Quantum mechanical model of the atom
Quantum mechanical model of the atom
The atom consists of a small nucleus (containing the protons and
neutrons) surrounded by a much larger volume of space
containing the electrons.
An electron is described by four parameters:
1. Principal energy level
2. Sublevel
3. Individual orbital
•
This space is divided into regions called
principal energy levels (“electron shells”)
•
Principal energy levels are designated by the letter n,
where n is a positive integer
4. Spin
-- the lowest energy level corresponds to n = 1
-- higher energy levels correspond to n = 2, 3, 4,....
•
As n increases:
-- the energy of the electron increases
-- the electron is found on average farther from the nucleus
Analogy: Airspace zones
used in air traffic control
Principal energy levels
As n increases:
n=4
• the energy of the electron increases
• the electron is found on average farther
from the nucleus
Energy
n=3
n=2
In our ladder analogy, the
principal energy levels
correspond to the rungs on the
ladder that is climbed by the
electrons in an atom
electron (e-) =
Example: Class D airspace
• Surface to 2500 ft
• 5 mile radius
n=1
The electron can occupy one of the ladder rungs
-- but not any of the spaces in between
Principal energy levels
Quantum mechanical model of the atom
Energy levels
The principal energy levels
occupied by electrons in an
atom are like the rungs of a
ladder
n=7
n=6
n=5
Increasing energy
n=4
• but the rungs are not spaced
evenly
n=3
As the principal energy level
increases:
n=2
An electron is described by four parameters:
1. Principal energy level
2. Sublevel
3. Individual orbital
4. Spin
• distance from the nucleus
increases
• the difference in energy
n=1
floor
nucleus
between successive levels
becomes smaller
Energy
Sublevels (“subshells”)
Each principal energy level is divided
into sublevels (“subshell”)
f
d
p
s
n=4
d
p
s
n=3
Analogy: Airspace zones
used in air traffic control
• subshells are indicated by the letters
s, p, d, or f
For an atom with more than one electron:
• subshells within a given principal
energy differ in energy
s < p < d < f
p
s
n=2
s
n=1
(the difference in energy between
subshells is small relative to the
difference in energy between
principal energy levels)
Each subshell contains orbitals of
a specific type
Example: Class D airspace
• Surface to 2500 ft
• 5 mile radius
Orbitals
Types of orbitals: s orbitals
Remember that in quantum mechanics, it is not possible to specify the
exact location of an electron
• an orbital defines the region in space around the nucleus where
there is a high probability of finding an electron
There are four types of orbitals:
• s orbitals
• p orbitals
• d orbitals
• f orbitals
Different types of orbitals have different shapes
• the surface of an orbital encloses the space around the nucleus
where there is a 90% probability of finding an electron in that orbital
Each s sublevel contains one s orbital
An s orbital is spherical in shape
The spherical surface
encloses a region of space
around the nucleus where
there is a 90% probability
that an electron in the orbital
may be found
• orbitals have indistinct boundaries (electron “cloud”)
Types of orbitals: p orbitals
Types of orbitals: p orbitals
Each p sublevel contains
three different p orbitals
• The three p orbitals share a
common center
Each p sublevel contains three different p orbitals
• each p orbital has two lobes
• The three p orbitals point in
different directions
Types of orbitals: d orbitals
Types of orbitals: f orbitals
Each d sublevel contains five different d orbitals
• the five d orbitals all point in different directions
Each f sublevel contains seven different f orbitals
Review: Quantum mechanical model of the atom
Quantum mechanical model of the atom
d
p
s
n=4
The n = 1 principal energy level
contains only one sublevel
f
d
p
s
• the 1s sublevel contains
one s orbital
n=3
p
s
n=2
s
n=1
Energy
Energy
f
d
p
s
Text
1s orbital
d
p
s
The n = 2 principal energy
level contains two sublevels
n=4
• the 2s sublevel contains
one s orbital
• the 2p sublevel contains
three p orbitals
n=3
2s orbital
p
s
n=2
s
n=1
2p orbitals
Quantum mechanical model of the atom
Quantum mechanical model of the atom
n=4
• the 3s sublevel contains
one s orbital
• the 3p sublevel contains
three p orbitals
f
d
p
s
n=4
d
p
s
n=3
n=3
p
s
n=2
p
s
n=2
s
n=1
s
n=1
• the 3d sublevel contains
five d orbitals
Points to remember about orbitals
The n = 4 principal energy level
contains four sublevels
• the 4s sublevel contains
one s orbital
d
p
s
Energy
Energy
f
d
p
s
The n = 3 principal energy level
contains three sublevels
• The 4p sublevel contains
three p orbitals
• The 4d sublevel contains
five d orbitals
• The 4f sublevel contains
seven f orbitals
Electron probability distribution
defines orbital shapes
Orbitals are not orbits (i.e., fixed paths around the nucleus)
• the shape of an orbital defines a region in space around
the nucleus where there is a high probability of finding an
electron in that orbital
• the shape of an orbital does not give any information
about the actual path followed by an electron as it moves
around the nucleus
1s orbital
boundary surface
Electron probability distribution
Electron probability distribution
defines orbital shapes
Electron probability distribution
defines orbital shapes
3d orbitals
2p orbital
Points to remember about orbitals
Each orbital is not a region separate in space from other orbitals
• i.e., orbitals overlap one another
Cross-section of the s
orbitals of the first
three principal energy
levels showing their
relative size and
overlap
Points to remember about orbitals
Each orbital is not a region separate in space from other orbitals
• i.e., orbitals overlap one another
Individual orbitals of the
s and p sublevels
Combined orbitals of
the s and p sublevels
Atomic orbitals
Quantum mechanical model of the atom
An electron is described by four parameters:
2s orbital
Nucleus
1. Principal energy level
2. Sublevel
3. Individual orbital
2p orbital
4. Spin
1s orbital
3s orbital
An orbital can contain a maximum of two electrons
Electron spin
An orbital can contain zero, one, or two electrons
You can think of an electron spinning on its axis (like a globe)
If the orbital contains two
electrons, the electrons must have
opposite spin
• it can only spin in two directions:
--positive (represented by an up arrow)
-- negative (represented by a down arrow)
ee-
positive spin
e-
negative spin
An orbital can hold a maximum of two electrons, which must have
opposite spins
-- i.e., electrons with the same spin can not occupy the same orbital
This rule is called the Pauli exclusion principle
e-
-- i.e., electrons with the same spin
can not occupy the same orbital
This rule is called the Pauli exclusion principle
Every individual electron within an
atom has a specific “address”
Just like a street address, the precise location is
described by terms that become increasingly specific
An orbital can contain a maximum
of two electrons
A s sublevel can hold up to 2 electrons
• 1 s orbital
1 x 2 = 2 electrons
A p sublevel can hold up to 6 electrons
• 3 p orbitals
2 x 3 = 6 electrons
State: California
Principal Energy Level: n = 2
A d sublevel can hold up to 10 electrons
City: Oakland
Sublevel: p sublevel
• 5 d orbitals
Street: Fallon St.
Individual orbital: px
Number: 900
Spin: +1/2
Each principal energy level can contain
up to 2n2 electrons
Principal
energy level
(n)
Sublevels
Number of
orbitals in each
sublevel
Electron
capacity of
orbitals
1
s
1
2
2
s
1
2
p
3
6
3
4
2 x 5 = 10 electrons
Ground state and excited states
The lowest possible energy state of an atom is called its
ground state
2 electrons
8 electrons
• when an atom is in its ground state, its electrons fill
the lowest energy orbitals completely before
occupying higher energy orbitals
s
1
2
p
3
6
d
5
10
Any state with energy higher than the ground state is
called an excited state
s
1
2
• when an atom is in an excited state, its electrons
p
3
6
d
5
10
f
7
14
18 electrons
32 electrons
occupy higher energy orbitals without having the lower
energy orbitals completely filled
Ground state and excited states
Ground state and excited states
n=4
n=4
4s
4p
4d
n=3
Energy
Energy
4f
n=3
3s
3p
n=2
2s
n=1
2p
3d
When an electron drops from an excited
state to a lower energy level, it emits
energy as a photon of light with a
specific wavelength (energy)
n=2
n=1
When an electron absorbs energy, it moves to a
higher energy level (excited state)
1s
Relative energies of subshells within a shell
Spectral lines and transitions between energy levels
0
Lyman
series
(ultraviolet)
(infrared)
4p
4d
4f
n=3
1
Energy
Balmer
series
(visible)
4s
2
Principal energy level, n
Paschen
series
Energy
n=4
6
5
4
3
3s
3p
3d
n=2
2s
1s
2p
For the hydrogen atom (1 electron), the energies
of all subshells within a given principal energy
level are the same
n=1
Relative energies of subshells within a shell
Homework problems
n=4
Chapter 3 Problems:
4s
4p
4d
3.30, 3.72, 3.74, 3.75, 3.76, 3.77, 3.78, 3.79
4f
Energy
n=3
3s
3p
3d
n=2
2p
2s
For atoms with more than 1 electron, the
subshells within a given principal energy
level differ in energy: s < p < d < f
This is due to electron-electron repulsive forces
1s
n=1