Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
Notes chemistry university calgary
Typology: Study notes
1 / 75
This page cannot be seen from the preview
Don't miss anything!
Electron wave functions / orbitals
CHEM 201 – Fall 2023 © Dr. Farideh Jalilehvand
University of Calgary
U of C Online textbook Chapter 1
From orbits to orbitals
=
Self-learning
(includes the Periodic Tables slides between SL 22 and S29)
=
For your information
Electronic structure
Core Valence
Periodic properties
of the elements
Bonding between theatoms in a single chemical
species
Ionic
Covalent
Lewis diagrams
Bond energy^ Bond dipoles
Moleculardipoles
VSEPR
VB and MO
theories
Chapter 1
Atoms
Chemical Species
Chemistry 201: Structure and Bonding
e.g. C, H, O
e.g. H
C=O 2
Resonance
Isomers
Functional
Groups
Nomenclature
2D
3D
make up
often used as
Electronic structure
of atoms
How atoms come together
to make molecules?
?
2
In a given orbit, electron can have certain amount of energy.
n = 1, 2, 3, 4, 5, ….,
An electron in orbit n = 1 has the lowest energy, and is closest to the nucleus.
An electron in orbit n =
∞
is “unbound” electron, escaped from nucleus.
Each orbit is labeled with a number n, called quantum number.
E
1
E
2
E
3
E
4
E
4
> E
3
> E
2
> E
1
When the electron is further away from the nucleus, it has higher energy.
low E ~ stable
high E ~ unstable
Bohr model could only explain other atoms with more than one electron.
Bohr model was at least one step forward in finding electronic structure of atoms, because:
e
-^.
E
1 E
2 E
5
Image from Ref. 4
The circumferences of electronorbits from n = 1 to n = 4 shown“straightened out”
n = 1 n = 2 n = 3 n = 4
An
e
-^
can only take certain orbits, where it
will complete a whole number of wavelengths.
Image from Ref. 6
“Standing wave” a 2D image of an
e
-^
confined in an atom.
2
2
Energy =
of
e
-^
2
(^2)
Even if we be able to calculate the wavelength and the energy of an electron, how can we find out ‘where the electron is”?^
Schrödinger used mathematical functions, called “wave functions”, to describe the wave associatedwith the electron in 3D space.
Wave function (symbol:
, psi)
Erwin SchrödingerNobel prize
1933
Image from Ref. 7
Schrödinger introduced wave functions (
; waves associated
with electrons) to answer this question: “where is the electron”?
Three quantum numbers are used to define the probability of finding
e
-^
in 3D space in the atom; i.e. the position (energy, shape
and size) of the electron wave (orbital):
n
= principal quantum number
m
l^
= magnetic quantum number
l
= secondary quantum number (orbital angular momentum no.) All orbitals with the same principle quantum no. are in the same shellIt divides the orbitals in a shell into smaller groups called subshellsIt divides the subshells into individual orbitals
l
= secondary quantum number defines the shape of the orbitals.
l
n
s, p, d, f, g,…
In a specific shell
n
, the value of
l
can range from 0 to (
n
There are n subshells in each shell.
n
l^
1s
2s
2p
3s
3p
3d
4s
4p
4d
4f
Subshell
l
; i.e., within a shell,
the subshell with higher
l
has slightly higher energy.
4s < 4p < 4d < 4f^ Increasing energy Shells
Subshells
n
n
n
n
4s , 4p , 4d , 4f3s , 3p , 3d2s , 2p1s
For
n
Orientation of p-orbitals in X, Y and Z directions
p 1
Subshell
x
y
z
y
z
x
l
Image from Ref. 8
x2-y
Orbitals are centered around the nucleus inside the atom:
Images from Ref. 9
2s 1s
2p
3s
3p
3d
4s
4p
4d
4f
Potential Energy
Shells spread over a range of energy.
2s 1s
2p
3s
3p
3d
4s
4p
4d
4f
Potential Energy
Orbitals in a given subshell have the same energy.When an electron wave adopts a specific energylevel, we say that it “occupies the orbital”. Example
: an electron occupied a 2p orbital.
5 d orbitals have same energy
= degenerate
