1. Atomic Structure and Periodicity
Chapter 7
Atomic Structure and Periodicity
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Overview
Introduce Electromagnetic Radiation and The Nature of Matter.
Discuss the atomic spectrum of hydrogen and Bohr model.
Describe the quantum mechanical model of the atoms and quantum numbers.
Use Aufbau principle to determine the electron configuration of elements.
Highlight periodic table trends.
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Matter and Energy
Matter and Energy were two distinct concepts in the 19th century.
Matter was thought to consist of particles, and had mass and position.
Energy in the form of light was thought to be wave-like.
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4. Physical Properties of Waves
Wavelength (l) is the distance between identical points on successive waves.
Amplitude is the vertical distance from the midline of a wave to the peak or trough.
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5. Properties of Waves
Frequency (n) is the number of waves that pass through a particular point in 1 second (Hz = 1 cycle/s).
The speed (v or c) of the wave = l x n
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1-waves can bend
around small obstacles
2-and fan out
from pinholes
3-particles effuse
from pinholes
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7. Electromagnetic Radiation
Electromagnetic radiation is the emission and transmission of energy in the form of electromagnetic waves.
Electromagnetic radiation travels through space at the speed of light in a vacuum.
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8. Speed of light (c) in vacuum = 3.00 x 108 m/s
Maxwell (1873), proposed that visible light consists of electromagnetic waves.
Speed of light (c) in vacuum = 3.00 x 108 m/s
All electromagnetic radiation
l x n = c
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7.1

9. Electromagnetic Waves
Electromagnetic Waves have 3 primary characteristics:
1. Wavelength: distance between two peaks in a wave.
2. Frequency: number of waves per second that pass a given point in space.
3. Speed: speed of light is  m/s.
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Electromagnetic Wave Movie
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12. Wavelength and frequency can be interconverted.
 = frequency (s1)
 = wavelength (m)
c = speed of light (m s1)
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Electromagnetic Spectrum
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Plank
Studied radiation emitted by heated bodies.
Results could not be explained by the old physics which stated that matter can absorb and emit any quantity of energy.
Black Body Radiation
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Planck’s Constant
Transfer of energy is quantized, and can only occur in discrete units, called quanta. n
E = change in energy, in J
h = Planck’s constant,  1034 J s
 = frequency, in s1
= wavelength, in m
n = integer = 1,2,3…
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16. Particle Properties of Lighthn
Photoelectric Effect Solved
by Einstein in 1905
KE e-
Photon is a “particle” of light
hn = KE + BE
KE = hn - BE
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7.2

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Diffraction
X-Ray Diffraction showed also that light has particle properties.
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Figure 7.5: (a) Diffraction occurs when electromagnetic radiation is scattered from a regular array of objects, such as the ions in a crystal of sodium chloride. The large spot in the center is from the main incident beam of X rays. (b) Bright spots in the diffraction pattern result from constructive interference of waves. The waves are in phase; that is, their peaks match. (c) Dark areas result from destructive interference of waves. The waves are out of phase; the peaks of one wave coincide with the troughs of another wave.
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Diffraction Movie
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Photoelectric Effect Movie
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21. E = mc2 Einstein Equation
Energy and Mass
Energy has mass
E = mc2 Einstein Equation
E = energy
m = mass
c = speed of light
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Energy and Mass
Radiation in itself is quantized
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Wavelength and Mass
de Broglie’s Equation
 = wavelength, in m
h = Planck’s constant,  1034 J s = kg m2 s1
m = mass, in kg
v = speed, in ms1
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A photon has a frequency of 6.0 x 104 Hz. Convert
this frequency into wavelength (nm). Does this frequency
fall in the visible region? l n
l x n = c
l = c/n
l = 3.00 x 108 m/s / 6.0 x 104 Hz
l = 5.0 x 103 m
l = 5.0 x 1012 nm
Radio wave
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Atomic Spectrum of Hydrogen
Figure 7.6: (a) A continuous spectrum containing all wavelengths of visible light. (b) The hydrogen line spectrum contains only a few discrete wavelengths.
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26. Atomic Spectrum of Hydrogen
Continuous spectrum: Contains all the wavelengths of light.
Line (discrete) spectrum: Contains only some of the wavelengths of light.
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27. ( ) Bohr’s Model of the Atom (1913) z2 En = -RH n2
e- can only have specific (quantized) energy values
light is emitted as e- moves from one energy level to a lower energy level
En = -RH
( ) z2 n2
n (principal quantum number) = 1,2,3,…
RH (Rydberg constant) = 2.18 x 10-18J
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7.3

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E = hn
E = hn
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Ephoton = DE = Ef - Ei
nf = 1
ni = 3
nf = 2
ni = 3
Ef = -RH
( ) 1 n2 f
nf = 1
ni = 2
Ei = -RH
( ) 1 n2 i i f
DE = RH
( ) 1 n2
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What is the de Broglie wavelength (in nm) associated with a 2.5 g Ping-Pong ball traveling at 15.6 m/s?
l = h/mv
h in J•s
m in kg
u in (m/s)
l = 6.63 x / (2.5 x 10-3 x 15.6)
l = 1.7 x m = 1.7 x nm
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Calculate the wavelength (in nm) of a photon emitted by a hydrogen atom when its electron drops from the n = 5 state to the n = 3 state. i f
DE = RH
( ) 1 n2
Ephoton =
Ephoton = 2.18 x J x (1/25 - 1/9)
Ephoton = DE = x J
Ignore the (-) sign for
l and 
Ephoton = h x c / l
l = h x c / Ephoton
l = 6.63 x (J•s) x 3.00 x 108 (m/s)/1.55 x 10-19J
l = 1280 nm
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The Bohr Model
Ground State: The lowest possible energy state for an atom (n = 1).
Ionization: nf =  => 1/nf2 = 0 => E=0 for free electron.
Any bound electron has a negative value to this reference state.
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To be well memorized
E = h = hc l
P = mv
E = mc2 i f
DE = RH
( ) 1 n2
Ephoton =
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34. Schrodinger Wave Equation
In 1926 Schrodinger wrote an equation that described both the particle and wave nature of the e-
Wave function (Y) describes:
. energy of e- with a given Y
. probability of finding e- in a volume of space
Schrodinger’s equation can only be solved exactly for the hydrogen atom. Must approximate its solution for multi-electron systems.
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Quantum Mechanics
Based on the wave properties of the atom
 = wave function
= mathematical operator
E = total energy of the atom
A specific wave function is often called an orbital.
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36. Schrodinger Wave Equation
Y = fn(n, l, ml, ms)
principal quantum number n
n = 1, 2, 3, 4, ….
distance of e- from the nucleus
n=3
n=1
n=2
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Quantum Numbers (QN)
1. Principal QN (n = 1, 2, 3, . . .) - related to size and energy of the orbital.
2. Angular Momentum QN (l = 0 to n  1) - relates to shape of the orbital.
3. Magnetic QN (ml = l to l) - relates to orientation of the orbital in space relative to other orbitals.
4. Electron Spin QN (ms = +1/2, 1/2) - relates to the spin states of the electrons.
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38. Pauli Exclusion Principle
In a given atom, no two electrons can have the same set of four quantum numbers (n, l, ml, ms).
Therefore, an orbital can hold only two electrons, and they must have opposite spins.
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39. Probability Distribution
SQUARE of the wave function: Y2
probability of finding an electron at a given position
Radial probability distribution is the probability distribution in each spherical shell.
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Where 90% of the
e- density is found
for the 1s orbital
e- density (1s orbital) falls off rapidly
as distance from nucleus increases
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Figure 7.12: (a) Cross section of the hydrogen 1s orbital probability distribution divided into successive thin spherical shells. (b) The radial probability distribution.
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Figure 7.20: A comparison of the radial probability distributions of the 2s and 2p orbitals.
P orbital is more diffuse
Zero probability to be
in the nucleus
Probability to be
in the nucleus
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Figure 7.21: (a) The radial probability distribution for an electron in a 3s orbital. (b) The radial probability distribution for the 3s, 3p, and 3d orbitals.
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44. Heisenberg Uncertainty Principle
x = position
mv = momentum
h = Planck’s constant
The more accurately we know a particle’s position, the less accurately we can know its momentum.
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45. Schrodinger Wave Equation
Y = fn(n, l, ml, ms)
angular momentum quantum number l
for a given value of n, l = 0, 1, 2, 3, … n-1
l = s orbital
l = p orbital
l = d orbital
l = f orbital
n = 1, l = 0
n = 2, l = 0 or 1
n = 3, l = 0, 1, or 2
Shape of the “volume” of space that the e- occupies
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ml -l to +l
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Each orbital can take a maximum of two electrons and a minimum of Zero electrons.
Zero electrons does not mean that the orbital does not exist.
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Degenerate
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Figure 7.13: Two representations of the hydrogen 1s, 2s, and 3s orbitals.
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Figure 7.14: Representation of the 2p orbitals. (a) The electron probability distributed for a 2p orbital. (b) The boundary surface representations of all three 2p orbitals.
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ml = 0
ml = 1
ml = -1
Degenerate Orbitals
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52. Figure 7.16: Representation of the 3d orbitals.
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ml = -2
ml = -1
ml = 0
ml = 1
ml = 2
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How many 2p orbitals are there in an atom?
n=2
If l = 1, then ml = -1, 0, or +1 2p
3 orbitals
l = 1
How many electrons can be placed in the 3d subshell?
n=3
If l = 2, then ml = -2, -1, 0, +1, or +2 3d
5 orbitals which can hold a total of 10 e-
l = 2
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55. ( ) Energy of orbitals in a single electron atom 1 En = -RH n2
Energy only depends on principal quantum number n
n=3
n=2
En = -RH
( ) 1 n2
n=1
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56. Energy of orbitals in a multi-electron atom
Energy depends on n and l
n=3 l = 2
n=3 l = 1
n=3 l = 0
n=2 l = 1
n=2 l = 0
n=1 l = 0
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57. “Fill up” electrons in lowest energy orbitals (Aufbau principle)? ?
Li 3 electrons
B 5 electrons
Be 4 electrons
C 6 electrons
Li 1s22s1
B 1s22s22p1
Be 1s22s2
He 2 electrons
H 1 electron
H 1s1
He 1s2
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Figure 7.25: The electron configurations in the type of orbital occupied last for the first 18 elements.
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The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins (Hund’s rule).
C 6 electrons
O 8 electrons
Ne 10 electrons
F 9 electrons
Ne 1s22s22p6
N 7 electrons
F 1s22s22p5
N 1s22s22p3
C 1s22s22p2
O 1s22s22p4
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60. Order of orbitals (filling) in multi-electron atom
1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s
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61. Figure 7.26: Electron configurations for potassium through krypton.
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Figure 7.27: The orbitals being filled for elements in various parts of the periodic table.
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63. What is the electron configuration of Mg?
Mg 12 electrons
1s < 2s < 2p < 3s < 3p < 4s
1s22s22p63s2
= 12 electrons
Abbreviated as [Ne]3s2
[Ne] 1s22s22p6
What are the possible quantum numbers for the last (outermost) electron in Cl?
Cl 17 electrons
1s < 2s < 2p < 3s < 3p < 4s
1s22s22p63s23p5
= 17 electrons
Last electron added to 3p orbital
n = 3
l = 1
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ml = -1, 0, or +1
ms = ½ or -½
7.7

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Valence Electrons
The electrons in the outermost principle quantum level of an atom.
Inner electrons are called core electrons.
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65. Broad Periodic Table Classifications
Representative Elements (main group): filling s and p orbitals (Na, Al, Ne, O)
Transition Elements: filling d orbitals (Fe, Co, Ni)
Lanthanide and Actinide Series (inner transition elements): filling 4f and 5f orbitals (Eu, Am, Es)
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Figure 7.36: Special names for groups in the periodic table.
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Ionization Energy
The quantity of energy required to remove an electron from the gaseous atom or ion.
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I1 + X (g) X+(g) + e-
I1 first ionization energy
I2 + X+ (g) X2+(g) + e-
I2 second ionization energy
I3 + X2+ (g) X3+(g) + e-
I3 third ionization energy
I1 < I2 < I3
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Figure 7.31: The values of first ionization energy for the elements in the first six periods.
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Exceptions
Be 1s2 2s2
B 1s22s22p1 Shielded Electron
N 1s22s2sp3
O 1s22s22p4
Repulsion to doubly electrons
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Periodic Trends
First ionization energy:
increases from left to right across a period;
decreases going down a group.
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74. General Trend in First Ionization Energies
Increasing First Ionization Energy
Increasing First Ionization Energy
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Electron Affinity
The energy change associated with the addition of an electron to a gaseous atom.
X(g) + e  X(g)
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X (g) + e X-(g)
F (g) + e X-(g)
DH = -328 kJ/mol
EA = +328 kJ/mol
O (g) + e O-(g)
DH = -141 kJ/mol
EA = +141 kJ/mol
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Figure 7.33: The electron affinity values for atoms among the first 20 elements that form stable, isolated X- ions.
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Exceptions
C-(g) can be formed easily while N-(g) cannot be formed easily:
C- 1s22s2p3
N- 1s22s22p4
O-(g) can be formed because the larger positive nucleus overcome pairing repulsions.
Extra repulsion
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Periodic Trends
Atomic Radii:
decrease going from left to right across a period;
increase going down a group.
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Figure 7.35: Atomic radii (in picometers) for selected atoms.
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82. Information Contained in the Periodic Table
1. Each group member has the same valence electron configuration (these electrons primarily determine an atom’s chemistry).
2. The electron configuration of any representative element.
3. Certain groups have special names (alkali metals, halogens, etc).
4. Metals and nonmetals are characterized by their chemical and physical properties.
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Paramagnetic
Diamagnetic
unpaired electrons
all electrons paired 2p 2p
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