorrespond to the s, p, d and f orbitals
s pd
f
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Four Quantum Numbers
Each electron in an atom can be described uniquely by the four quantum numbers.
Three rules involving quantum numbers • Pauli Exclusion Principle
• Aufbau Principle • Hund's Rule
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Pauli Exclusion Principle
Only one electron in an atom may have the same four quantum numbers.
it’s like a house address
3 1 1 1/2
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Aufbau Principle
In the ground state, electrons fill in the lowest available energy state (orbital) first
it’s like the best available seatin the house
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Hund's Rule
If more than one electron occupies a degenerate set of orbitals (orbitals of the same energy), then the electrons will fill in such a way as to maximize the number of orbitals filled.
each electron would prefer to be singlerather than be doubled up
It is more stable for the spin of the electrons to be aligned in the same direction.