Download Ch. 7 – Atomic Structure and Periodicity

Ch. 7 – Atomic Structure and
Periodicity
AP Chemistry
Ch. 7 – Atomic Structure and
Periodicity
• In this chapter we will see that the modern
theory of atomic structure…accounts for
periodicity in terms of the e- arrangements in
atoms
• Quantum mechanics was developed to
account for … the behavior of light and atoms
7.1 Electromagnetic Radiation
Electromagnetic radiation - exhibit wavelike behavior
- travels at the speed of light
Ex’s sunlight, microwaves, x-rays, radiant heat
Wavelength (l) distance between two consecutive peaks
or troughs in a wave (m or nm)
Frequency (n) – the number waves or cycles per second
1/s or s-1 or Hz
Eqn: ln = c
Note units
Sample exercise 7.1 – Frequency of
Electromagnetic Radiation (complete below)
n = c/l = 2.9979 x 108 m/s = 4.61 x 1014 Hz
650. x 10-9 m
7.2 Nature of Matter
At the end of the 19th century the idea prevailed that
… matter and energy are distinct
MATTER
ENERGY
1) Consists of particles
1) described as a wave
2) Have mass
2) massless
3) Position can be specified 3) delocalized
7.2 Nature
of Matter
Max Plank
Studied…radiation profiles emitted by solid
bodies heated to incandescence
Found … results couldn’t be explained in terms
of physics of his day (which held that
matter could absorb or emit any
quantity of energy)
Postulated… the energy could only be gained or
lost in whole-number multiples of
the quantity hn
7.2 Nature of Matter
ΔE =
nhn
Where n =# photons
h = 6.626 x 10-34 Js
Had assumed energy of matter was continuous.
Energy is in fact quantized.
which means… it can occur only in discrete
units of size hn.
KEY: This means energy has particulate properties.
Sample Exercise 7.2 – The energy of a photon
(complete below)
DE = hn (Δ not always used)
n = c/l = 2.9979 x 108 m/s = 6.66 x 1014 s-1
4.50 x 10-7 m
What is this in kJ/mol?
7.2 Nature of Matter
Albert Einstein
Proposed…electromagnetic radiation itself is
quantized.
Suggested that electromagnetic radiation can be
viewed as… a stream of particles.
Ephoton = hn = hc
l
Photoelectric effect when electrons are emitted
from the surface of a metal
when light strikes it.
Observations:
1. Studies in which the frequency of the light is varied show that no
electrons are emitted by a given metal below a specific threshold
frequency, no
2. For light with frequency lower than the threshold frequency, no
electrons are emitted regardless of the intensity of the light.
3. For light with frequency greater than the threshold frequency, the
number of electrons emitted increases with the intensity of the
light.
4. For light with frequency greater than the threshold frequency, the
kinetic energy, of the emitted electrons increases linearly with the
frequency of the light.
Photoelectric Effect
KEY: These observations can be explained by
assuming… that electromagnetic radiation
is quantized (consists of photons)
(and that the threshold frequency represents
the minimum energy required to remove the
electrons from the metal’s surface.)
Light intensity is a measure of number of
photons.
Related development, famous eqn:
E = mc2
Main significance: Energy has mass!
Thus we can calculate the mass of a photon.
Note: This is only in a relativistic sense; there is
no rest mass.
7.2 Nature of Matter
Summary of Plank and Einstein
1. Energy is quantized – it can occur only in
discrete amounts
2. Electromagnetic radiation has wave and
particle properties “Dual nature of light”
De Broglie Eqn:
l=h
mv
Key: it allows us to calculate the wavelength for a particle.
Sample Exercise 7.3 – Calculations of Wavelength
(complete below)
(Take note of the relative l’s you just calculated. How do
they compare in size?)
the smaller the object, the longer the wavelength.
7.2 Nature of Matter
Diffraction – when light is scattered from a
regular array of points or lines.
Ex’s CD
7.2 Nature of Matter
x-rays directed at a NaCl crystal produce
diffraction pattern.
7.2 Nature of Matter
X-ray diffraction of
a beryl crystal
KEY: diffraction patters can only be explained in
terms of waves.
Thus diffraction provides a test for deBroglie’s
postulate that electrons have wavelengths.
7.2 Nature of Matter
Diffraction patterns occur most efficiently when …the
spacing between the scattering points is about the
same length as the wavelength being diffracted.
When a beam of electrons were
directed at a Ni crystal, Davisson and
Germer observed a diffraction
pattern which verified deBroglie’s
relationship.
KEY: This means electrons have
wavelike properties.
Pg. 282 Electron
diffraction of a
titanium/nickel alloy
7.2 Nature of Matter
SUMMARY:
• Electromagnetic Radiation has dual properties
(wave & particles).
• Electrons have dual properties (waves &
particles).
All matter exhibits…particulate and wave
properties.
7.3 The Atomic Spectrum of Hydrogen
Impt. Expt. – study of the emission of light by excited
hydrogen atoms.
Hydrogen atoms release excess energy by emitting light
(of various wavelengths) to produce emission
spectrum.
7.3 The Atomic Spectrum of Hydrogen
7.3 The Atomic Spectrum of Hydrogen
Significance: only certain energies are allowed for the
electron in a hydrogen atom.
…in other words: the energy of the electron in
hydrogen is quantized.
ΔE = hn = hc
l
7.3 The Atomic Spectrum of Hydrogen
7.4 The Bohr Model
• Bohr developed the first quantum model for the
hydrogen atom.
• He proposed… electrons in Hydrogen move
around the nucleus in certain allowed circular
orbits.
• He calculated… orbit radii.
– With the assumption that angular momentum… of the
electron could occur only in certain increments.
• Bohr’s model gave the hydrogen atom energy
levels consistent with the hydrogen emission
spectrum.
7.4 The Bohr Model Fig. 7.8
7.4 The Bohr Model
Important equation is the expression for the energy levels
available to the electron in the hydrogen atom:
energy level
E = - 2.178 x 10-18 J Z2
n = integer
n2
Z = nuclear charge
Negative sign means…energy of the e- bound to the nucleus is
lower than it would be if the e- were at an infinite distance (n = )
from nucleus.
Bohr calculated hydrogen atom energy levels that …exactly
matched by experiment.
Calculate the energy of a hydrogen atom when its electron
is…
at n = 6
at n = 1
Calculate ΔE when the electron falls from n = 6 to n = 1.
Calculate the wavelength of this emitted photon.
.
7.4 The Bohr Model
• Sample Exercise 7.4 – Energy Quantization in
Hydrogen
7.4 The Bohr Model
Two Points of emphasis for Bohr’s model:
1. Correctly fits quantized hydrogen; certain
circular orbits
2. As the electron gets closer to nucleus,
energy is lower/more negative; energy is
released
7.4 The Bohr Model
In the space below, derive the general equation for
determining the energy change when an electron
moves from one level to another. (pg. 287)
Sample Exercise 7.5 – Electron Energies
7.4 The Bohr Model
NOTE: Bohr’s model applied to other atoms did
NOT work.
KEY: Bohr’s model paved the way for later
theories.
Electrons do NOT move around the
nucleus in circular orbits.
Lyman, Balmer, Paschen Series
(Emission)
n=5
n=4
n=3
n=2
n=1
Balmer, Lyman, and Paschen Series:
Balmer, Lyman, and Paschen Series:
7.5 The Quantum Mechanical Model
of the Atom
Werner Heisenberg –
Louis deBroglie originated the idea that…the
electron shows wave properties.
Erwin Schrodinger gave emphasis to…the wave
properties of the electron.
• Electron bound to the
nucleus is similar to a
standing wave.
• KEY: there are
limitations on the
allowed wavelengths of
a standing wave.
• Considering the
wavelike properties of
the electron is a
possible explanation for
the observed
quantization of the
hydrogen atom.
Schrodinger’s eqn:
^Hy = Ey
y(psi) = wave function
^H Contains mathematical terms that produce the total
energy of an atom when they are applied to the wave
function
• When the equation is analyzed many solutions are
found.
• Each solution consists of a wave function (y) that is
characterized by a particular value of E (for an
electron).
• A specific wave function is often called an orbital.
• An orbital is NOT a Bohr orbit.
• The wave function gives us NO information about the
detailed pathway of the electron.
7.5 The Quantum Mechanical Model
of the Atom
Heisenberg Uncertainty Principle – there is a
fundamental limitation to just how precisely we
can know both the position and momentum of a
particle at a given time.
Eqn: Δx·Δ (mv) ≥ h
4p
What this equation really says is…the more
accurately we know the particle’s position, the
less accurately we know its momentum.
7.5 The Quantum Mechanical Model
of the Atom
The physical meaning of a wave function
• Psi itself has NO easily visualized meaning.
• psi2 indicates the probability of finding an
electron near a particular point in space.
Eqn:
7.5 The Quantum Mechanical Model
of the Atom
psi2 is conveniently represented as a probability
distribution.
Fig. 7.11
This is of a hydrogen 1s wavefunction
7.5 The Quantum Mechanical Model
of the Atom
The total probability of finding the electron at a
particular distance is called radial probability
distribution.
Fig. 7.12
The total probability of finding the electron at a particular
distance is called radial probability distribution.
Fig. 7.12
• The maximum in the curve occurs because of
the two opposing effects.
1. Probability finding the electron is greatest near the
nucleus
2. The volume of the spherical shell increases w/distance
from the nucleus.
• Orbitals usually described as the radius of the sphere
that encloses 90%of the total electron probability.
7.6 Quantum Numbers
1st number: principal quantum number (n)
n = 1,2,3…
As n increases, orbital size and energy increases
2nd number: angular momentum quantum numbers (l)
s
p
d
f
l = (0…n-1)
3rd number: magnetic quantum number (ml)
7.6 Quantum Numbers
Sample Exercise 7.6 – Electron subshells
(complete below)
7.7 Orbital Shapes and Energies
Methods of representing an
orbital
1. Probability distribution
2. The surface that surrounds
90% of the total electron
probability
nodes/nodal surfaces –
Orbital
# nodes
s
p
d
f
7.7 Orbital Shapes and Energies
p-orbitals (fig. 7.14)
Surfaces of orbitals increases as the value of n
increases.
7.7 Orbital Shapes and Energies
7.7 Orbital Shapes and Energies
7.7 Orbital Shapes and Energies
Degenerate – have the same
• all H’s of same n degenerate
• energypolyelectronic atoms have orbitals in
the same sublevel that are degenerate
Ex. All 3d orbitals are degenerate in a polyelectronic atom
Fig. 7.18
7.7 Orbital Shapes and Energies
4th Quantum Number:
electron spin quantum number (ms) + ½ or - ½
Quantum # Summary
n = 1, 2, 3, 4…
l = 0, 1, 2, 3 … (n-1)
ml = -l…0…+l
ms = +1/2 or -1/2
7.7 Orbital Shapes and Energies
1. Give the set of
quantum numbers for
the highest energy
electron in each of the
following:
• Mg
• Cu
• Fe
• P
• I
• U
2.






Which of the
following sets of
quantum #’s are NOT
possible?
3, 1, -1, +1/2
4, 4, 0, +1/2
2, 1, 0, -1/2
2, 0, -1, +1/2
2, 2, 1, +1/2
3, 2, -3, -1/2
7.7 Orbital Shapes and Energies
Pauli Exclusion Principle – in a given atom no
two electrons can have the same set of 4
quantum numbers.
Which means an orbital can only….
– Hold two electrons
– Which must have opposite spins
7.9 Polyelectronic Atoms
Three energy contributions are important:
1. KE of e2. PE (+) nucleus …(-) e3. PE (-) e-…..(-) eElectron correlation problem – since electron
paths are unknown, their repulsions cannot
be calculated exactly
7.9 Polyelectronic Atoms
• We treat electrons as if it were moving in a
field of charge that is the net results of the
nuclear attraction and the average repulsions
of all the other electrons.
• Each electron is screened/shielded from
nuclear charge by the repulsions of the other
electrons.
i.e. It’s not held as tightly due to their presence.
7.9 Polyelectronic Atoms
Hydrogen-like orbitals
• Have the same general shapes
• Have different sizes and energies due to the
interplay between nuclear attractions and the
electron repulsions.
7.9 Polyelectronic Atoms
Hydrogen:
Polyelectronic atoms:
Ens
Enp
End
Enf
Ens
Enp
End
Enf
7.9 Polyelectronic Atoms
• The hump of electron density that
occurs in the 2s profile very near the
nucleus means that although an
electron in the 2s orbital spends
most of its time a little farther from
the nucleus than does an electron in
the 2p orbital, it spends a small but
very significant amount of time very
near the nucleus.
• We say the 2s electron penetrates
the nucleus more than the electron
in the 2p orbitals.
7.9 Polyelectronic Atoms
• This penetration effect causes and
electron in the 2s orbital to be
attracted to the nucleus more
strongly than an electron in the
2p orbital.
• The 2s orbital is lower in energy
than the 2p orbitals for a
polyelectronic atom.
7.9 Polyelectronic Atoms
In general, the more effectively an orbital allows
its electron to penetrate the shielding electrons
to be close to nuclear charge, the lower is the
energy of that orbital.
Orbtial Shapes/Energies –
(See fig. 7.21)
3s = ___ nodes
An s-orbital with __ nodes,
thus from ___ quantum level
___.
3p = ___ nodes
3d = ___ nodes
7.9 Polyelectronic Atoms
7.10 The History of the Periodic Table
Johann Dobereiner – 1st to recognize patterns “triads”
John Newlands – Law of octaves
Julius Lothar Meyer
used atomic masses
Dmitri Ivanovich Mendeleev
– Given most credit because… could be used to make
predictions of exitence and properties
– Predicted the existence of …Ga, Sc, Ger
– Corrected several…values for atomic masses
– The only fundamental difference between our current
periodic table and Mendeleev’s is…uses atomic # now
7.10 The History of the Periodic Table
7.10 The History of the Periodic Table
7.10 The History of the Periodic Table
7.11 The Aufbau Principle and the
Periodic Table
Valence electrons – in outermost energy level
Core electrons – inner electrons
Key: the elements in the same group (vertical
columns) have the same valence electron
configuration.
7.11 The Aufbau Principle and the
Periodic Table
7.11 The Aufbau Principle and the Periodic Table
Electron filling rules:
1. (n+1)s orbitals always fill before nd orbitals (e.g. 4s
before 3d)
Which can be explained by…the penetration effect
2. Note that sometimes and electron occupies a 5d
orbital instead of a 4f orbital because…4f and 5d
energies are similar
3. Note that sometimes and electron occupies a 6d
orbital instead of a 5f orbital because…6d and 5f are
similar
4. The group labels for Groups 1A, 2A, 3A, 4A, 5A, 6A,
7A, and 8A indicate…# valence e5. The groups 1A, 2A, 3A, 4A, 5A, 6A, 7A, and 8A are
called main group elements
2n2
Energy
Level
1
2
3
4
5
6
#
electrons
n2
#
orbitals
# of each orbital type
7.12 Periodic Trends in Atomic
Properties
Ionization Energy – the energy required to remove
an electron from a gaseous atom or ion.
(usually expressed in kJ/mol)
I1
I2
I3
I4
(use <, >, or =)
Because…. Increase in (+) charge binds the
electrons more firmly.
7.11 The Aufbau Principle and the
Periodic Table
7.11 The Aufbau Principle and the
Periodic Table
First Ionization energies
Increase as we go across a period
because…electrons in the same level do
not shield the increasing nuclear charge
thsu the electrons are held more tightly.
Decrease as we go down a group because…
electrons are on average farther from
nucleus and are thus less tightly held.
Discontinuities:
Be B
NO
7.11 The Aufbau Principle and the
Periodic Table
• Sample Exercise 7.8 The first IE for phosphorus is
1060 kJ/mol, and that for sulfur is 1005 kJ/mol.
Why?
• Sample Exercise 7.9 Which atom has the largest
1st IE, and which one has the smallest second IE?
Explain your choices.
7.11 The Aufbau Principle and the
Periodic Table
Electron Affinity – the energy change associated with the
addition of an electron to a gaseous atom.
X(g) + e-  X- (g)
Note: Many books define it as the energy released.
The more negative the energy, the greater the quantity
of energy released.
.
7.11 The Aufbau Principle and the
Periodic Table
Generally become more negative across periods
because…there is a stronger nuclear pull without more
electron repulsions.
Does NOT
form
Does
form
N vs. C-
vs. O-
Does
form
O2-
Does NOT
form
Electron affinity becomes more positive down
columns because…the electron is added farther
from the nucleus.
7.11 The Aufbau Principle and the
Periodic Table
Table 7.7 Electron Affinities
Of the Halogens
Fluorine has a smaller
Electron
electron affinity
Affinity
Atom
because…
(kJ/mol)
F
-327.8
Attributed to smaller
Cl
-348.7
size of 2p orbitals; eBr
-324.5
is closer thus there
I
-295.2
are more e-/erepulsions.
7.11 The Aufbau Principle and the
Periodic Table
Atomic Radius –
Covalent radii – ½ distance between
two covalently bonded diatomic molecules
Metallic radii – ½ distance between metal atoms in
solid metal crystals.
Decreases across periods because… effective nuclear
charge is increasing.
Increases down columns because… there is an
increase in orbital sizes in
successive principal quantum
#’s.
7.11 The Aufbau Principle and the
Periodic Table
• Sample Exercise 7.10 – Trends in Radii – Predict
the trends in radius for the following ions:
Be2+, Mg2+, Ca2+, Sr2+.
7.13 – The Properties of a Group: The Alkali Metals
Information Contained in the Periodic Table:
1.
2.
3.
4.
# and type of valence e- determine an atom’s chemistry
e- configurations are important: Cr, Cu exceptions
know group names
Metals – tendency to give up e- making (+) ions
low IE’s
reactivity increases toward Fr (smallest IE)
Nonmetals – gain e- making (-) ions
large IE’s
more reactive toward F
Metalloids – metallic/nonmetallic properties
7.13 – The Properties of a Group: The
Alkali Metals
Alkali Metals
Down columns
Densities increase
mp/bp
decrease
First IE’s decrease
Atomic radii
increases
Ionic radii increases
Ionic radii are smaller than covalent radii
7.13 – The Properties of a Group: The
Alkali Metals
• Most characteristic chemical property of metals
is ….ability to lose valence e• Metal + nonmetal 
– Nonmetal acts as oxidizing agent (gets reduced)
– Metal acts as reducing agent (gets oxidized)
2 Na(s) + S(s)  Na2S (s)
6 Li(s) + N2 (g)  2 Li3N (s)
2 Na(s) + O2(g)  Na2O2 (s)
7.13 – The Properties of a Group: The
Alkali Metals
Expected trend in reducing ability:
Cs> Rb > K > Na > Li
With water..
2 M(s) + 2 H2O(l)  H2 (g) + 2 M+(aq) + 2 OH-(aq) + energy
The order of reducing ability is: Li > Na > K
7.13 – The Properties of a Group: The
Alkali Metals
Hydration Energies for Li+, Na+, and K+ Ions.
Ion
Hydration Energy
kJ/mol
Li+
-510
Na+
-402
K+
-314
Hydration energy – change in energy that occurs
when water molecules attach to the M+ ion.
7.13 – The Properties of a Group: The
Alkali Metals
Li atoms become Li+ ions more easily in water than
in gas phase. Polar water molecules
are more strongly
attracted to Li+ ddue to
its small size than K+
Potassium appears to react more violently with
water because… K melts thus more surface area
leads to a more vigorous reaction.
7.13 – The Properties of a Group: The
Alkali Metals
Peroxide Rxns:
metal peroxide + H2O  base + hydrogen peroxide
Na2O2 +
BaO2 +
H 2O 
H 2O 
Metal Oxide + H2O  base
Nonmetal oxide + H2O  acid