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)

Orbital ShapesEdward A. Mottel

Department of Chemistry

Rose-Hulman Institute of Technology

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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=

3/21

Zao

e

Zrao

no radialnodes

no angulardependence

2s=

3/21

32

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 =

3/21

32

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 =

3/21

32

Zao

Zrao

e

Zr2ao (sin cos

noradialnodes

= 0°or

= 90°

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Orbital Wave Functions

z

x

y

RadialNodes

AngularNodesWave Function

2py =

3/21

32

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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d Orbitals

xy

z

3dxy

xy

z

3dyz

xy

z

3dxz

xy

z

3dx2

-y2

3dz2

x

y

z

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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.

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04/18/23

Laboratory

Special extra lab period today periods 7-9

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Problem Set

Electron Filling PS due Thursday Four Ions PS to be done (but not submitted)

by Exam 2