Transcript Four Quantum Numbers

• Four Quantum Numbers:
– Specify the “address” (zip code) of each
electron in an atom
First number…Principal Quantum
Number ( n)
• Energy level (associated with the electron)
• Size if orbital
– Lowest energy level is assigned principle quantum number of 1
(n=1)
• Ground state
– What do you think happens as we increase n?
• Orbital becomes larger
• Electron spends more time farther away from the nucleus
atom’s energy increases
Principle energy levels
contain…
Energy Sublevels
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Principle energy level 1 single sublevel
Principle energy level 2 two sublevels
Principle energy level 3 three sublevels
What pattern do you see in the number of
sublevels as we move further away from the
nucleus?
– They increase as n increases (the further we get from
the nucleus)
UPPER LEVEL
• Electron’s are labeled
according to n value
• In atom’s with more than
one electron, two or more
electron’s may have the
same n value
– They are in the same
“electron shell”
Second quantum number
Angular Momentum Quantum
Number (l)
• Each value of l corresponds to a different
type of orbital with a different shape
• Value of n controls l (subshells possible)
• Angular momentum numbers can equal 0, 1,
2, 3…
• l=n-1
– When n=1, l=0 only one possible subshell
– When n=2, l=0,1 two possible subshells
What the number of l means…
• Corresponds to the name of the subshell
– L=0 subshell s
– L=1 subshell p
– L=2 subshell d
– L=3 subshell f
S P D F: THE SUBLEVELS
• Each of these 4 sublevels has a unique shape
• Each orbital may contain at most, 2 electrons
• LETTERS ORIGINATED FROM
DESCRIPTIONS OF THEIR SPECTRAL LINES
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S sharp…spherical
P principal…dumbbell shaped
D diffuse…not all the same shape
F fundamental…not all the same shape
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When principle energy level n=1, then l=0, which means there is only a
single sublevel (one orbital) which is the small, spherical 1s
When principle energy level n=2, then l can equal 0 or 1, which means
that there are two sublevels (orbitals) 2s and 2p
– 2s sublevel bigger than 1s, still sphere
– 2p sublevel three dumbbell shaped p orbitals of equal energy called 2px,
2py, and 2pz
• The letters are just there to tell you what axis the electrons go on: x,y, or z axis
•
When the principle energy level n=3, then l can equal 0,1, or 2, which
means that there are 3 possible sublevels:
– 3s, sphere, bigger than 1s and 2s
– 3p, dumbbells
– 3d
•
• Each d sublevel consists 5 orbitals of equal energy
• Four d orbitals have same shape but different orientations
• Fifth d orbital, 3dz2 is shaped and oriented different from the other four
When the principle energy level n=4, then 1 can equal 0,1,2, or 3 which
means l=n-1=4 possible sublevels:
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Seven f orbitals of equal energy ( 2 electrons in each orbital)
4s, sphere
4p, dumbbells
4d,
4f
n
=
# of sublevels per level
n2 =
# of orbitals per level
Sublevel sets: 1 s, 3 p, 5 d, 7 f
Orbitals combine to form a spherical
shape.
2s
2px
2py
2pz
Remember…
1. Principal # energy level
2. Ang. Mom. #
sublevel (s,p,d,f)
There are two more quantum
numbers (3 and 4) we will
discuss next class
Third Quantum Number
• Ml specifies the orientation of the orbital
in space containing the electron
• Tells us whether the orbital is on the x, y,
or z axis
Fourth Quantum Number
• Ms related to the direction of the
electron spin
• Tells us if electron has a clockwise
spin or counter clockwise spin
• Specifies orientation of electrons
spin axis
Recap…
• Bohr?
– Orbits explained hydrogen’s quantized energy
states
• De Broglie?
– Dual particle and wave nature of electrons
• Schrodinger?
– Wave equation predicted existence of atomic
orbitals containing electrons
Electron Configuration
• Definition: arrangement of electrons in an atom
• Basic rules for filling up orbital's with electrons
• Which is more stable, low energy or high
energy?
– So which orbitals are going to be filled up first?
– We are going to want an arrangement that gives us
the lowest possible energy
Ground state electron configuration
• The most stable, lowest energy electron
arrangement of an atom
• Each element has a ground-state electron
configuration
Three Rules for Electron
Arrangement
• Aufbau Principle
• Pauli Exclusion Principle
• Hund’s Rule
Aufbau Principle
• Each electron occupies the lowest energy orbital
available
• In order to do this, you must learn the sequence
of atomic orbitals from lowest to highest energy
• Aufbau Diagram
– Each box represents an orbital
– Each arrow represents an electron
– Only two arrows per box…
• Only two electrons per orbital
Some important things to
remember about Aufbau…
• All orbitals related to an energy sublevel
are of equal energy
– All three 2p orbitals have the same energy
• In a multi-electron atom, the energy
sublevels within a principle energy level
have different energies
– All three 2p orbitals are of higher energy than
the one 2s orbital
• In order of increasing energies, the
sequence of energy sublevels within a
principle energy level is s, p, d, f
• Orbitals related to energy sublevels within
one principle energy level can overlap
orbitals related to energy sublevels within
another principle level
– Ex. An orbital related to the atoms 4s sublevel
has a lower energy than the five orbitals
related to 3d sublevel.
Pauli Exclusion Principle
• States that a
maximum on 2
electrons can occupy
a single atomic orbital
but only if the
electrons have
opposite spins
• Wolfgang Pauli
• Austrian Physicist
• Observed atoms in
excited states
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Each electron has a spin
Kinda like a spinning top
It can only spin in one of 2 directions
In order for electrons to be together in an
orbital, they must have opposite spins
Hund’s Rule
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What kind of charge do electrons have?
Do they attract or repel each other?
So……..
Hund’s Rule states that single electrons with the
same spin must occupy all each energy equal
orbital before additional electrons with opposite
spins can occupy the same orbital
2p orbitals
Read
section 5-3!