Download Electronic Structure of Atoms

Electronic Structure of Atoms
Chapter 6
Light
• Made up of
electromagnetic
radiation.
• Waves of electric and
magnetic fields at right
angles to each other.
Parts of a wave
Wavelength
l
Frequency (n = number of cycles in 1 second
Measured in hertz 1 hertz = 1cycle/second
Frequency = n
Kinds of EM waves
• There are many different EM waves
• different l and n
• Visible Light is only the part our eyes can
detect. (colors of the rainbow)
• Greater wavelength means, smaller frequency
Gamma
Rays
X-Rays
UV
Infrared
Microwave
Radio
Visible Spectrum
The speed of light, c
• in a vacuum is 2.998 x 108 m/s
• c = 3.0 x 108 m/s
• c = ln
Examples
What is the wavelength of light
with a frequency 5.89 x 1014 Hz?
l =
c
v
=
3.0 x 108 m/s
5.89 x 1014 Hz
= 5.09 x 10-7 m = 509 nm
(green light)
What is the frequency of blue light
with a wavelength of 484 nm?
v=
c
l
=
3.0 x 108 m/s
484 x 109 m
= 6.20 x 1014 Hz
Planck and the Quantum Theory
• Energy is gained or lost in whole number multiples
(n) of the quantity hv.
• Similar to energy required to go up stairs (opposed
to going up a ramp)
• Planck found that Energy is transferred to matter in
“energy packets” called a quantum (hv)
• Frequency = v
• Planck’s constant = h = 6.63 x 10-34 J-s
DE = nhn
Einstein, the Photoelectric Effect, and
Photons
• EM radiation is quantized a stream of
particles -- “photons”
• Ephoton = hn = hc/l
• Combine this with E = mc2
• You get the apparent mass of a photon.
m = h / (lc)
Is light a Wave or
does it consist of particles?
• Both…
• Macroscopically like a wave,
• But consists of a collection of photons that
we only see at the atomic level.
• called The Wave-Particle Duality
(Like describing an entire beach and then
beginning to examine the grains of sand.)
Examples
• Calculate the energy of one photon of
yellow light whose wavelength is 589nm
1. Find the frequency
• 5.09 x 1014 s-1
2. Then use Plank’s equation to find E
• 3.37 x 10-19 J
Matter as a wave
• Using the velocity (v) instead of the
frequency (n we get:
• De Broglie’s equation l = h/mv
• Can calculate the wavelength of an object.
Line Spectra
• Spectrum = the range of frequencies present
in light
• Continuous Spectrum = contains all
wavelengths of light. (white light… can be
broken down into “rainbow”)
• Line Spectrum = contains only specific
wavelengths of light.
Hydrogen spectrum
• Emission spectrum because these are the colors
it gives off or emits.
• Called a bright line emission spectrum.
• There are just a few discrete lines showing
656 nm
434 nm
410 nm
486 nm
Visible Spectrum
Bright Line Spectra
• Excited electrons return to lower NRG states
• NRG is emitted in the form of a photon of definite
wavelength.
• Definite change in energy corresponds to:
– Definite frequency
– Definite wavelength
• Use DE = hn = hc / l
• Only certain energies are possible within any atom.
Niels Bohr
• Developed the Quantum Model
• Described the atom like a solar system
• Electrons attracted to (+) nucleus because of
their (-) charge
• Electrons didn’t fall into nucleus because
they were moving around
Bohr’s atom
• Found only certain NRGs were allowed;
called them NRG levels.
• Putting NRG into atom moves electron away
from the nucleus (ground state  excited
state)
• When e- returns to ground state, it gives off
light of a certain NRG
The Bohr Atom
n=4
n=3
n=2
n=1
Available NRG levels
E = -2.178 x 10-18 J (Z2 / n2 )
• n = quantum number (NRG level)
• Z = nuclear charge (+1 for Hydrogen)
• J = energy in joules
• The more negative the NRG is, the more
stable the atom will be.
change in Energy
• When the electron moves from one
energy level to another:
• DE = Efinal - Einitial
DE = -2.178 x 10-18J [(1/ nf2)–(1/ ni2)]
l = hc / DE
Shortcomings of Bohr Model
• Only works for Hydrogen atoms
• Electrons don’t move in circular orbits
• The quantization of energy is right, but not
because they are circling like planets
• Questions Bohr couldn’t answer:
Why are e- confined to only certain energy levels?
Why don’t e- eventually spiral and crash into the
nucleus?
The Quantum Mechanical Model
• New approach that viewed electron as a
standing wave of NRG
• Standing waves don’t propagate through
space
• Standing waves are fixed at both ends
(similar to vibrations of a stringed
instrument)
What’s possible?
• You can only have a standing wave if you have
complete waves.
• There are only certain allowed waves.
• In the atom there are certain allowed waves
called electrons.
• 1925 Erwin Schroedinger described the wave
function of the electron. “The Schroedinger
Equation”
• Much math but what is important are the
solutions.
Schroedinger’s Equation

2x2
22
•
•
•
•
•
•

2y2
22

2z2
22


82m
h2

(E  V)  = 0
The wave function,  is a F(x, y, z)
Solutions to the equation are called orbitals.
These are not Bohr orbits.
Each solution is tied to a certain energy.
These are the energy levels.
Many strange and seemingly impossible behaviors
occur when the electron is treated as a wave!
Orbitals
• Orbitals are not circular orbits for
electrons
• Orbitals are areas of probability for
locating electrons
There is a limit to what we can
know…
• about how the electron is moving or how it gets
from one energy level to another.
• about both the position and the momentum of
an object.
• The Heisenberg Uncertainty Principle - “we
cannot know the exact location and exact
momentum of an electron at the same time.”
Quantum Mechanical Model and Quantum
Numbers
• Note: A quantum mechanical orbital is not
the same as a Bohr orbit because the
motion of the electron in an atom cannot be
precisely measured or tracked. (Heisenberg
uncertainty Principle)
• There are 4 quantum numbers to describe the
“location” of an electron. (sort of like how a zip
code works)
Principal Quantum Number (n)
• Indicates probable distance from the
nucleus (old Bohr orbitals)
• Gives the size and energy of the orbital
• Has integer values >0
• According to the periodic table, what would
the highest principal quantum number be?
Angular Momentum Quantum (l )
• Gives the shape of the orbital (more detail to
come)
• Integral values from 0 to (n-1) for each principal
quantum number (n)
Value of l
0 1 2 3 4
Letter used for shape* s p d f g
*letters s, p, d, f come from the words sharp, principal,
diffuse, and fundamental, which were used to describe
certain features of spectra before quantum mechanics
was developed.
Magnetic Quantum Number (ml )
• Relates to the orientation of the orbital in
space relative to the other orbitals. (It tells
you if the orbital will be on the x, y or z
axis.)
• Integral values from l to –l including 0.
n
l
1
2
3
4
0
0
1
0
1
Orbital
designation
1s
2s
2p
3s
3p
ml
0
0
-1, 0, 1
0
-1, 0, 1
# of
orbitals
1
1
3
1
3
2
0
1
2
3
3d
4s
4p
4d
4f
-2, -1, 0, 1, 2
0
-1, 0, 1
-2, -1, 0, 1, 2
-3, -2, -1, 0, 1, 2, 3
5
1
3
5
7
Important Observations
1. The shell w/ quantum #n will have exactly n
subshells.
2. Each subshell has a specific number of orbitals.
Each orbital corresponds to a different allowed
value of ml. For a given value of l, there are 2l +
1 allowed values of ml.
3. The total number of orbitals in a shell is n2. The
resulting number of orbitals for the shells – 1, 4, 9,
16 – is related to a pattern seen in the periodic
table… We see the number of elements in the
table – 2, 8, 18, 32 – equal twice these numbers…
S orbitals
n=1 n=2
n=3
P orbitals
At another energy level the solutions are
“dumbell” shaped.
There are 3 possible solutions for this energy leve
P Orbitals
All 3 p orbitals may exist at the same time.
d orbitals
At another energy we get “flower” shaped orbitals for a solution.
All 5 may exist
at the same
time
F orbitals
And finally, at another energy, 7 f orbitals are the solution.
Orbital Energies
• All orbitals with the same value of n have
the same energy
• The lowest energy state is called the
“ground state”
• When the atom absorbs energy, electrons
may move to higher energy orbitals –
“excited state”
Electron Spin
Quantum Number (ms )
• An individual orbital can hold only 2
electrons
• Electrons must have opposite spins (why
important?)
• Spin can have two values +½ or –½
Pauli Exclusion Principle
“in a given atom, no two electrons can have
the same set of four quantum numbers”
What this means for the atom?
• Each atomic sub-orbital may contain a
maximum of 2 electrons
• Those electrons must have opposite spins
Increasing energy
7s
6s
5s
4s
3s
2s
1s
7p
6p
6d
5p
4d
4p
5d
3d
3p
2p
Helium with 2
electrons
5f
4f
Increasing energy
7s
6s
5s
4s
3s
2s
1s
7p
6p
6d
5p
4d
4p
5d
3d
3p
2p
Li with 3 electrons
5f
4f
Increasing energy
7s
6s
5s
4s
3s
2s
1s
7p
6p
6d
5p
4d
4p
5d
3d
3p
2p
Boron with 5 electrons
5f
4f
2 more important rules:
• Aufbau Principle – electrons enter orbitals
of lowest energy first.
• Hund’s Rule -- When electrons occupy
orbitals of equal energy, one electron enters
each orbital before they pair.
For Example:
2s
2p
After the s sublevel gets
two electrons, three
electrons enter the p
orbitals before they pair.
Increasing energy
7s
6s
5s
4s
3s
2s
1s
7p
6p
6d
5p
4d
4p
3p
2p
5d
3d
5f
4f
Electron Configuratoin
p
s
d
f
3 QUESTIONS TO ASK
• What Row?
–(principle energy level)
• What section?
–(type of sub-orbital)
• What seat?
–(how many electrons in that suborbital)
Example 1:
Write the electron
configuration for nitrogen.
7N
2
2
3
1s 2s 2p
Example
Write the electron
2:
configuration for Fe.
26Fe
2
2
6
2
6
2
6
Condensed Electron Configurations
• Put the symbol for the Noble gas from the
previous principal energy level, then add the
electron configuration after that point.
• Example 1 for Nitrogen:
[He] 2s22p3
• Example 2 for Iron:
• [Ar] 4s23d6
The History of
the Modern
Periodic Table
See separate slide show for Periodic Table History
Periodic Law
• When elements are arranged in order of
increasing atomic #, elements with similar
properties appear at regular intervals.
Atomic Radius (pm)
250
200
150
100
50
0
0
5
10
Atomic Number
15
20
Chemical Reactivity
Families  Similar valence e- within a group
result in similar chemical properties
1
2
3
4
5
6
7
•Alkali Metals
•Alkaline Earth Metals
•Transition Metals
•Halogens
•Noble Gases
Periodic Table Reveals Periodic Trends
• Effective Nuclear charge
• Reactivity
• atomic size or radius
• bonding characteristics
• ionization energy
• crystal configurations
• electron affinity
• acidic properties
• electronegativity
• densities
• metallic character
• Melting/Boiling points
Electron screening or shielding
• Electrons are attracted to the nucleus
• Electrons are repulsed by other electrons
• Electrons would be bound more tightly if
other electrons weren’t present.
• The net nuclear charge felt by an electron is
called the effective nuclear charge ( Zeff ).
Quantum Mechanical Model
Zeff is lower than actual
nuclear charge.
Zeff increases
toward nucleus
ns > np > nd > nf
This explains certain periodic
changes observed.
Effective Nuclear Charge ( Zeff)
• The effective nuclear charge acting on an
electron equals the number of protons in
the nucleus, Z, minus the average number
of electrons, S that are between the nucleus
and the electron in question.
Zeff = Z  S
Zeff = attractive forces  repulsive forces
Zeff = # protons  # shielding electrons
For Example, Lithium vs. Carbon
Li Zeff = 3  2 = 1
C
Zeff = 6  2 = 4
When moving across a row:
The greater the Zeff value,
the smaller the atom’s radius.
So, carbon has a much smaller atomic radius compared to lithium: Rcarbon =77
pm Rlithium = 152 pm
Trend #1 Atomic Radii
Increases to Left and Down
1
2
3
4
5
6
7
•Why larger going down?
•Higher energy levels have larger orbitals
•Shielding - core e- block the attraction between the nucleus and the valence e•Why smaller to the right?
• Increased nuclear charge without additional shielding pulls e- in tighter
Practice…
• Referring to a periodic table, arrange the
following atoms in order of increasing size:
– Phosphorus
– Sulfur
– Arsenic
– Selenium
• S < P < Se < As
Atomic radii
The Periodic Table & Radii
Periodic Trend is Due to
Effective Nuclear Charge
Atomic Radii vs. Zeff:
Trends in Ionic Radii
• Using your knowledge of Zeff, how would
the size of a cation compare to neutral
atom? Anion?
Trends in Ionic Radii
• The cation of an atom decreases in size.
• The more positive an ion is, the smaller it is because
Zeff increases
• The anion of an atom increases in size.
• The more negative an ion, the larger it is because
Zeff decreases.
Cations  lose electrons, become smaller
Anions  gain electrons, become bigger
Ion Radii
Increases down
1
2
3
4
5
6
7
Increases moving across, but depends
if cation OR anion
+3 +4 -3 -2 -1
Ions and Ionic Radii
Practice…
• Arrange the following atoms and ions in order
of decreasing size:
– Mg2+
– Ca2+
– Ca
• Which of the following ions is the largest:
– S2–S
– O2-
Practice…
• Arrange the following ions in order of decreasing
size:
– S2– Cl– K+
– Ca2+
• Which of the following ions is the largest?
– Rb+
– Sr2+
– Y3+
Trend in Ionization Energy
• Ionization NRG is the NRG required to
remove an electron from an atom
Successive Ionization NRG
• Ionization energy increases for successive
electrons from the same atom.
Why do you think there is such a big jump for Mg3+?
*Notice the large jump in ionization energy
when a core e is removed.
• The smaller the atom, the higher the
ionization energy due to Zeff
• Bigger atoms have lower ionization NRG
due to the fact that the electrons are
further away from the nucleus and
therefore easier to remove.
Decreases
Increases
Practice…
• Which of the following elements would
have the highest second ionization
energy? Justify your answer.
–Sodium, Sulfur, or Calcium
• Which will have the greater third
ionization energy, Ca or S? Justify your
answer.
Practice…
• Referring to a periodic table, arrange the
following atoms in order of increasing first
ionization energy (Ne, Na, P, Ar, K) Justify your
answer.
• Based on the trends discussed in this section,
predict which of the following atoms (B, Al, C
or Si) has the lowest first ionization energy
and which has the highest first ionization
energy.
Electron Affinity
• The energy change associated with the addition of
an electron
• Tends to increase across a period
• Tends to decrease as you go down a group
• Abbreviation is Eea, it has units of kJ/mol. Values are
generally negative because energy is released.
• Value of Eea results from interplay of nucleus
electron attraction, and electron–electron
repulsion.
Ionization NRG vs. Electron Affinity
• Ionization energy measures the ease with
which an atom loses an electron
• Electron affinity measures the ease with
which an atom gains an electron
Electron Affinity
Trends in Electronegativity
• tendency for an atom to attract
electrons when it is chemically combined
with another atom.
• decreases as you move down a group
• increases as you go across a period from
left to right.
Trend #5 Metallic Character
• The metallic character of atoms can be related
to the desire to lose electrons.
• The lower an atom’s ionizatoin energy, the
greater its metallic character will be.
• On the periodic table, the metallic character of
the atoms increase down a family and decreases
from left to right across a period.
Metals
Nonmetals
• Shiny Luster
• Various colors (most
silvery)
• Solids are malleable and
ductile
• Good conductors of heat
and electricity
• Most metal oxides are
ionic solids that are basic
• Tend to form cations in
aqueous solution
•
•
•
•
No luster
Various colors
Brittle solids
Poor conductors of heat
and electricity
• Most nonmetal oxides
are molecular
substances that form
acidic solutions
• Tend to form anions or
oxyanions in aqueous
solution
Metallic Character
Increases moving down and across to the left
1
2
3
4
5
6
7
Rb
Cs Ba
Fr Ra
Lower left corner -- elements most
likely to lose their valence electrons
Metals and Nonmetals
• Low ionization energies of metals means they
tend to form cations (positive ions) relatively
easily
• Due to their electron affinities, nonmetals
tend to gain electrons when they react with
metals.
# 6 Melting/Boiling Points
• Highest in the middle of a period (generally).
1
2
3
4
5
6
7
Some Important Properties of Alkali Metals
• Soft metallic solids
• Easily lose valence electrons (Reducing
Agents)
– React with halogens to form salts
– React violently with water
• Large Hydration NRG
– Positive ionic charge makes ions attractive to
polar water molecules
Alkaline Earth Metals…
• Harder and more dense than Alkali Metals
• Less reactive than alkali metals (lower first
ionization energies)
• Reactivity increases as you move down the
periodic table.
The Halogens…
• “Salt Formers”
• Melting and Boiling Points increase with
atomic number.
• Highly negative electron affinities
• Tendency to gain electrons and form halide
ions
Noble Gases …
•
•
•
•
Monoatomic ions
Gases at room temperature
Large 1st ionization energies
“Exceptionally” unreactive
Practice…
• Look at Sample Integrative Exercise 7 on page
264