Quantum Numbers
and
Electron Configuration
Hyperfine Spectral Lines
http://hyperphysics.phy-astr.gsu.edu/hbase/hyde.html
In the hydrogen atom, you observe in an emission
spectrum occur.
What will you see?
http://www.giangrandi.ch/optics/spectrum/visible-a.jpg
3 lines at
exactly
•656 nm,
•434 nm, and
•410 nm????
1936 -- Neils Bohr and
Arnold Summerfeld
– found hyperfine lines
made up the large
principal spectral lines
What does this mean?
• The presence of hyperfine lines indicated that
there are sublevels within each principal
quantum level!
Locating an electron
• If there are multiple levels within each
principal quantum level, how do we specify
where (in a general sense) the electrons are?
• How do we locate where YOU are?
– How many pieces of information do we need?
Quantum Numbers Preview
• Four Quantum Numbers:
– Principal Quantum #
– Angular Momentum Quantum #
– Magnetic Quantum #
– Spin Quantum #
Principal Quantum Numbers
• Principal Quantum Number
– Symbolized by n
– Main energy level occupied
by an electron
– Values of n are positive 1, 2,
3, etc.
– As n ↑ so does the energy
Angular Momentum Quantum #s
• Angular Momentum Quantum #s
– Symbolized by l
– Often referred to as sublevels
– Indicates the shape of the orbital
• Orbital: 3-D region around the nucleus that indicates the
probable location of the electron
– Values of l less than or equal to n-1
• Examples:
– n=1, then l = 0 (one orbital shape)
– n=2, then l = 1 and 0 (two orbital shapes)
– n=3, then l = ?
• Balloons as a visual aid
l
Letter Designation
0
s
1
p
2
d
3
f
• What do s, p, d, and f
actually stand for?
– Free point for the first
person who finds the
naming scheme.
– A second free point if
you find the second
naming scheme.
Magnetic Quantum #s
• Magnetic Quantum Number
– Symbolized by m
– Indicates the orientation of the orbital
– For a given l, there are (2 l +1) integral values of m
– from - l, (- l +1),. . . 0. . . (+ l -1), + l
• Examples:
– For the d orbital, l = 2 so m = -2, -1, 0, 1, 2
s orbitals
Which one
represents the
highest energy
level?
Electron density plot
The lowest?
s Orbital shape
Each s sublevel
holds 2 electrons
From Zumdahl, Chemistry 5th edition
p orbitals
Each p orbital holds:
2 electrons x 3 orientations = 6 total electrons in the p sublevel.
d orbitals
Each d orbital holds:
2 electrons x 5 orientations = 10 total electrons in the d sublevel.
f orbitals
Each f orbital holds:
2 electrons x 7 orientations = 14 total electrons in the f sublevel.
Spin Quantum #
• Spin Quantum #
– Electrons are spinning on an internal axis which
creates a magnetic field
– There are 2 possible spins
• +½
• -½
– How do magnets work?
Back to the original question
• How do we specify where (in a general sense)
the electrons are?
• Electron configuration: the arrangement of
electrons in an atom.
• Rules governing electron configuration
– Aufbau Principle
– Pauli Exclusion Principle
– Hund’s Rule
Aufbau Principle
• Aufbau Principle: an electron will occupy the
lowest-energy orbital that can receive it.
http://chemed.chem.purdue.edu/genchem
/topicreview/bp/ch6/graphics/6_22.gif
Pauli Exclusion Principle
• Pauli Exclusion Principle: no two electrons in
the same atom can have the same set of four
quantum numbers.
– Example: For the electrons in He (ground state),
what are:
• the principal quantum number(s),
• orbital type, and
• Spin?
Hund’s Rule
• Hund’s Rule: orbitals of equal energy are each
occupied by one electron before any orbital is
occupied by a second electron, and all
electrons in singly occupied orbitals must have
the same spin.
– The school bus analogy
• Example:
– What are the spin quantum numbers for the
electrons in the 2p orbital of oxygen?
What is the electron arrangement for Nitrogen?
1. How many electrons does Nitrogen have?
Principal
Total e(2n2)
Orbital
(sublevel)
Max # ein sublevel
Total e- in
sublevel
Spin
What is the electron arrangement for Nitrogen?
1. How many electrons does Nitrogen have? (7 e-)
2. Electrons in the first quantum level?
Principal
Total e(2n2)
Orbital
(sublevel)
Max # ein sublevel
Total e- in
sublevel
Spin
What is the electron arrangement for Nitrogen?
1. How many electrons does Nitrogen have? (7 e-)
2. Electrons in the first quantum level?
3. Electrons in the second quantum level?
Principal
Total e(2n2)
Orbital
(sublevel)
Max # ein sublevel
Total e- in
sublevel
Spin
1
2
1s
2
2
+1/2, -1/2
What is the electron arrangement for Nitrogen?
1. How many electrons does Nitrogen have? (7 e-)
2. Electrons in the first quantum level?
3. Electrons in the second quantum level?
Principal
Total e(2n2)
Orbital
(sublevel)
Max # ein sublevel
Total e- in
sublevel
Spin
1
2
1s
2
2
+1/2, -1/2
2
8
1s
2
2
+1/2, -1/2
2p
6
3
+1/2, -1/2
Nitrogen:
Nitrogen:
Daily Questions
1. In what orbitals (sublevels) can you find electrons in
the ground state of oxygen?
2. What are the quantum spin #s for the 2 outermost
electrons in magnesium?
3. What are the quantum spin numbers for the
electrons in the 3d orbital of titanium?
4. How many electrons are in the 2p orbital of neon?
5. Which principal energy level can hold 18 electrons?
6. Do the 2 electrons in the 3s orbital of calcium have
the same or different spin quantum number? Why?
Do the 2 electrons in the 2p orbital of carbon have
the same or different spin quantum number?
Notations for Electron Configuration
• There are 3 ways to show electron
configuration
– Orbital Notation Model
– Electron Configuration Model
– Lewis Dot (Electron Dot) Notation
Orbital Notation Model
1s
2s
2p
or
1s
2s
Closer to
the nucleus
What are the
advantages and
disadvantages of this
notation?
Each arrow represents
a spinning electron
2p
Further from
the nucleus
Each box
represents an
orbital
Electron Configuration Notation
1s2
1s
2s
# of electrons in
the orbital
2p
Angular momentum
quantum #
Principal
Quantum #
Another example:
1s22s22p3
1s
2s
2p
What element is this?
What are the
advantages and
disadvantages of this
notation?
The Ultimate Cheat-sheet
What is the electron configuration notation for:
Carbon?
Potassium?
Chromium?
Neodymium?
Daily Questions
1. Use the orbital notation model to represent
the electron arrangement in fluorine.
2. What is the orbital notation for sodium?
3. Use the electron configuration notation to
represent vanadium.
4. Use the electron configuration notation to
represent iron.
5. What element has its 4 outermost electrons
in the 3d orbital?
A Short Cut
• Noble Gas Configuration
– Can shorten the notation by beginning with the
last completed noble gas, then adding what is left:
• For example: Mg
– Long version: 1s22s22p63s23s2
– Short version: [Ne] 3s2
– Imagine the time you’ll save when you have to do
Uranium. . .
Lewis Dot (Electron Dot)
• Only represents the outer-most s & p sublevel
electrons (these are called valence electrons).
• Represents the electrons as dots in pairs (or
orbitals) around the element symbol.
• Example:
– Oxygen: O
– Boron:
B
s
d
p
f
Daily Questions
1. Use the Noble Gas electron configuration notation
to represent Titanium.
2. Use the Lewis Dot notation to represent Carbon.
3. Use the Lewis Dot notation to represent Fluorine.
4. Use the (Noble Gas) electron configuration notation
to represent gold (Au).
5. Use the Noble Gas electron configuration notation
to represent Neodymium (Nd).
6. Use the Lewis Dot notation to represent Selenium
(Se).