Download Quantum Numbers

Quantum Numbers
Basics of Periodic Table
• Each box on the table represents an element.
• In each box…
– an element symbol
– the element’s atomic number
– the element’s average atomic mass
• Elements arranged in order of increasing
atomic number.
Remember…
• Aufbau principle – electrons fill energy levels
and sublevels in order of increasing energy
• Pauli Exclusion principle – no two electrons
can have the same set of four quantum
numbers (which means no two electrons can
be in the same place at the same time)
• Hund’s rule – when adding electrons to
sublevels with more than one orbital, each
orbital gets its own electron first before
pairing
Also….
• There are energy levels (AKA shells)
• Inside energy levels, there are sublevels (AKA
subshells)
• Inside sublevels, there are orbitals
• Inside orbitals, there are electrons.
The Basics of the 4 QN
• Principle Quantum number (or 1st QN) tells
you the energy level
• 2nd Quantum number tells you which sublevel
(s, p, d, or f)
• 3rd Quantum number tells you which orbital of
that sublevel
• 4th Quantum number tells you the spin
direction of the electron
Principal Quantum number
• Tells you the relative electron cloud size
– The higher the quantum number, the larger the
cloud
• Corresponds to the rows on the periodic table
– 1st energy level = Row 1
– 2nd energy level = Row 2, etc
• You can determine how many electrons are
possible within any energy level by using the
formula 2n2 (where n is the energy level #)
2nd Quantum number
• Tells you the shape of the electron cloud
– The “s” sublevel is spherical
– The “p” sublevel is dumbbell shaped
– The “d” and “f” sublevels are unusually shaped
• Can also determine how many sublevels are
within an energy level
– Energy Level 1 has 1 sublevel (s)
– Energy level 2 has 2 sublevels (s and p)
– Energy level 3 has 3 sublevels (s, p, and d)
– Energy level 4 has 4 sublevels (s, p, d, and f))
s orbitals
p orbitals
d orbitals
f orbitals
3rd Quantum Number
• Tells you the orientation in space of the sublevel
– Does it surround the origin? (s orbital)
– Do they lie on the x-, y-, or z- axis? (p orbitals)
• Defines how many orbitals are contained in a
sublevel.
– s sublevel has 1 orbital
– p sublevel has 3 orbitals
– d sublevel has 5 orbitals
– f sublevel has 7 orbitals
4th Quantum number
• Tells you that there can be only 2 electrons
per orbital and they must have opposite spins
– This is known as the Pauli Exclusion Principle
• Which means that no two electrons can be in the same
place at the same time
• The electrons will be either going clockwise or
counterclockwise.
Drawing Energy Levels
Ground State vs Excited State
• In a ground state atom, all electrons are in the
lowest available sublevels.
• For an atom in the excited state, one or more
electrons have absorbed enough energy to
jump to higher energy levels.
– As soon as possible, those excited electrons will
release that energy in the form of a photon,
possibly as colored light.
Energy
• The above is called an aufbau diagram.
• When using an aufbau diagram, it is easy to
place electrons following the aufbau principle.
• But, when using strips of boxes (like a previous
slide), you need to follow the diagonal rule.
Better yet….
Learn to read the
periodic table.
Blank
Periodic
table
revisited
How the sublevels relate to the periodic table
• The s sublevel has only one orbital, which can hold 2
electrons. That is why there are two columns in the “s”
block.
• The p sublevel has three orbitals, each of which can
hold 2 electrons. That is why there are six columns in
the “p” block.
• The d sublevel has five orbitals, each of which can hold
2 electrons. That is why there are ten columns in the
“d” block.
• The f sublevel has seven orbitals, each of which can
hold 2 electrons. That is why there are fourteen
columns in the “f” block.
Schrödinger’s Equation
• This is not a “derivable” equation.
• This is called an “inspired” equation
• Somehow, from this equation the four quantum
numbers were born.
Quantum Numbers
• Just as a point on an xy-graph needs a set of
two coordinates, each electron has a unique
set of four coordinates.
• These four coordinates represent energy level
(shell), sublevel (subshell), orbital, and spin
direction of the electron.
Principal Quantum number
•
•
•
•
Represented by n
Tells the size of the electron cloud
Corresponds to the rows of the periodic table
Therefore n = 1, 2, 3, and so on
– Which means row 1 on the periodic table
corresponds to energy level 1
2nd Quantum number
• Represented by l
• Called the angular momentum quantum number
• Describes the shape of the orbital
• l can have the values from 0 to n-1 (where n is the
row number)
0 = s sublevel
1 = p sublevel
2 = d sublevel
3 = f sublevel
3rd Quantum Number
• Called the magnetic quantum number
• Describes the orientation in space of the orbital
– Whether the path of the electron lies on the x, y, or z axis
• Represented by ml
•
ml can have values from –l
to +l
– if l = 2, then ml = -2, -1, 0, +1, +2
4th Quantum Number
•
•
•
•
Corresponds to the spin of an electron
Represented by ms
Clockwise represented by +1/2
Counterclockwise represented by -1/2
Therefore
• Mg
(3, 0, 0, -1/2)
• Bi
(6, 1, +1, +1/2)
• Co
(3, 2, -1, -1/2)
• Cf
(5, 3, -1, -1/2)
Diamagnetism/Paramagnetism
• Diamagnetic elements have all of their
electrons spin paired.
– Which means they have complete sublevels.
– Are not affected by a magnetic field
• Paramagnetic elements do not have all of
their electrons spin paired.
– Strongly affected by a magnetic field