Transcript The Electronic Structure of the Atom

The Electronic Structure of the
Atom
Created 30March2005
by Dan Smith
Fundamental questions:
• How are the electrons arranged within
atoms of different elements?
• How do the arrangements affect an
element’s chemical and physical
properties?
What do we know about electrons?
• They’re very small, having on about
1/2000th the mass of a proton.
• They move around the nucleus of an atom
at about 35% of the speed of light.
• Like light, they behave both like particles,
and like waves!
Quantum Mechanics
• Because they’re tiny, move so fast, and
have wave-like properties, we can’t use
ordinary physics to describe the
movement of electrons.
• Instead, we use quantum mechanics, a
statistical approach which tells us where
electrons are most likely to be found
around an atom’s nucleus.
Quantum Mechanics
• An equation called Schrodinger’s
Equation, describes the most likely regions
for electrons around an atom’s nucleus.
OK, so what part of…
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Just kidding!
…don’t you understand?
Heisenberg’s Uncertainty Principle
• Another physicist in the early 20th century,
Werner Heisenberg, stated that the
problem of understanding electrons was so
severe that “both the exact position and the
velocity (movement) of an electron can’t be
determined at the same time.”
• We call this problem “Heisenberg’s
Uncertainty Principle.”
Huh?
• Imaging trying to play pool in the dark.
The pool balls are electrons bouncing
around inside an atom, but we can’t see
them..
• Since you can’t see the balls, the only way
to know where a ball is or how it’s moving
is to reach out and try to grab a pool ball.
Doesn’t that change things?
• The problem with reaching out for a
moving billiard ball is that your interaction
with it changes how it moves.
• It’s the same with electrons inside atoms.
By reaching in with a wave of light to study
what the electrons are doing, we change
what they are doing.
Describing an electron’s position
• Even though we can’t know where an
electron is at a given instant, we can
describe its most probable location with a
set of 4 quantum numbers.
• Here’s an analogy…
Going away to college
• When you go to college, you’ll probably live in a
dorm room, and you’ll probably have a
roommate.
• If you ordered pizza one night, the delivery
person would need to know what floor of the
dorm you lived on, what hallway or wing on that
floor, what room, and finally which person (you
or your roommate) to hand the pizza to.
The 1st quantum number
• The 1st quantum number is called the
principle quantum number or “energy
level” of the electron.
• It has the symbol “n” and n = 1, 2, 3,…,7.
• In other words, there are 7 energy levels
or “floors” that electrons can live on inside
an atom.
The first energy level (n=1) is pretty far away from the nucleus.
The spacing between levels becomes progressively smaller,
the farther from the nucleus one moves.
1
2
3
4
5
Energy levels
• The lower energy levels are smaller, meaning
they can’t hold as many electrons.
• The maximum number of electrons that an
energy level can hold is 2n2.
•
•
•
•
The first energy level holds 2(12) or 2 e-.
The 2nd level holds 2(22) = 8 e-.
The 3rd level holds 2(32) = 18 e-.
How many could the 4th level hold? 32 e-
The 2nd quantum number
• Energy levels are divided into sublevels, just like
the floors of your dorm will have different
hallways.
• These sublevels have a quantum number called
the “azimuthal” quantum number, with the
symbol “l”. For each “n”, “l” is allowed to have
values of 0…n-1.
• Another way of saying this is the larger the
energy level (higher n), the more sublevels it can
have.
Sublevels
• An energy level can have as many
sublevels as its “n” number.
• The 1st energy level has only 1 sublevel;
the 2nd level has 2 sublevels; the 3rd level
has 3 sublevels; the 4th has 4 sublevels.
• An atom usually only uses 4 sublevels, so
the 5th, 6th, and 7th energy levels still only
have electrons in 4 sublevels.
Here are the possible level /
sublevel combinations…
•
•
•
•
•
•
•
1s
2s
3s
4s
5s
6s
7s
2p
3p
4p
5p
6p
7p
3d
4d
5d
6d
7d
4f
5f
6f
7f
(5g is possible, but not used)
(6g, 6h possible but not used)
(7g, 7h, 7i possible but not used)
More about sublevels
• The 4 types of sublevels are given the
symbols s, p, d, and f.
• s is for “simple” or “spherical”.
The illustration at
the left shows
the 1s, 2s, and 3s
sublevels.
p sublevels
• p sublevels are
shaped like dumbbells. There are 3
types of p
sublevels: px, py,
and pz.
• The little subscript
letters simply show
the direction that
the p sublevel
points.
Which levels can have p sublevels? Only level 2 and higher
d sublevels
• The d
sublevels
are more
complicated
in shape.
• There are 5
types of d
sublevels:
Which levels can have d sublevels?
Only level 3 and higher.
f sublevels
• The 7 types
of f sublevels
have the
most
complicated
shapes:
What energy levels
can have f sublevels?
Only level 4 and above
Sublevel summary
• s sublevels are the simplest. An s
sublevel can only hold 2 electrons in 1
orbital. (More about orbitals in a minute.)
• p sublevels can hold 6 electrons in 3
orbitals (px py and pz).
• d sublevels can hold 10 electrons in 5
orbitals.
• f sublevels can hold 14 electrons in 7
orbitals.
So what is an orbital?
• Just like levels are divided into sublevels…
• Sublevels are divided into orbitals.
• Going back to our dorm analogy, orbitals
are like the individual dorm rooms where
people live.
• An orbital can hold from 0 to 2 electrons
(but never more than 2).
Orbitals – the 3rd quantum number
• Orbitals within a sublevel are described by the
magnetic quantum number, symbol m.
• m is allowed to have values of
- l…0…+l
• The larger the sublevel, the more orbitals it can
have:
• s sublevels have 1 orbital
p’s have 3
• d’s have 5 orbitals and f’s have 7 orbitals
Let’s double-check the math
• We already know that the 4th energy level
can hold 32 electrons: 2(42) = 32.
• Does this agree with the orbitals? Sure!
• 4s = 2 e• 4p = 6 e• 4d = 10 e• 4f = 14 e• Add them together: 2 + 6 + 10 + 14 = 32 e-
The 4th quantum number
• The last quantum number describes the
individual electrons within an orbital.
• It’s called the “spin” quantum number,
symbol ms.
• This quantum number has a value of
either +½ or -½.
electrons spin!
• Just like the earth spins on its axis while it
revolves around the sun, electrons also
spin while they orbit the nucleus.
• Their spin is either clockwise (+½) or
counter-clockwise (-½).
• When 2 electrons share the same orbital,
they always have opposite spins!
The Pauli Exclusion Principle
• Just like no 2 people in a dormitory would
have an identical address, no 2 electrons
in an atom have the exact same set of
quantum numbers.
• This is the Pauli Exclusion Principle
(Within an atom, no two electrons have the
same set of quantum numbers.)
An example
• Let’s say that 2 electrons occupy the 3rd
energy level, p sublevel, and they both
share the px orbital.
• If the quantum numbers for the first
electron are (3, 1, -1, +½), what are the
quantum numbers for the other electron?
Since they share the same orbital, the first three
quantum numbers will be the same. However, they
must have different spins: 3, 1, -1, -½.
A shift in focus
• Now that we know how to describe an individual
electron in terms of its 4 quantum numbers…
• …let’s shift focus, and learn how to describe an
entire atom full of electrons, and where all the
electrons live.
• This would be similar to the master list of who
lives in what room for our dorm analogy.
• This master list is called the atom’s electron
configuration.
Electron configurations
• An electron configuration for an atom will look
like this:
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p5
• This is the electron configuration for Br.
• The large numbers show the energy levels that
contain electrons.
• The letters show the sublevels which contain
electrons.
• The superscripts show how many electrons live
in each sublevel.
Putting an atom together
• When an atom is put together, the
electrons always fill the lowest energy
level and sublevel first, until it’s full, then
they begin filling the next higher energy
level / sublevel.
• s sublevels are slightly lower in energy
than p’s, which are lower than d’s , which
are lower than f’s.
Here you can see how the sublevels spread out in
terms of energy.
A problem develops
• One problem with these sublevels
spreading out in energy, is that some
overlap develops between sublevels of the
3rd and 4th level, the 4th and 5th level, etc.
• This means that we don’t fill sublevels in
numerical order (but we do in order of
increasing energy!)
Here, you
can see the
overlap
between the
4s and 3d
sublevels.
These
overlaps
become
more
complicated
as you go
farther up.
Keeping the order straight
• So, how can we get the proper order for
filling up these energy level / sublevel
combinations?
• We use a chart called the Aufbau
Principle, also known as the “Diagonal
Rule”.
The Diagonal Rule
1s
2s
3s
4s
5s
6s
7s
2p
3p
4p
5p
6p
7p
3d
4d
5d
6d
7d
4f
5f
6f
7f
Start with the top
arrow. Follow
the next arrow
in order until
all electrons have
been placed into
the proper
level / sublevel.
Let’s try some examples
• H has only 1 electron. It’s e- configuration
is 1s1.
• He has 2 electrons: 1s2
• Li has 3 electrons: 1s2 2s1
• Be has 4 electrons: 1s2 2s2
• B has 5 electrons: 1s2 2s2 2p1
• F has 9 electrons: 1s2 2s2 2p5
• Notice something: the superscripts add up
to the atomic number of the element!
Quick Quiz
• Fe has 26 electrons. What would it’s
electron configuration be?
1s2 2s2 2p6 3s2 3p6 4s2 3d6
The superscripts add up to 26.
The sublevels are in order according to
the arrows on the Diagonal Rule.
Connection between atomic
structure and the periodic table
• You know that the periodic table has an
unusual shape and arrangement. This
isn’t by chance, but actually reflects the
arrangement of electrons within the
elements.
• The periodic table is broken into 4 blocks
or regions called the s block, p block, d
block and f block.
Each row of each block is filling up one of the level /
sublevel combinations on the diagonal rule!
Notice that the d block is forced down 1 level (3d
follows 4s) because of the overlap in sublevels.
The f block is forced down 2 levels (4f follows 6s).
How many columns in each block?
• Look at your own periodic table and count
the number of columns in each block.
• The s block has 2 columns (s2). We
already know that an s sublevel has only 1
orbital which can hold a maximum of 2 e-.
• The p block has 6 columns (p6). The p
sublevel has 3 orbitals which can hold a
maximum of 6 e-. Not a coincidence!
It’s easy to find an element’s
electron configuration.
• To find an element’s electron
configuration, look for its position on the
periodic table.
• Argon (Ar, atomic # 18) is on the 3rd row,
in the p block, in the 6th column of the p
block. Its electron configuration will end in
3p6.
• 1s2 2s2 2p6 3s2 3p6 (= 18 electrons)
You try a couple…
• What will the electron configuration for Sr
end in? (5th row, s block, 2nd column in s
block)
If you said it will end in 5s2, you were right.
• What will the full electron configuration for
Sr be?
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2
38 e-, superscripts total 38
What element?
• What element would have the electron
configuration
1s2 2s2 2p6 3s2 3p6 4s2 3d3
(4th row because 3d’s are forced down 1
row, d block, 3rd column of the d block)
I sure hope you said V, vanadium
Another quick quiz
• Which of the following pieces of electron
configurations can’t exist?
• 2p7
3s3
3d9
2d5
4f14
1p3
2p7 – no more than 6 electrons in a p sublevel
2d5 – the 2nd energy level has no d sublevel
1p3 – the 1st energy level has no p sublevel
Shorthand notation
• Some of these electron configurations can
get pretty long:
1s22s22p63s23p64s23d104p65s24d105p66s2
4f145d106p67s25f3 is U, uranium
• Shouldn’t there be a quicker way of writing
these things? There is – shorthand
notation.
More shorthand
• 1s22s22p63s23p64s23d104p65s24d105p66s2
4f145d106p6 is the electron configuration
for Rn, radon, a noble gas.
• We can write U as [Rn] 7s25f3. Lots
shorter than the full thing.
• What you write in the brackets is the
symbol of the noble gas that is just lighter
in atomic number than the element you’re
working with.
Example
• What’s the shorthand notation electron
configuration for Ca?
• The noble gas which is just lighter than Ca
is Ar. You can write Ca as [Ar] 4s2.
• What would the shorthand notation for Sb,
antimony, be?
If you said [Kr] 5s24d105p3, you were right.
exceptions to “normal” electron
configurations
• There are always exceptions to every rule.
• 2 exceptions are Cr and Cu.
• Cr should be 1s22s22p63s23p64s23d4.
However, it is …4s13d5.
• The reason for this is that the atom can be
slightly lower in energy (a goal of every
atom!) if it can have a half-full d sublevel.
Another exception…Cu
• Cu is also an exception.
• It should be 1s22s22p63s23p64s23d9.
• However, it is …4s13d10.
• This time, the atom is a lot lower in energy
because it has a full 3d sublevel. Being
lower in energy makes the atom more
stable.
Other exceptions
• There are several other exceptions:
– Mo behaves like Cr: …5s24d4 becomes
…5s15d5
– Ag and Au behave like Cu: …s2d9 becomes
…s1d10 for a full d sublevel.
Orbital filling diagrams
• Orbital filling diagrams are a way of
visually accounting for the electrons in an
atom.
• We make a box or dash for each orbital
within an atom, then use up and down
arrows to show the electrons. The
different arrow directions reflect the
electrons’ different spins.
An example
• Neon has the electron config 1s22s22p6.
• The orbital filling diagram would look like
this:
1s
2s
2p
Another example
• Zinc is 1s22s22p63s23p64s23d10
• It’s orbital filling diagram would look like:
1s2
2s2
2p6
3s2
3p6
4s2
3d10
What about elements that don’t
have full sublevels?
• How about something like nitrogen, with
1s22s22p3 ?
• Another rule comes into play: Hund’s rule.
• Hund’s rule says that within a sublevel, no
orbital can have a 2nd electron before all
orbitals get their first electron.
More Hund’s Rule
• I think of Hund’s rule as the Thanksgiving
Dinner rule. Nobody gets seconds at
Thanksgiving dinner before everybody has
gotten their first plate.
• How does this apply to nitrogen? 1s22s22p6
Each of the 2p orbitals
- before any
got
an
e
1s2
2s2
2p3
orbital got a 2nd e-.
The spins of the electrons always line up.
Another example
• How about oxygen? 1s22s22p4
1s2
2s2
2p4
• You try Si, silicon.
1s2
2s2
2p6
3s2
3p2
Thanks!
• If you kept up with all this stuff – terrific! It
can be tough to learn.
• If not, please ask! I’ll be happy to explain
it to you.
• Be sure you complete “The Electronic
Structure of the Atom and the Electron
Configurations of the Elements”
homework.