Download CHE 106 Chapter 6

CHE 106
Chapter 6
The Dual Nature of Light
Much of what we know about electronic structure – the arrangement
and energies of electrons around the nucleus came from studying the
light that atoms both absorb and release.
Dual Nature of Light:
Light behaves both as a wave and particle (photons). Even electrons
and other solid particles can exhibit wavelike properties.
Much of our experience with light has been light as visible light, but
visible light is only one type of electromagnetic radiation. There are
many other types of ER or radiant energy – x-rays, infrared, gamma
etc. They transmit energy in a wavelike behavior, much as waves in the
ocean.
The Dual Nature of Light
Properties of waves:
Wavelength: distance between two adjacent peaks or troughs
Frequency: the number of complete wavelengths that pass a
given point in one second
These two variables can be related to the speed of light which is
defined as:
c = lu
l: wavelength (lambda)
u: frequency (nu) cycles/sec = Hertz (Hz), s-1 or /s
C: speed of light: 3.0 x 108 m/s
The Dual Nature of Light
Example: A laser is used in eye surgery to fuse
detached retinas and produces radiation with a
frequency of 4.69 x 10-14 s-1. What is the
wavelength of this radiation?
The Dual Nature of Light
Although much of our experience with light is as a
wave, the wave-like properties of light could not
be used to explain several other phenomena:
blackbody radiation, the photoelectric effect and
emission spectra of elements.
The Dual Nature of Light
• Light has both wave-like and particle-like nature
Particulate
Behavior
Wave-like
Behavior
electrons
ejected from
bulk material
Photoelectric Effect
White
Light
Source
Dispersion by Prism
The Dual Nature of Light
• Matter has both wave-like and particle-like nature
Particulate
Behavior
Wave-like
Behavior
electrons
ejected
Electron Ionization
Electron
Beam
Source
Electron Diffraction
The Dual Nature of Light
Blackbody Radiation: Max Planck
When objects are heated, the give off radiation. And
this radiation is related to the temperature.
Red Hot vs. White Hot: Different color and intensity of
radiation is dependent on temperature.
Classical physics could not explain the relationship
between temperature and the color of the emitted
light.
The Dual Nature of Light
Max Planck was able to explain this phenomena
by assuming that energy can be released in
discrete packets called quanta.
Quanta: the minimum energy absorbed or
emitted, whose energy is related to it’s frequency.
E = hv
Where h is Planck’s constant = 6.626 x 10-34 J-s.
The Dual Nature of Light
How to interpret Planck’s equation:
“As the frequency of radiation increases, the energy of that
radiation increases by the increment “h”.”
source:http://www.kentchemistry.com/links/AtomicStructure/PlanckQuantized.htm
So only certain energies are “allowed”, all energy must be a
multiple of Planck’s constant. So in that regard – energy is
quantized – it only exists in distinct quantities. It is not
continuous.
The Dual Nature of Light
The Dual Nature of Light
Light energy may behave as waves or as small particles
(photons).
Particles may also behave as waves or as small particles.
Both matter and energy (light) occur only in discrete units
(quantized).
Quantized
(can stand only on steps)
Non-Quantized
(can stand at any position on the ramp)
The Dual Nature of Light
A laser emits light with a frequency of
4.69 x 1014 s-1. What is the energy of one quantum of
this energy?
ANSWER: 3.11 X 10-19 J
The laser emits in energy in pulses of short duration. If
the laser emits 1.3 x 10-2 J of energy during a pulse.
How many quanta of energy are emitted during the
pulse?
ANSWER: 4.2 x 1016 quanta
The Dual Nature of Light
Albert Einstein and the Photoelectric Effect
When light with a certain amount of energy is shone
on a surface, it can cause the surface to emit
electrons.
Different materials require different frequencies of
light in order to observe this effect. Einstein built
upon the idea of light as a particle to explain this
phenomena.
He used Planck’s equation to assume
Energy of photon = hv
The Dual Nature of Light
Photoelectric Effect: Discrete particles of light
called photons strike the surface and transfer all of
their energy to the electrons on the surface of the
metal.
With enough energy, electrons can overcome the
attractive forces holding them to the surface and
bounce off the metal.
This can generate a measurable voltage and
generate electricity.
The Dual Nature of Light
The Dual Nature of Light
De Broglie – particles (photons, electrons, matter) will
behave like particles and like waves, depending on the
circumstance and what we are trying to observe:
l = h/mv
M = mass; v = velocity; h = Planck’s constant.
Examples: A 0.1 kg fastball traveling at 20 meters/sec
will have a wavelength of 3 x 10-22 pm.
A 9 x 10-31 kg electron travelling at 1 x 105 m/s will
have a wavelength of 7000 pm.
The Dual Nature of Light
Neils Bohr: Explanation of Emission Spectra
A source of radiation often emits radiation that
can be broken down into a continuous spectra –
just like visible light through a prism will form a
continuous rainbow.
However, certain elements would not produce a
continuous spectrum. Only light of certain
wavelengths would be present = line spectrum.
The Dual Nature of Light
The first spectra to be studied was that of hydrogen. With
only 1 electron – the spectrum was relatively simple: 4 lines.
Johann Balmer was able to write an equation that would allow us to
calculate the wavelengths of all the spectral lines of hydrogen.
Rh = 1.09776 x 107 m-1
Where n2 is greater than n1
The Dual Nature of Light
Bohr used this to explain hydrogen’s emission
spectra: relating the different wavelengths being
produced to the energy transitions between
principle energy levels.
He proposed the electrons travel in circular orbits
around the nucleus, and each orbit has a quantized
energy state.
When electrons change state, the energy that is
either gained or emitted is equal to the energy
difference between states.
The Dual Nature of Light
With this he was able to manipulate Rydberg’s equation to
calculate the energy for electrons in each orbit:
En = (-RH)(1/n2)
And the energy associated with transitions:
DE = (-RH) 1 _ 1
2
2
in
fn
Rydberg’s constant is redefined in this equation as -Rhhc so
Rh = 2.18 x 10-18 J and n = principal quantum number
The Dual Nature of Light
Sample exercise: Calculate the wavelength of hydrogen emission
line that corresponds to the transition of the electron from the
n=3 to the n=1 state.
1. Solve for energy:
1.
1.94 x 10-18 J
2. Solve for frequency:
1.
2.92 x 1015 s-1
3. Solve for wavelength:
1.
1.03 x 10-7 m
In what portion of the electromagnetic spectrum is this line
found?
103 nm = ultraviolet
Wave Behavior of Matter
Finally, Louis de Broglie further extended the idea of energy
behaving as a particle and wave. Any particle – energy or matter
can behave then as a wave (our interests are electrons).
The wavelength is dependent upon it’s mass and velocity:
l= h
mv
The wavelength for most objects is so small, it is not observable
because there mass is so large. However, for electrons – which
have a incredibly small mass, their wavelengths become more
important.
Wave Behavior of Matter
Example: At what velocity must a neutron be
moving in order for it to exhibit a wavelength of
500 pm?
ANSWER: 7.94 X 102 m/s
Wave Behavior of Matter
X-ray diffraction: when x-rays which are considered to
exhibit wavelike properties are passed through a crystal,
the waves are diffracted in a specific pattern.
http://www.pbs.org/wgbh/nova/photo51/
The Dual Nature of Light
Wave Behavior of Matter
When similar work was done with electrons moving at a
high velocity, they also produced a diffraction pattern as
the waves interacted with the structure of the sample.
Electrons moving as a wave and bouncing off structures as
small as atoms is the basis for the electron microscope.
The electron microscope can magnify things nearly three
million times because the wavelength of electrons is so
much smaller than that of visible light.
The Uncertainty Principle
When electrons can be thought of to have wavelike
properties, this makes it much more difficult to
describe an exact location.
Waves extend in space and their location cannot be
specifically defined to one particular point at a given
time.
So then, how can we estimate the location of the
electrons in an atom?
Can we determine where an electron is located at a
particular moment in time in an atom?
Uncertainty Principle
Werner Heisenberg: Proposed that there is a
limitation on how much of the location and the
momentum of an object at given time.
The uncertainty principle states: it is impossible
for us to know simultaneously both the exact
momentum of the electron and its exact location
in space.
The act of measuring affects what we are
measuring:
(Dx)D(mv) > h / 4P
Quantum Mechanics and Atomic Orbitals.
Erwin Shrodinger: Shrodingers equation
Leads to wave functions that describe the location
of electrons in an atom. Wave funtions are
symbolized with the letter y (Greek: psi).
When y is squared (Y2) – it gives us the probability
distribution of an electron in atom. Rather than
knowing an exact location, Shrodinger’s equations
gives us regions of probability where an electron is
found.
Quantum Mechanics and Atomic Orbitals.
The intersection of the three
axises represent the nucleus.
This electron density
distribution shows that
where the more intense
color, the greater the value
of Y2… there is a greater
chance of finding an
electron.
These regions are a certain
amount of energy and will
also have specific shapes
depending on the type of
orbital.
Quantum Mechanics and Atomic Orbitals.
The wave functions gave rise to the orbitals, each
with a shape and energy. This was a much
different model than Bohr had proposed for
hydrogen.
Bohr proposed principal quantum number: “n”
which corresponded with the orbits.
The quantum mechanical model uses n, l, m1.
Quantum Mechanics and Atomic Orbitals.
Principal Quantum Numbers (n): can have integral values >
0 ( 1, 2, 3 ,4 etc.) .
- As n increases, the electron density is farther
away from the nucleus. Size of orbital increases.
- As n increases, the electron is less tightly
bound and has more energy
Angular Momentum Azimuthal Quantum Number (l): Can
have integral values from 0 to n-1. Defines the 3D shape of
the orbital. Rather than lists as numbers, often referred to
by letter:
S=0
p=1
d=2
f=3
Quantum Mechanics and Atomic Orbitals.
Magnetic Quantum Number ‘ml’: has
integral values between ‘l’ and ‘–l’.
Describes how the orbital is arranged in
space.
- A collection of orbitals with the same
value of ‘n’ is the electron shell
- A collection of orbitals with the same
value of n and l belong to the same
subshell.
Quantum Mechanics and Atomic Orbitals.
Example: Electron orbitals with a principle number
of 3 would have the following available values
n:
principal
quantum
number
3
l:
Subshell Ml
azimutha designati
l
on
Number
of orbital
in each
0
1
2
1
3
5
3s
3p
3d
0
-1,0,1
-2,1,0,1,2
Quantum Mechanics and Atomic Orbitals.
A couple of patterns that exist:
Each shell is divided into a number of subshells,
equal to the principal quantum number.
Each subshell is divided into orbitals, that increase
by odd numbers.
Quantum Mechanics and Atomic Orbitals
Combinations of the quantum numbers specifies which
specific electron we are referring to in an atom (address)
n
l subshell
1
2
0
0
1
0
1
2
3
1s
2s
2p
3s
3p
3d
ml
no. of orbs no. of e-l
0
1
2
2
0
1
2
8
1, 0, -1
3
6
0
1
2
1, 0, -1
3
6
18
2, 1, 0, -1, -2
5
10
Quantum Mechanics and Atomic Orbitals
Quantum Numbers also specify energy of the
occupying electrons,
l=0
l=1
l=2
l=3
n=•
0
n=4
n=3
E
N
E
R
G
Y
n=2
4s
3s
4p
3p
2s
2p
4d
3d
2+6=8
electrons
2 electrons max
max
n=1
1s
4f
2+6+10+14=
32 electrons
max
2+6+10=18
electrons
max
Quantum Mechanics and Atomic Orbitals.
Example: What is the designation for the subshell
with n = 5 and l = 1? How many orbitals in this
subshell? Indicate the value of ml for each.
N = 5 is 5th principal energy level
L = 1 is the p sublevel
P has 3 orbitals
3 orbitals are labeled -1, 0, 1
Orbitals
Ground State: electron is in the the lowest energy
orbital available.
Excited State: electron is in another orbital –
presumably by gaining energy.
All orbitals of the same l value are the same
shape. Depending on the n value – they will differ
in size and relative energies.
Orbitals
Orbitals
The 1s orbital is a symmetrical spherical. A plot of
the distribution Y2 versus the distance (r) from the
nucleus shows that as the radius gets farther, the
probability of finding an
electron drops off
significantly.
Orbitals
The higher energy s orbitals
are also spherical and
symmetrical. However, there
are regions of zero electron
density, called nodes.
2s has 1 node, 3s has 2 nodes.
- In the higher s orbitals, the
electron density distribution
tells us that there is a higher
probability of finding an
electron farther away from the
nucleus.
Orbitals
In the p orbitals, the electron density is
concentrated in two regions (two lobes) on either
side of the nucleus… considered “dumbbell”
shaped, with a node at the nucleus.
In the p sublevel – there are 3 orbitals ( 3
dumbbells), and they differ in their orientations
around the nucleus (origin).
Orbitals
l=1
p
Orbitals
y
y
z
py
px
x
y
z
x
x
2p
y
2
(p)
z
z
pz
Radial Electron
Distribution
3p
x
radius
Orbitals
Orbitals
In the third shell and beyond, we see the d sublevels – with
five d orbitals.
Orbitals
In the 4th shell and beyond, we encounter the f
orbitals which are very complicated to represent.
The shapes of the orbitals and how many are in
each sublevel will assist you in understanding how
molecules bond and exchange/share electrons.
Orbitals
Orbitals
All of this is based on the hydrogen atom, because the
mathematical equations are relatively simplistic when
dealing with only one electron.
While the shapes o the orbitals are essentially the
same from Hydrogen to multi-electron atoms, the
energies differ drastically.
For hydrogen, the energy is largely dependent on the
value of n. For bigger atoms the sublevel (l) also plays
a role because now we have to worry about electron –
electron repulsion.
Many Electron Atoms
In the graph below, the
2s orbital has less energy than
the 2p orbital… and this can
be attributed to like
charge repulsion as
well as the effective nuclear
charge on
electrons.
Many Electron Atoms
In atoms with more than one electron, there are
two forces acting on each electron at the same
time:
1. Attraction to the protons in the nuclear
2. Repulsion by other electrons
To understand the energy of the electron, we have
to know the net “feeling” each electron
experiences in it’s environment.
Many Electron Atoms
The net attractive force that an electron will feel is
called the effective nuclear charge: Zeff
Zeff = Z – S
Where Z = nuclear charge and S = screening value.
The screening value is the average number of other
electrons between the electron in question and the
nucleus.
** The effective nuclear charge is always less than the
full nuclear charge**
Many Electron Atoms
Zeff = Z - S
Average electronic charge
(S) between the nucleus
and the electron of interest
The larger the
Zeff an electron
feels leads to a
lower energy for
the electron
r
Z
Electrons outside of sphere of radius r have
very little effect on the effective nuclear
charge experienced by the electron at radius
r
Many Electron Atoms
For a given n value, the Zeff decreases with
increasing values of l.
The effective nuclear charge will depend on what
type of sublevel and therefore number of orbitals
are participating in the screening.
Screening ability: s>p>d>f
Many Electron Atoms
Example: The sodium atom has 11 electrons. Two
occupy a 1s orbital, two occupy a 2s orbital and
one occupies a 3s orbital. Which of these s
electrons experience the smallest effective nuclear
charge?
Answer: 3s electrons because they have a greater
number of electrons between them and the
nucleus (S increases). So Zeff decreases and energy
increases.
Many Electron Atoms
With a principal quantum number, 3s electrons will
experience less screening/shielding than the 3d
electrons. So the 3d electrons have less Zeff.
In a many electron atom, for a given ‘n’.. Zeff
decreases as ‘l’ increases.
Because Zeff decreases for 3d electrons, they will have
more energy.
In a many electron atom, for a given ‘n’… the energy
level of an orbital increases as ‘l’ increases.
Electron Spin
Electrons have spin properties – in which they spin
along an axis. Electron spin: ms. The spinning electrons
produces two magnetic field: in opposite directions
Electron spin is quantized:
ms = +1/2 or -1/2
Because two electrons can be in the same principal
energy level, sublevel and orbital – they will share 3 of
the 4 principal quantum numbers: n, l, ml. They must
have a different 4th principal quantum number: ms.
Electron Spin
N
-
Magnetic Fields
-
N
Electron Spin
Pauli Exclusion Principle: No two electrons can
have the same set of four quantum numbers n,l,
ml and ms.
In order to put electrons in the same orbital, they
must have different ms numbers = opposite spins.
Electron Configurations
Electrons fill in order of increasing energy, with no
more than two electrons per orbital.
Reminder: two electrons will not occupy the same
orbital before each orbital has at least one. Why?
Degenerate orbitals are orbitals that are all at the
same energy level.
Hund’s Rule: the lowest energy configuration for an
atom is the one having the maximum number of
unpaired electrons with the same spin.
Electron Configurations
Guidelines for electron configurations:
- Obey Pauli Exclusion Principle
- Obey Hund’s Rule
- Fill from lowest to highest energies
- Shorthand:
- Na: 11 electrons: 1s22s22p63s1 or [Ne]3s1
- Closed shell (filled), half filled and empty orbital
configurations most stable
- Outer electrons are valence electrons
- Inner electrons are core electrons.
Electron Configurations
After argon with 18 electrons, potassium was studied and
its outermost electron was found in an s orbital, rather
than the 3d sublevel. Which mean the the 4s sublevel must
have less energy than the 3d.
After calcium the 4s is filled, and the the next 10 elements
begin filling the d sublevel. After 3d is filled then 4p is filled
for the remaining elements in that row.
This pattern repeats itself for the remaining rows in the
periodic table, with n increasing by 1 as you go down.
Electron Configurations
Electron Configurations
The transition metals are also referred to as the
“d block” while the Lanthanide and Actinide series
at the bottom of the periodic table is known as
the
“f block”. Many of them are radioactive and rarely
found in nature.
By knowing the location of an element on the
periodic table, elements fall into categories
depending on their electron configurations.
Electron Configurations
S Block: First two groups on the periodic table
P Block: Six rightmost groups on the PT
Together – these makeup our main group elements.
D Block: 10 elements (transition elements)
F Block: Lanthanide and Actinide Series
**The number of columns in each block is equal to the
number of electrons required to fill that sublevel.**
Electron Configurations
To write the electron configuration for Selenium:
To use shorthand, we are able to start with the noble
gas core which in this case is argon.
Se: [Ar]
Then you are able to work your way across the
periodic table until you get to selenium: 4s23d104p4.
Final: [Ar]4s23d104p4.
Electron Configurations
Example: What family of elements is characterized by having an
ns2p2 outer electron configuration?
ANSWER: Group 14 or Group IVA
Example: Use the periodic table to write the e- configurations
for the following atoms by giving the appropriate noble gas
inner core plus the electrons beyond it: Co, Te.
Co: [Ar]4s23d7
Te: [Kr]5s24d105p4