Chapter 5 Mendeleev`s Periodic Table

Chapter 5
Perodicity and Atomic Structure
Mendeleev’s Periodic Table
• In the 1869, Dmitri Mendeleev proposed that
the properties of the chemical elements repeat
at regular intervals when arranged in order of
increasing atomic mass.
• Mendeleev is the architect of the modern
periodic table.
Chapter 5
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Prediction of New Elements
• Mendeleev noticed that there appeared to be some elements
missing from the periodic table so he left spots for undiscovered
elements.
• Based on his periodic table, he accurately predicted the properties
of some of these the unknown elements before their discovery.
Chapter 5
3
Periodic Trends
• The arrangement of the periodic table means that
the physical properties of the elements follow a
regular pattern.
• Some trends include:
– Atomic Radius (end of Chapter 5)
– Ionization Energy (Chapter 6)
– Electron Affinity (Chapter 6)
– Electronegativity (Chapter 7)
Chapter 5
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The Structure of Atoms
Plum Pudding Model
Tootsie Pop Model
Chapter 5
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The Dual Nature of Light:
The Particle and The Wave
• From the time of the ancient
Greeks, people have thought of
light as a stream of tiny
particles - like marbles or
billiard balls
• Thomas Young (in 1807)
performed the now classic
double slit experiment to test
this theory.
Chapter 5
A great animation of the idea of light as waves and particles can be found here:
http://video.google.com/videoplay?docid=-4237751840526284618&q=quantum
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3
The Dual Nature of Light: The Wave
• As evidenced by the double slit
experiment, light travels through space as
a wave, similar to an ocean wave.
• Wavelength (λ) is the distance light
travels in one cycle.
• Frequency (ν) is the number of wave
cycles completed each second.
• Amplitude is the height measured from
the center of the wave. The square of this
value gives the Intensity.
Velocity (c) = λ • ν
• Light has a constant velocity (c) of 3.00 × 108 m/s.
Chapter 5
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Frequency - Wavelength
• The red light in a laser pointer comes from a
diode laser that has a wavelength of about 632
nm. What is the frequency of the light?
Chapter 5
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4
The Dual Nature of Light: The Particle
• In 1900, Max Planck proposed
that radiant energy is not
continuous, but is emitted as
small bundles of energy
– This is the quantum concept.
• Planck determined that the energy of an emitted bundle is directly
proportional to the frequency of the emitted light times a constant (h)
E = hν =
hc
λ
h = 6.626 × 10 −34 J ⋅ s
Chapter 5
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The Photoelectric Effect
• The Photoelectric Effect shows that when light is
shined on the surface of a metal, electrons are ejected
and a current can be detected.
• Albert Einstein used Planck’s idea of quanta to
explain this phenomona.
– If the light were waves only, then the energy of that
radiation would depend only on the intensity of the
light.
– Einstein hypothesized that electrons are only ejected
if the frequency of the light exceeds a threshold
value specific to the metal, regardless of light
intensity
– Even at low light intensities, electrons are ejected
immediately if the frequency exceeds the threshold
• Millikan tested Einstein’s hypothesis in 1914 and
proved that is was correct
• Einstein wins the Nobel Prize! Yea!
Chapter 5
Figure above from http://en.wikipedia.org/wiki/Photoelectric_Effect
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5
Energy of Emission
• For red light with a wavelength of about 632
nm, what is the energy of a single photon and
one mole of photons?
Chapter 5
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Wave – Particle Duality
• Louis de Broglie suggested that if light can behave
like matter (particles) then matter can behave as light.
This concept is called wave – particle duality.
For a Particle
For Light
E = mc2
E = hν
λ =
h
mv
h = 6.626 x 10-34 kg • m2 / s
Chapter 5
λ =
h
mc
h = 6.626 x 10-34 J • s
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Wave – Particle Duality
• How fast must an electron be moving if it has a
de Broglie wavelength of 551 nm?
• How fast must an electron be moving if it has a
de Broglie wavelength of 631 nm?
me = 9.109 x 10–31 kg
Chapter 5
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The Electromagnetic Spectrum
• The complete electromagnetic spectrum (all possible
wavelengths and frequencies) is an un-interrupted
band, or continuous spectrum.
• The radiant energy spectrum includes most types of
radiation, most of which are invisible to the human
eye.
ROY G BIV
Chapter 5
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The Atomic Spectra
• When a particular element is
heated and the light emitted is
focused and passed through a
prism, the resulting breakdown
results in a non-continuous
spectrum or a discrete line
spectrum
• This spectrum is called the
element’s atomic spectrum
• The discrete lines indicate a
light is emitted or absorbed
in a series of discrete
frequencies rather than
continuously
Chapter 5
• Each element has its own,
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unique spectrum
The Bohr Model of the Atom
• In 1913, Niels Bohr suggested a new model of the atom that explained why
hydrogen had a discrete line spectrum rather than a continuous spectrum.
• Bohr's basic theory: electrons in atoms can only be at certain energy levels,
and they can give off or absorb radiation only when they jump from one level
to another.
• In his model that an atom consists of an
extremely dense nucleus that is surrounded by
electrons that travel in set orbits around the
nucleus.
• He hypothesized that the energy possessed by
these electrons and the radius of the orbits are
quantized, meaning it is limited to specific
values and is never between those values.
• These “orbits” were of varying energies,
The
dependent on their distance from the nucleus
Chapter 5
Gobstopper Model
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Quantized versus Continuous
• The quantum concept means that the energy of the electron and
its radius of orbit around the nucleus is limited to specific values
(and cannot be anywhere in between!).
• If these values were continuous, they would be free to have any
value.
Energy
E3
hv = E3 – E2
E2
hv = E3 – E1
hv = E2 – E1
E1
Chapter 5
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Atomic Spectra:
The Balmer-Ryberg Equation
• In 1885, Johann Balmer determined that the pattern of the atomic
spectra of hydrogen could be predicted by a mathematical formula.
• Balmer determined that the wavelength or frequency of the lines in
the spectrum could be expressed by the following equations:
∆E = RH
(
)
1
1
2
ni
n f2
RH is the Ryberg constant (2.18 x 10-18 J)
ni and nf are integers with nf > ni
• In addition to the lines seen in the visible region (Balmer series),
there are additional sets of lines found in the UV region (Lyman
series) and the IR region (the Paschen series).
• All conform to the above equations.
Chapter 5
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The Bohr Theory: Problems
• Bohr’s theory only works for
hydrogen atoms.
• Once you have more than one
electron, the calculations for the
electron energy and the orbit radii
breakdown.
• Therefore, a new theory needed to be
developed for multi-electron
elements.
• Bohr’s theory did make two
important contributions:
– It suggested a reasonable explanation
for the discrete line spectrum of the
elements
– It introduced the idea of quantized
electron energy levels (orbits!)
Chapter 5
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The Quantum Mechanical Model of the Atom
• In the 1920’s Erwin Schrödinger applied
the principles of wave mechanics to
atoms and developed the Quantum
Mechanical Model of the Atom
– Basically, Schrödinger said to give up on the
idea of literal orbits for the electrons and
instead concentrate on the electron as a
wave.
• This theory builds on Bohr’s idea of
quantized energy levels (orbits) and adds
additional requirements for electron
location and energy.
Chapter 5
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Quantum Mechanics
• Werner Heisenberg (1901–1976): supported this
idea by showing that it is impossible to know (or
measure) precisely both the position and velocity
(or the momentum) at the same time.
• The simple act of “seeing” an electron would change its energy and
therefore its position.
– Think about pinpointing a fly on the wall. What happens when you try to
swat it?
Heisenberg Uncertainty Principle : (∆x)(∆mυ ) ≥
Uncertainty in electron' s position : (∆x) ≥
Chapter 5
h
4π
h
(4π )(∆mυ )
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Quantum Mechanics
• Working with Heisenberg’s Principle, Schrödinger
developed a compromise which calculates both the energy
of an electron and the probability of finding an electron at
any point in the molecule.
• This is accomplished by solving the Schrödinger equation,
resulting in the wave function, Ψ.
Wave
Equation
solve
Wave Function
or Orbital (Ψ)
Probability of finding
an electron in a
region of space (Ψ2)
• These regions were termed orbitals
Chapter 5
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Quantum Numbers
• The wave function contains three variables
known as the Quantum Numbers which
describe the size, energy, shape and position of
the orbitals.
– n is the principal energy level (Bohr’s Orbits!)
– l is the sublevel
– ml is the orbital
• These numbers serve as an “address” of the
probable location of the electron.
Chapter 5
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Principal Quantum Number (n)
• The Principal Quantum Number (n)
provides info about the distance of
the electron from the nucleus
– As n increases, the number of allowed
orbitals also increases as does the size
of those orbitals.
– This increased size allows the electron
to reside further from the nucleus
– As the electron moves away from the
nucleus its energy increases, therefore n
also indicates the energy of electrons
• We often state that electrons and
orbitals denoted by the same n value
are in the same shell
Allowed Values: n = 1, 2, 3, ... never 0
Chapter 5
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Angular-Momentum Quantum Number (l)
• The angular momentum
quantum number (l) defines the
three dimensional shape of the
orbitals found within a particular
shell
• These discrete sets of orbitals
are called sublevels
• The number of sublevels within
a shell is equal to the principal
quantum number (n)
l Value:
Letter Used:
Chapter 5
Allowed Values:
l = 0, 1, 2 ... n - 1
0
s
1
p
2
d
3
f
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increasing energy
Magnetic Quantum Number (ml)
• The Magnetic Quantum Number (ml) describes the orientation in 3D
space of the sublevel, thereby denoting a specific orbital.
• The number of orientations (and therefore orbitals) per sublevel is
determined by the equation:
2l + 1
Allowed Values: ml = - l, … , + l
y axis
l
0 (s) 1 (p) 2 (d)
3 (f)
2l + 1
x axis
Chapter 5
z axis
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Spin Quantum Number (ms)
• The Pauli Exclusion Principle states
that no two electrons can have the
same four quantum numbers
• This results in no more than double
occupancy in any one orbital
– only two electron per orbital and
they must have opposite spins
Chapter 5
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Electron Occupancy in Sublevels
• The Pauli Exclusion Principle states that an orbital can hold
up to two electrons
• The maximum number of electrons in each of the sublevels
depends on the number of orbitals within that sublevel:
– The s sublevel holds a maximum of 2 electrons (1 orbital).
– The p sublevel holds a maximum of 6 electrons (3 orbitals).
– The d sublevel holds a maximum of 10 electrons (5 orbitals).
– The f sublevel holds a maximum of 14 electrons (7 orbitals)
• The maximum electrons per principle quantum level (n) is
obtained by adding the maximum number of electrons in each
sublevel.
Chapter 5
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Quantum Number Combinations
• Why can’t an electron have the following quantum numbers?
(a) n = 2, l = 2, ml = 1
(b) n = 3, l = 0, ml = 3
(c) n = 5, l = –2, ml = 1
• Give orbital notations for electrons with the following
quantum numbers:
(a) n = 2, l = 1, ml = 1
(b) n = 4, l = 3, ml = –2
(c) n = 3, l = 2, ml = –1
Chapter 5
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Shapes of the Orbitals
• Each orbital has a specific shape determined by its
angular momentum quantum number (l).
• As you increase the principle quantum number (n), the
orbitals increase in size but not shape!
• Remember, these orbitals represent a region in space
where there is a high probability of finding the electron.
– These are not discrete locations!
– They are also not pictures of the path that an electron follows
around a nucleus
Chapter 5
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l = 0 : The s Orbitals
• The s orbitals are spherical, meaning the probability of finding the
electron depends only on distance from the nucleus, not direction.
• The value of Ψ2 is greatest near the nucleus then drops off as you
move away.
• It never reaches zero however so there is technically no definite
boundary to the atom.
Chapter 5
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l = 1 : The p Orbitals
• The p orbitals are dumbbell shaped with their electron density concentrated in
identical lobes residing on opposite sides of a nodal plane.
• This shape means that a p electron will never be found near the nucleus.
• The two lobes of a p orbital have different phases (are opposite in sign) which
becomes important in bonding among atoms.
• The three orientations (ml = -1, 0, +1) are 90° differentials along the x, y and
z axes.
• The orbitals are designated px (along the x axis), py (along the y axis), and pz
(along the z axis)
Chapter 5
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l = 2 : The d Orbitals
Chapter 5
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Effective Nuclear Charge (Zeff)
• The nuclear charge (Z) of an atom is
determined by the number of protons found
in the nucleus
– It is felt by the electrons as an attraction
• Multiple electrons in an atom lead to a
shielding effect on the outer electrons.
• This electron shielding (S) leads to energy
differences among orbitals within a shell.
• Net nuclear charge felt by an electron is
called the effective nuclear charge (Zeff).
Chapter 5
Zeff = Z + S
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Effective Nuclear Charge (Zeff)
Note that the 3d
sublevel is actually
higher in energy than
the 4s sublevel.
WHY??
Chapter 5
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The Modern Periodic Table
•
H.G.J. Moseley discovered that the nuclear charge increased by 1 for each element in the
Mendeleev’s table.
•
He concluded that the changing atomic number rather than the changing mass explained the
repeating trends of the elements
•
The periodic law states that the properties of elements recur in a repeating pattern when arranged
according to increasing atomic number.
•
With the introduction of the concept of electron energy levels by Niels Bohr, the periodic table took
its current arrangement.
Chapter 5
http://www.webelements.com/
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Electron Configurations
• Many of an element’s chemical
properties depend on its electron
configuration
• The electron configuration of an atom is a shorthand method of
writing the location of electrons by sublevel.
• The principal quantum level (n) is written first, followed by the
letter designation of the sublevel (l) then a superscript with the
number of electrons in the sublevel.
• There are rules for the order and manner that each sublevel is
filled called the Aufbau Principle.
Chapter 5
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Electron Configurations: Aufbau Principle
Pauli Exclusion Principle: No two electrons in an atom can
have the same quantum numbers (n, l, ml, ms).
Hund’s Rule: When filling orbitals in the same sublevel,
maximize the number of parallel spins (so fill then pair!).
Rules of Aufbau Principle:
1. Lower n orbitals fill first.
2. Each orbital holds two electrons; each with different ms.
3. Half-fill degenerate orbitals before pairing electrons.
Chapter 5
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Using the Periodic Table for Electron Configurations
• The periodic table took on its current shape once the quantum model of the
atom was developed.
• You can use it to fill up your sublevels and orbitals to build your electron
configurations.
Chapter 5
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Writing Electron Configurations
• Step 1: Locate the element on the periodic table.
• Step 2: Determine the number of electrons the element
Iron has 26 electrons
has:
• Step 3: Starting at the beginning of the Periodic Table,
move left to right across the periods, filling each sublevel
with electrons until you reach the location of your
element:
Fe: 1s2 2s2 2p6 3s2 3p6 4s2 3d 6
• Step 4: Check that the sum of the superscripts equals the
atomic number of iron (26).
Chapter 5
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An Alternative Method
Increasing Energy
Core
[He]
[Ne]
[Ar]
[Kr]
[Xe]
[Rn]
1s
2s
3s
4s
5s
6s
7s
2p
3p
4p
5p
6p
7p
3d
4d 4f
5d 5f
6d
Chapter 5
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Writing Electron Configurations
↑↓
1s
↑
2s
1s2 2s1
Be ↑↓
1s
↑↓
2s
1s2 2s2
Li
B
↑↓ ↑↓ ↑
1s 2s 2px 2py 2pz
1s2 2s2 2p1
C
↑↓ ↑↓ ↑
↑
1s 2s 2px 2py 2pz
1s2 2s2 2p2
Chapter 5
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Writing Electron Configurations
N
↑↓ ↑↓ ↑ ↑ ↑
1s 2s 2px 2py 2pz
1s2 2s2 2p3
O
↑↓ ↑↓ ↑↓ ↑ ↑
1s 2s 2px 2py 2pz
1s2 2s2 2p4
Ne ↑↓ ↑↓ ↑↓ ↑↓ ↑↓
1s 2s 2px 2py 2pz
1s2 2s2 2p5
[Ne] ↑↓ ↑↓ ↑ ↑
3s 3px 3py 3pz
Chapter 5
[Ne] 3s2 3p4
S
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Writing Electron Configurations
• Give the ground-state electron configurations for:
Ne (Z = 10)
Mn (Z = 25)
Zn (Z = 30)
Eu (Z = 63)
W (Z = 74)
Lw (Z = 103)
• Identify elements with ground-state configurations:
1s2 2s2 2p4
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d6
1s2 2s2 2p6
[Ar] 4s2 3d1
Chapter 5
[Xe] 6s2 4f14 5d10 6p5
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Exceptions to the Filling Order
• When filling the d sublevel, exceptions occur for the
chromium (Cr) and copper (Cu) families:
Cr
Cu
4s
3d
4p
4s
3d
4p
4s
3d
4p
4s
3d
4p
Chapter 5
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Periodic Trends
• The arrangement of the periodic table means that
the physical properties of the elements follow a
regular pattern.
• Some trends include:
– Atomic Radius (end of Chapter 5)
– Ionization Energy (Chapter 6)
– Electron Affinity (Chapter 6)
– Electronegativity (Chapter 7)
Chapter 5
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Atomic Radius
• An atom’s atomic radius is the distance from the nucleus to the
outermost electrons.
Why do you think the radius
increases in this way?
Chapter 5
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