Transcript AP electron theory

Electron Structure within
an Atom
An NaClmann Presentation
Contributing Theories
Before we talk about electrons, we actually must
first have a discussion of light. Why? They are
more similar than you might think
Light is one small portion of the
electromagnetic spectrum
Is light made of waves
or particles?
Some scientists believed that light is a wave because:
it has a measurable frequency and wavelength
it reflects & refracts just like a wave
it can be diffracted like a wave
Some scientist believed that light is a particle because:
waves cannot travel in the vacuum of space; particles
can and so can light
How about both?
Thomas Young theorized that Light could be comprised
of particles that moved in wave-like patterns.
Max Planck proved that light does have tiny particles
which he called photons. These photons create the
medium upon which the light waves travel.
“Light” Facts
Light travels through space (and air) at a speed
of about 186000 miles per second or
300,000,000 meters per second. The symbol for
the speed of light is c.
The speed of a light wave is equal to the
wavelength times the frequency. c =   ***
The energy of a photon depends on its
frequency. E=H  (h= 6.626 x 10-34 Js)
About units
For speed, we will use 300,000,000 m/s.
For wavelength, we will use meters.
For frequency, we will use Hertz (Hz) which is the
same thing as 1/s.
Energy is measured in Joules (J), just as we did for
heat and work.
Sample Questions
If the wavelength of a photon is 425 nm, what is its
frequency?
How much energy would the photon in the previous
question have?
The Answers
c=   c = 3.00e8 m/s &  = 425nm = 4.25e-7 m
so,  = c/ = (3.00e8 m/s) / (4.25e-7 m)
 = 7.06e14 Hz
E=H  H = 6.626e-34 Js &  = 7.06e14 Hz
so E =(6.626e-34 Js)*(7.06e14 Hz)
E = 4.68e-19 J
So what does this have to
do with electrons?
We have already seen that different elements give off
different colored light when heated.
We have also seen that elements like neon give off
colored light when electrified.
Spectral Line Emissions
Element Fingerprinting
When chemicals are subjected to high voltage and
viewed through a spectroscope, a very specific
spectral emission pattern is generated.
Every element has its own unique spectral emission.
What is different then about each element that it would
have a different spectral emission?
Niels Bohr
Planetary model of
electrons - electrons move
in circular orbits about the
nucleus. When an
electron jumps up to a
larger orbit, energy is
absorbed. When the
electron moves back
down, it emits light. This
would explain the spectral
line emissions.
Excited States
When an electron absorbs energy, it jumps to a bigger
ring. This is called an excited state.
When all electrons are in the lowest possible rings, the
atom is said to be in the ground state.
When an electron releases this energy, it returns to a
smaller ring, releasing energy in the form of light.
Energy and Energy Levels
The energy for any particular energy level (n) is:
E = (-2.178x10-18 J)/n2
The Energy for any particular jump then depends on
the initial energy level Ni and the final energy level Nf
∆E = (-2.178x10-18 J)*[(1/nf2) - (1/ni2)]
Wavelength
Because we know of the relationship between energy and
frequency (E =  ), we know that:  = E/
Because we know of the relationship between frequency and
wavelength (c =   we know that c / 
So, we can infer that 
Substituting in, we can then say that if an electron is moving
towards the nucleus, and thus emitting a photon of light, the
wavelength of the light is : 1/ = (1.097x107 m-1)(1/nlow2 – 1/nhigh2)
Another example
An electron drops back from the 7th energy level to
the 2nd energy level, emitting a photon. What is the
wavelength of the photon?
The wavelength is...
1/ = (1.097x107 m-1)(1/nlow2 – 1/nhigh2)
1/ = (1.097x107 m-1)(1/22 – 1/72)
1/ = (1.097x107 m-1)(1/4 – 1/49)
1/ = (1.097x107 m-1)(.22959)
1/ = 2518622 m-1
 = 3.97 x 10-7 m = 397 nm
Calculate...
Calculate the energy needed for an electron to go from
the 6th energy level to the 2nd.
Two ways to solve this
We can first find the wavelength (1/ = (1.097x107 m1)(1/n
2
2
low – 1/nhigh ))  
Teweouldfidtefrequey( = c/  = 7.32x1014 Hz
Teweouldfidteeergy(E=H  4.84x10-19 J
Or we could combine
 = c/ o1/ = (1.097x107 m-1)(1/nlow2 – 1/nhigh2) becomes
 = c(1.097x107 m-1)(1/nlow2 – 1/nhigh2)
E=H  oE=H c(1.097x107 m-1)(1/nlow2 – 1/nhigh2)
H, c, and (1.097x107 m-1) are all constants. If we multiply them
together we get 2.18 x10-18 J
so E = (2.18 x10-18 J)*(1/nlow2 – 1/nhigh2)
E = (2.18 x10-18 J)*(1/22 – 1/62) = 4.84x10-19 J(aeabefore
A few more Scientists
Louis deBroglie - Particles (electrons) can exhibit
wavelike behavior.
Werner Heisenberg - The Uncertainty Principle - It is
impossible to see the location or momentum of an
electron without changing it!
Irwin Schrodinger - Quantum Probability Theory - If we
can’t know the position and speed of an electron, we
can still make good estimations.
The first Quantum Number
1) The Principal (Primary) Quantum Number - n Indicates the energy level or shell about the nucleus
in which an electron can be found
n can be a positive integer, usually from 1 to 7
(although in theory higher numbers are possible).
n=1 means the energy level closest to the nucleus.
The Second Quantum Number
2) The Azimuthal Quantum Number - l - Indicates the shape of
the path or orbit (subshell) which the electron takes about the
nucleus.
L must be an integer from zero to n-1.
So if n=2, L can only be zero or one.
Any given energy level can have n subshells
So the first energy level can have 1 subshell, the second
energy level can have 2 subshells, etc.
Subshells
If l=0, the subshell
is called s.
If l =1, the subshell is called p.
If l=2, the subshell is called d.
If L=3, the subshell is called f.
The third Quantum Number
The magnetic quantum number - m(ml) - describes the
orientation of the orbital in 3D space. An s has 1
orbital, a p has 3 orbitals, a d has 5 orbitals, and an f
has 7 orbitals. Refer back to the images of the
subshells.
Each orbital can hold a maximum of 2 electrons.
M is an integer value from -L to +L. So if L=2, M can
be -2, -1, 0, 1, 2.
There were only 3 quantum #s
Now thanks to Wolfgang Pauli we have four.
The Pauli Exclusion Principle states that every
electron in an atom must have a different set of 4
quantum numbers.
This means that if one electron in an atom is
described by n=4, l=2, m=2, s=½, then no other
electron in that atom can have the same exact
description.
The Fourth Quantum Number
The spin quantum number - s (ms) - describes the
rotation of the electron on its axis. Clockwise or
counterclockwise.
Based on calculations, s can only be +1/2 or -1/2.
The spin quantum number was determined by Pauli
(as part of the Pauli Principle), not by Schrodinger.
Each shell (n) can only have n subshells. So, the first shell (or
energy level) can only have 1 subshell. The second shell can
have two subshells, etc.
Key Facts to remember
The subshells are filled according to their numeric value. So
for each shell, first comes the s subshell, then the p if possible,
then the d if possible, and then the f if possible.
Each subshell has a specific number of orbitals as mentioned
earlier. An s subshell only has 1 orbital, a p has 3 orbitals, a d
has 5 orbitals and an f has 7 orbitals.
Each shell has n2 orbitals total.
Because there are only two possible spins, each orbital can
only hold 2 electrons.
Each shell can have up to 2n2 electrons.
How many subshells can the 4th shell hold?
Sample
If n=2, and l=1, whatquestions
type of subshell is described?
How many orbitals are in the subshell described in #2?
How many electrons can occupy the subshell described in #2?
If n=5 and l=3, what are the possible values of the m?
How many electrons in an atom can have n=4?
How many electrons in an atom can have n=4 and l=2?
How many electrons in an atom can have n=4, l=2, and m = 3?
How many electrons in an atom can have n=4, l=2, and m = 2?
How many subshells can the 4 shell hold?
Each shell can have up to n subshells. The 4th energy
level can hold 4 subshells.
Answers and Explanations
If n=2, and l=1, what type of subshell is described?
Whenever l=1, the subshell is a p.
How many orbitals are in the subshell described in #2?
A p subshell always has 3 orbitals.
How many electrons can occupy the subshell described in #2?
Since a p has 3 orbitals, and any orbital can hold 2
electrons, a p can hold up to 6 electrons.
The 4th energy level can hold 32 electrons. Each shell can
have up to 2n2 electrons.
Answers and Explanations
How many electrons in an atom can have n=4 and l=2?
When l=2, the subshell is a d. A d has 5 orbitals and any
orbital holds 2 electrons, so there are 10 electrons with those
2 quantum numbers.
How many electrons in an atom can have n=4, l=2, and m = 3?
m must be from +l to -l. This is not possible.
How many electrons in an atom can have n=4, l=2, and m = 2?
m specifies a particular orbital, and any orbital holds 2
electrons.
The Aufbau Principle
Electrons fill orbitals based on
lowest energy. So in general,
the first shell (or energy level)
will fill before the 2nd, etc.
Likewise, the s subshell is
lower energy than the p
subshell, so the subshells fill
as expected. However, d
orbitals and f orbitals are very
complex and require more
energy, so they fill out of
order.
There is a simple way!
The actual order of orbital filling
is best described by the diagonal
rule, seen here. Since an orbital
holds 2e-, and an s subshell has
1 orbital, we can deduce that an
s subshells can hold up to 2e-.
Likewise we can deduce that a p
can hold up to 6e-, a d can hold
up to 10e-, and an f can hold up
to 14e-. By following the
diagonal rule, we can map out
all of the electrons location in an
atom.
The Electron Configuration of
Carbon
Carbon has 6 electrons. So
we look at the diagonal rule.
The first line goes through
1s2. The next line goes
through 2s2. The next line
starts through 2p6, but we
don’t need 6, we only need 2
more. The electron
configuration is: 6C: 1s2 2s2
2p2
Try These
19K
51Sb
82Pb
And
the
are
19K: 1s
2 2s2answers
6
2
6
2p 3s 3p 4s1
51Sb:
2
1s
2
2s
6
2p
2
3s
6
3p
2
4s
10
3d
6
4p
5s2 4d10 5p3
82Pb:
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6
5s2 4d10 5p6 6s2 4f14 5d10 6p2
Using Quantum numbers
In the electron configuration, only two quantum
numbers are used for each electron.
Example 2p6 :
The 2 represents the principal quantum number we are saying n=2; the electrons are in the 2nd
shell.
The p represents the azimuthal quantum
number - we are saying l=1; the shape of the
orbit is a p.
Orbital Notations
An orbital notation is often used along with an electron
configuration to indicate all 4 quantum numbers.
Remember that an orbital is one possible orientation
within a subshell in which 2 electrons can reside.
The two electrons must spin in different directions.
An s can only have 1 orbital, a p can have 3, a d can
have 5, and an f can hold 7.
How to draw an Orbital Notation
In an orbital notation, a line, circle or a box is drawn for each
orbital. Arrows are placed inside, going up or down, to indicate
the spin of the electron.
We need to draw a single line under each s, 3 lines under each
p, 5 lines under each d, and 7 lines under each f.
Count off the electrons in each subshell, first placing an up
arrow in each orbital, then going back to place a down arrow in
each orbital, as needed
Hund’s Rule
Friedrich Hund realized that electrons, being negatively
charged, would repel one another. So, additional energy is
required to put two electrons into the same energy, even if they
have opposite spins.
If an atom is in its ground state (meaning lowest possible energy
state) then its electrons must be spread out into empty orbital
BEFORE they could be paired up to share an orbital.
Think of it this way, would you share a bed with your brother or
sister if there was an empty bed right next door? After all,
electrons are not afraid of the dark.
And what does that mean?
Let’s look at Carbon. Earlier we said that its electron
configuration was 6C: 1s2 2s2 2p2
Its orbital notation then would look like this:
There are two electrons paired up in the 1s and the 2s,
but in the 2p (which has 3 orbitals) the electrons are
split up.
Can you do these?
Write out the electron configuration
and the orbital notation for:
Oxygen
phosphorus
The answers are...
8O:
1s2 2s2 2p4
15P:
1s2 2s2 2p6
3s2
3p3
Electron Dot Structure
When two atoms interact, which electrons are more likely to be
involved? The outermost electrons!
The electrons in the highest energy level are called valence
electrons.
If we look at carbon’s electron configuration(1s2 2s2 2p2), we
see that the highest energy level is the 2nd. In the 2nd energy
level carbon has 2+2 or 4 electrons.
A dot structure is a way of drawing these valence electrons as
dots. So Carbon would look like
More examples
Cl: 1s2 2s2 2p6 3s2 3p5
The highest energy level is the 3rd. So there are 2+5
or 7 valence electrons.
P: 1s2 2s2 2p6 3s2 3p3
The Highest energy level is the 3rd. So there are 2+3
or 5 valence electrons.
Condensed Electron
Configurations
Writing out the full electron configuration is time
consuming.
When we consider how electrons interact, we are
mostly concerned with those subshells at or near
the valence, so why not show that?
Let’s consider lead again:
82Pb:
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2
4f14 5d10 6p2
82Pb:
[Xe] 6s2 4f14 5d10 6p2
How did you get that?
In the condensed form, we work back to the largest
previous Noble gas. in the case of lead, the previous
noble gas was Xenon
Xenon is element #54, and its electron configuration is
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6. So we write
down [Xe] for all of this and pick up from there.
All of this can be read from the periodic table too.