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
lWavelength
Frequency (n = number of cycles in 1 secondMeasured 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
X-RaysGamma
Rays UV InfraredMicro-
waveRadio
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
c 3.0 x 108 m/sv = = = 6.20 x 1014 Hz 484 x 109 m
c 3.0 x 108 m/sl = = = 5.09 x 10-7 m = 509 nm v 5.89 x 1014 Hz (green light)
What is the wavelength of light with a frequency 5.89 x 1014 Hz?
What is the frequency of blue light with a wavelength of 484 nm?
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
410 nm
434 nm
486 nm
656 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 = h n = 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 = 3n = 4
n = 2n = 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/ ni
2)]
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
• 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!
22 22 22 82m
2x2 2y2 2z2 h2 (E V) = 0
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 Orbital designation
ml # of orbitals
1 0 1s 0 1
2 0 2s 0 1
1 2p -1, 0, 1 3
3 0 3s 0 1
1 3p -1, 0, 1 3
2 3d -2, -1, 0, 1, 2 5
4 0 4s 0 1
1 4p -1, 0, 1 3
2 4d -2, -1, 0, 1, 2 5
3 4f -3, -2, -1, 0, 1, 2, 3 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 level.
P OrbitalsAll 3 p orbitals may exist at the same time.
d orbitalsAt another energy we get “flower” shaped orbitals for a solution.
All 5 may exist
at the same
time
F orbitalsAnd 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
Incr
easi
ng e
nerg
y
1s
2s
3s
4s
5s6s7s
2p
3p
4p
5p
6p
3d
4d
5d
7p
6d
4f
5f
Helium with 2 electrons
Incr
easi
ng e
nerg
y
1s
2s
3s
4s
5s6s7s
2p
3p
4p
5p
6p
3d
4d
5d
7p
6d
4f
5f
Li with 3 electrons
Incr
easi
ng e
nerg
y
1s
2s
3s
4s
5s6s7s
2p
3p
4p
5p
6p
3d
4d
5d
7p
6d
4f
5f
Boron with 5 electrons
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.
Incr
easi
ng e
nerg
y
1s
2s
3s
4s
5s6s7s
2p
3p
4p
5p
6p
3d
4d
5d
7p
6d
4f
5f
s p
d
f
Electron Configuratoin
3 QUESTIONS TO ASK
• What Row? –(principle energy level)
• What section? –(type of sub-orbital)
• What seat? –(how many electrons in that sub-
orbital)
Example 1:Write the electron configuration for nitrogen.7N 1s22s22p3
Example 2:Write the electron configuration for Fe.
26Fe 1s22s22p63s23p64s23d6
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 TableSee 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.
0
50
100
150
200
250
0 5 10 15 20
Ato
mic
Ra
diu
s (
pm
)
Atomic Number
Chemical ReactivityFamilies 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
• atomic size or radius
• ionization energy
• electron affinity
• electronegativity
• metallic character
• Reactivity
• bonding characteristics
• crystal configurations
• acidic properties
• densities
• 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 = # protons # shielding electrons
Zeff = attractive forces repulsive forces Zeff = Z S
For Example, Lithium vs. Carbon
Li Zeff = 3 2 = 1
C Zeff = 6 2 = 4
So, carbon has a much smaller atomic radius compared to lithium: Rcarbon =77
pm Rlithium = 152 pm
When moving across a row:The greater the Zeff value, the smaller the atom’s radius.
Trend #1 Atomic Radii
1
2
3
4 5
6
7
Increases to Left and Down
•Why larger going down?
•Why smaller to the right?
• Higher energy levels have larger orbitals
• Shielding - core e- block the attraction between the nucleus and the valence e-
• 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
1
2
3
4 5
6
7
+3 +4 -3 -2 -1
Increases downIncreases moving across, but depends if cation OR anion
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.
*Notice the large jump in ionization energy when a core e is removed.
Why do you think there is such a big jump for Mg3+?
• 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.
Increases
Dec
reas
es
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
1
2
3
4
5
6
7
Increases moving down and across to the left
Fr
Cs Ba
Ra
Lower left corner -- elements mostlikely to lose their valence electrons
Rb
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