Download Atomic Structure and Periodicity

Atomic
Structure and
Periodicity
AP Chemistry
Ms. Grobsky
Food For Thought

Rutherford’s model became
known as the “planetary model”

The “sun” was the positivelycharged dense nucleus and the
negatively-charged
electrons
were the “planets”
The Planetary Model is
Doomed!

The classical laws of motion and gravitation
could easily be applied to neutral bodies like
planets, but NOT to charged bodies such as
protons and electrons


According to classical physics, an electron in
orbit around an atomic nucleus should emit
energy in the form of light continuously (like
white light) because it is continually
accelerating in a curved path
Resulting loss of energy implies that the electron
would necessarily have to move close to the
nucleus due to loss of potential energy

Eventually, it would crash into the nucleus and
the atom would collapse!
The Planetary Model is Doomed!
Electron crashes into the nucleus!?
Since this does not happen, the Rutherford
model could not be accepted!
How did Scientists Study the
Structure of an Atom when They
Couldn’t Physically See It?
 Atomic
structure was often elucidated by
interaction of matter with light

James Maxwell developed a mathematical
theory to describe all forms of radiation in
terms of wave-like electric and magnetic
fields in space in 1864
 Classical
wave theory of light described most
observed phenomenon until about 1900
But What Exactly is Light?
 Light
is a form of ELECTROMAGNETIC
RADIATION
 A form of energy that exhibits wavelike
behavior as it travels through space

 In
Does not require a medium to travel
through
a vacuum, every electromagnetic
wave has a velocity (speed) of 3.00 x 108
m/s, which is symbolized by the letter “c”
Video Time!
Electromagnetic Spectrum
The Electromagnetic
Spectrum
 Electromagnetic
spectrum is the range of all
possible frequencies of electromagnetic radiation
 The highest energy form of electromagnetic
waves is gamma rays and the lowest energy form
is radio waves
Relationship of EM Wave
Properties
Some Properties of Waves

Wavelength (λ)



Frequency (ν)



Number of waves that
pass a given point per
second
Measured in hertz (sec-1)
Speed ( c )


Distance between two
consecutive peaks or
troughs in a wave
Measured in meters (SI
system)
Measured in meters/sec
Amplitude (A)

Distance from maximum
height of a crest to the
undisturbed position
Relationships of EM Wave
Properties
 Wavelength
and frequency are related via the
speed of light in a vacuum (c)

c = 3.00 x 108 m/s
 Speed

of light in a vacuum is a constant
c = λ· ν
ALL ELECTROMAGNETIC RADIATION TRAVELS AT
THIS SPEED!
 Therefore,
wavelength and frequency of light
are inversely proportional to each other


As wavelength increases, frequency decreases
As wavelength decreases, frequency increases
What’s the Matter with
Light?
The Nature of Matter
 By
the end of the 19th century, physicists
were feeling rather smug

They thought that all of physics had been
explained and that matter and energy
were two distinct entities:
 Matter
was a collection of particles
 Energy was a collection of waves
The Ultraviolet Catastrophe
 There
was a consistent observation of
matter that could NOT be explained with
the classical wave theory of light
 Elements in solid form glow when they
are heated
 Do
not emit UV light as predicted
Enter Max Planck…
 Around
the year 1900, a physicist named Max
Planck was studying the energy given off by
heated objects until they glow
•
Planck solved the “Ultraviolet Catastrophe” with an
incredible assumption:
 There is a minimum amount of energy that can
be gained or lost by an atom
 All energy gained or lost must be some integer
multiple, n, of that minimum as opposed to just
any old value of energy being gained or lost
Planck and Quanta
 Planck
called these restricted amounts of
energy “quantum”

No such thing as a transfer of energy in
fractions of quanta
 Only
whole numbers of quanta
 To
understand quantization, consider
walking up a ramp versus walking up the
stairs

For the ramp, there is a continuous change
in height whereas up stairs, there is a
quantized change in height
More on the Idea of Quanta
 Mathematically,
quantum (packet) of
energy is given by:


h = Planck’s constant = 6.626 x 10-34 J· s
ν is the lowest frequency that can be
absorbed or emitted by the atom
Planck’s Constant
 Planck’s


constant, h, is just like a penny
Planck determined that all amounts of
energy are a multiple of a specific value, h
This is the same as saying that all currency in
the US is a multiple of the penny
More Problems with the
Wave Theory of Light
And then there was a problem…
• In the early 20th century, several other effects were
observed which could not be understood using
the wave theory of light
• The Photo-Electric Effect
• Every element emits light when energized
either by heating the element or by passing
electric current through it
• Elements in gaseous form emit light when
electricity passes through them
What is the Photoelectric
Effect?

Electrons are attracted to the (positively charged)
nucleus by the electrical force

In metals, the outermost electrons are not tightly
bound, and can be easily “liberated” from the
shackles of its atom


It just takes sufficient energy
If light was really a wave, it was thought that if one
shined light of a fixed wavelength on a metal surface
and varied the intensity (made it brighter and hence
classically, a more energetic wave), eventually,
electrons should be emitted from the surface
Photoelectric Effect
“Classical” Method
Increase energy by
increasing amplitude
What if we try this ?
Vary wavelength, fixed amplitude
electrons
emitted ?
No
No
No
No
electrons
emitted ?
No
Yes, with
low KE
Yes, with
high KE
• No electrons were emitted until the frequency of the light
exceeded a critical frequency, at which point electrons were
emitted from the surface!
(Recall: small l  large n)
Light as a Particle – Einstein’s
Theory
 Einstein
used Planck’s idea of energy
quanta to understand the photoelectric
effect
 Proposed that EM radiation itself was
quantized

Light could be viewed as a stream of
“particles” called photons
 Each
photon carries an amount of energy
that is given by Planck’s equation
Einstein’s Theory of Quantized
Light
𝐸𝑝ℎ𝑜𝑡𝑜𝑛 = ℎν =
ℎ𝑐
λ
Einstein’s Particle Theory of
Light

You know Einstein for the famous E = mc2

This equation shows that energy has mass???



Blasphemy!
Rearranging this equation and substituting in Planck’s
equation:
𝐸
ℎ𝑐/λ ℎ
𝑚= 2= 2 =
𝑐
𝑐
𝑐λ
So, does a photon has mass?


Yep!
In 1922, Arthur Compton performed experiments involving
collisions of X-rays and electrons that showed photons do
exhibit the apparent mass calculated above!
Back to the Photoelectric
Effect…
•
The light particle must have sufficient energy to “free” the
electron from the atom
•
Increasing the amplitude is simply increasing the number of
light particles, but its NOT increasing the energy of each
one!
•
However, if the energy of these “light particle” is related to
their frequency, this would explain why higher frequency
light can knock the electrons out of their atoms, but low
frequency light cannot
Photoelectric Effect Animation
A Summary of Light as a
“Waveicle”
Light travels through space as a
wave
 Light transmits energy as a particle
 Each photon carries an amount of
energy that is given by Planck’s
equation
ℎ𝑐
𝐸𝑝ℎ𝑜𝑡𝑜𝑛 = ℎν =
λ

So is Light a
Wave or a
Particle ?
• On macroscopic scales, we can treat a large number of
photons as a wave
• When dealing with subatomic phenomenon, we are often
dealing with a single photon, or a few
• In this case, you cannot use the wave description of light
• It doesn’t work!
The Dualism of Light
 Dualism
is not such a strange concept
 Consider the following picture

Are the swirls moving, or not, or both?
Time for Practice!
Gallery Walk!
But How is This Related to
the Atom?
Atomic Spectroscopy and the
Bohr Model
 Discovery
of particle nature of light began
to break down the division that existed in
19th-century physics between EM
radiation (wave phenomenon) and small
particles
 Atomic spectroscopy is the study of EM
radiation absorbed and emitted by atoms

Observations suggested wave nature of
particles
Light and the Dilemma of
Atomic Spectral Lines
Experiments
show that
when white light is passed
through a prism, a
continuous spectrum
results
Contain
all
wavelengths of light
When
a hydrogen
emission spectrum in
visible region is passed
through a prism, a line
spectrum results
Only
a few
wavelengths of visible
light pass through
Seeing Atomic Spectral Lines
 Use
your diffraction grating to observe the
atomic spectra of:



Hydrogen
Oxygen
Neon
Just a Thought….
 With
a partner, answer the following
questions using your knowledge from your
homework:



How are electrons “excited” in this
demonstration?
What happens when the electrons relax?
What do the different colors in a line
spectrum represent? Why are the spectra
for each element unique?
hydrogen (H)
mercury (Hg)
neon (Ne)
Planck’s Quanta and
Atomic Spectra



In order to produce a line spectrum,
atoms’ electrons must somehow absorb
energy and then give the energy off in
the form of light at a specific wavelength
What is the relationship between energy
and wavelength?
Can we map the electrons by using these
energy relationships from the emission
spectrum?
Neils Bohr and the Atomic
Model


The answer is YES!
Neils Bohr was one of the first to see some
connection between the wavelengths an
element emits and its atomic structure

Related Planck’s idea of quantized energies
to Rutherford’s atomic model
Bohr and the Atomic Model

Bohr discovered that as the electrons in the
hydrogen atoms were getting excited and
then releasing energy, only four different color
bands of visible light were being emitted: red,
bluish-green, and two violet-colored lines


If electrons were randomly situated, as
depicted in Rutherford’s atomic model, then
they would be able to absorb and release
energy of random colors of light
Bohr concluded that electrons were not
randomly situated

Instead, they are located in very specific
locations that we now call energy levels
Bohr model of the Hydrogen
Atom
• Protons and neutrons compose
the nucleus
• Electrons orbit the nucleus in certain
well-defined ‘energy levels’
Niels Bohr
nucleus
Bohr’s Model of the Atom

Bohr suggested that electrons typically
have the lowest energy possible (ground
state), but upon absorbing energy via
heat or electricity:


Electrons jump to a higher energy level,
producing an excited and unstable state
Those electrons can’t stay away from the
nucleus in those high energy levels forever so
electrons would then fall back to a lower
energy level
Just a Thought…
But
if electrons are going from
high-energy state to a lowenergy state, where is all this
extra energy going?
Connecting Planck’s Quanta
to the Atomic Model
 Energy does not disappear
 First Law of Thermodynamics!
 Electrons
re-emit the absorbed
energy as photons of light

Difference in energy would correspond
with a specific wavelength line in the
atomic emission spectrum

Larger the transition the electron makes, the
higher the energy the photon will have
What is the Change in Energy when
Electrons Move Between Energy
Levels?
∆𝐸 = −2.178 ×
n

10−18 𝐽
1
2
𝑛𝑓𝑖𝑛𝑎𝑙
−
1
2
𝑛𝑖𝑛𝑖𝑡𝑖𝑎𝑙
= principal quantum number
Energy level
 -∆E
means electron emits a photon of
light
 +∆E means electron absorbs a photon of
light
More Useful Equation
 After
some substitutions and rearranging
of the previous equation, the possible
wavelengths of the photons emitted by a
hydrogen atom as its electron makes
transitions between different energy levels
are:
1
1
1
=𝑅
− 2
2
λ
𝑛𝑓 𝑛𝑖
R
= Rydberg constant = 1.097 x 107 m-1
More on Hydrogen Spectral
Lines
 Transitions
to the ground-state (nf = 1) give rise to
spectral lines in the UV region of EM spectrum
 Set of lines is called the Lyman series
 Transitions to the first excited state (nf = 2) give rise
to spectral lines in the visible region of EM
spectrum
 Set of lines is called the Balmer series
 Transitions to the second excited state (nf = 3)
give rise to spectral lines in the IR region of EM
spectrum
 Set of lines is called the Paschen series
Many Electron Atoms
 Recall
that because each element has a
different electron configuration and a
slightly different structure, the colors that
are given off by each element are going
to be different

Thus, each element is going to have its own
distinct color when its electrons are excited
(or its own atomic spectra)
Shortcomings of the Bohr
Model

Bohr’s model was too simple




Worked well with only hydrogen because H
only has one electron
Could only approximate spectra of other
elements with more than one electron
Electrons do not move in circular orbits
So there is more to the atomic puzzle…
The Wave Nature of
Matter
de Broglie, the Uncertainty Principle, and Quantum
Mechanics
Dual Nature of Matter?!
 As
a result of Planck’s and Einstein’s work,
light was found to have certain
characteristics of particulate matter

No longer purely wavelike
 But

is the opposite also true?
Does matter exhibit wave properties?
 Yes!

Enter the French physicist Louis de Broglie in
1923…
de Broglie and Wave Nature
of Matter


de Broglie derived an equation that relates mass,
wavelength, and velocity for any object NOT traveling at
the speed of light:
ℎ
λ=
𝑚ν
This equation shows that the more massive the object, the
smaller its associated wavelength and vice versa!


Hence the reason why on the macroscopic level, objects do
not seem to act as waves!
Experimentally confirmed by two employees of Bell
Laboratories (in NYC) - Davisson and Germer

Beam of electrons was diffracted like light waves by the
atoms of a thin sheet of nickel foil

de Broglie’s relation was followed quantitatively!
Interpretation of de Broglie’s
Work

Electrons bound to the nucleus are similar to standing waves


Standing waves do not propagate through space
Standing waves are fixed at both ends
 Think of a guitar or violin
 A string is attached to both ends and vibrates to produce a musical
tone

Waves are “standing” because they are stationary – the wave does not
travel along the length of the string
Wave Nature and Particle Nature of
Electrons-Complementary Properties

Complementary properties mean that the more
you know about one, the less you know about the
other


Velocity of an electron is related to its wave
nature
Position of an electron is related to its particle
nature


Particles have well-defined positions; waves do not
We are unable to observe an electron
simultaneously as both a particle and a wave

Therefore, we cannot simultaneously measure its
position AND velocity

Heisenberg Uncertainty Principle
Heisenberg Uncertainty
Principle and Complementary
Properties

“There is a fundamental
limitation on how
precisely we can know
both the position and
momentum of a
particle at a given
time”

It is impossible to know
both the velocity and
location of an electron
at the same time
How Can Something be Both
a Particle and a Wave?
 Saying
that an object is both a particle
and a wave is saying that an object is
both a circle and a square – a
contradiction

Complementary solves this problem
 An
electron is observed as either a particle or
a wave, but never both at once!
Energies and Electrons –
Introducing the Quantum
Mechanical Model

Many properties of an element depend on the
energies of its electrons

Remember, position and velocity of the electron
are complementary properties


Therefore, we can specify the energy of the
electron precisely, but not its location at a given
instant


Since velocity is directly related to energy via ½ mv2,
position and energy are also complementary
properties
Instead, the electron’s position is described as a
probable location where the electron is likely to be
found called an orbital
Enter Schrӧdinger…
Schrödinger Equation

Mathematical derivation of energies and orbitals
comes from solving the Schrödinger equation:
ℎ2
𝑑2 Ψ
−
+ 𝑉Ψ = 𝐸Ψ
8𝜋 2 𝑚
𝑑𝑥 2

General equation:
ĤΨ = 𝐸Ψ
Ĥ = set of mathematical instructions called an
“operator” that represent the total energy (kinetic
and potential) of the electron within the atom
Ψ = Wave function that describes the wavelike
nature of the electron


Orbitals
Solution of the equation has demonstrated that E
(energy) must occur in integer multiples

Quanta!
Orbitals


Orbitals are NOT circular orbits for electrons
Orbitals ARE areas of probability for locating
electrons


Square of absolute value of the wave function
gives a probability distribution
Ψ2
Electron density maps (probability distribution)
indicates the most probable distance from
the nucleus
Orbitals
 Wave
functions and probability maps DO
NOT describe:



How an electron arrived at its location
Where the electron will go next
When the electron will be in a particular
location
Quantum Numbers
Each electron has a specific ‘address’
in the space around a nucleus

An electrons ‘address’ is given as a set
of four quantum numbers

Each quantum number provides specific
information on the electrons location

Electron Configuration
state
town
house number
street
Electron configuration
(quantum numbers)
state
(energy level) - quantum number n
town
(shape of orbital) - quantum number l
street
(orbital room) - quantum number ml
house
number (electron spin) - quantum
number ms
Principal Quantum Number (n)
 Same
as Bohr’s n
 Integral values: 1, 2, 3, ….
 Indicates probable distance from the
nucleus


Higher numbers = greater distance from
nucleus
Greater distance = less tightly bound =
higher energy
Angular Momentum Quantum
Number (l)
 Integral
values from 0 to n - 1 for each
principal quantum number n
 Indicates the shape of the atomic orbitals
Table 7.1 Angular momentum quantum
numbers and corresponding atomic orbital
numbers
Value of l
0
1
2
3
4
Letter
used
s
p
d
f
g
Magnetic Quantum Number
(ml)
 Integral
values from l to -l, including zero
 Relates to the orientation of the orbital in
space relative to the other orbitals

3-D orientation of each orbital
Magnetic Quantum Number
Electron Spin Quantum
Number (ms)
 An
orbital can hold only two electrons,
and they must have opposite spins

Spin can have two values, +1/2 and -1/2
 Pauli

Exclusion Principle (Wolfgang Pauli)
"In a given atom no two electrons can have
the same set of four quantum numbers"
Orbital Shapes

Size of orbitals


Defined as the
surface that contains
90% of the total
electron probability
Orbitals of the same
shape (s, for instance)
grow larger as
principal quantum
number (n) increases

# of nodes (areas in
which there is zero
electron probability)
increase as well
Why Do We Care About the
Shape of the Orbitals?
 Covalent
chemical bonds depend on the
sharing of the electrons that occupy
these orbitals

Shape of overlapping orbitals determine
the shape of the molecule!
s sub-level (l = 0)
spherical shape
single orbital
seen in all energy levels
p sub-level (l = 1)
p (x)
y-axis
z-axis
p (y)
x-axis
p (z)
d sub-level (l = 2)
five clover-shaped orbitals
seen in all energy levels n=3 and above
f sub-level (l = 3)
seven equal energy orbitals
shape is not well-defined
seen in all energy levels n=4 and above
Orbital Energies
 Electron

in lowest energy state
Ground state
 When
an atom absorbs energy, electrons
may move to higher orbitals

Excited state
Orbital Energies in Polyelectronic
Atoms



Polyelectronic atoms are atoms with more than one
electron
 Atoms other than hydrogen
Must make approximations with quantum mechanical
model to compensate for repulsions between electrons
 Variations in energy within the same quantum level
 Atoms other than hydrogen have variations in
energy for orbitals having the same principal
quantum number
 Electrons fill orbitals of the same n value in
preferential order
 En-s < En-p < En-d < En-f
Electron density profiles show that s electrons penetrate
to the nucleus more than other orbital types
 Closer proximity to the nucleus = lower energy
Orbital Energies
Using the Periodic Table to
Predict Electron Locations
 Aufbau
principle
 Electrons
are added one at a time to
the lowest energy orbitals available
until all the electrons of the atom
have been accounted for
 “aufbau”
 German
for ‘build up or construct’
Hund’s Rule
must fill a sub-level such that
each orbital has a spin up electron before
they are paired with spin down electrons”
 “Electrons
Orbital Diagrams and Electron
Configurations




Electrons fill in order from lowest to highest energy
The Pauli exclusion principle holds. An orbital can hold
only two electrons
Two electrons in the same orbital must have opposite
signs
You must know how many electrons can be held by
each orbital





2 for s
6 for p
10 for d
14 for f
Hund’s rule applies. The lowest energy configuration for
an atom is the one having the maximum number of
unpaired electrons for a set of degenerate orbitals

By convention, all unpaired electrons are represented as
having parallel spins with the spin “up”
aufbau chart
1s
2s
2p
3s
3p 3d
4s
4p 4d
4f
5s
5p 5d
5f