1. ATOMIC STRUCTURE and PERIODICITY
CHAPTER 7
ATOMIC STRUCTURE
and
PERIODICITY

2. CHAPTER OVERVIEW

3. UNDERSTANDING BOHR’s MODEL of the ATOM
To understand the ring model that Bohr proposed, we have to understand how an electron is moving.
PARTICLE WAVE DUALITY
Who? Louis DeBroglie
What? The electron can travel as a particle or as a wave.
All matter has particle/ wave like properties. Some have such a small wavelength that we don’t notice.
When? 1923

4. WAVE MOTION
ROY G BIV
Visible region spans from 350 nm (violet) to 750 nm (red).

5. WAVE MOTION All EMR travels as waves. Wave motion is described by:
Wavelength
Defined as: the distance between two crests of a wave
Symbol:  (lambda)
Units: m or nanometers
1m = 109 nm
Amplitude
Defined as: height of the wave (from rest to crest)
Symbol: A
Units: m
Frequency
Defined as: the number of waves that pass per second
Symbol:  (nu)
Units: hertz
1 hz = 1/ second
106 hz = 1 Megahertz

6. SPEED of LIGHT All EMR travels at the speed of light.
c = x 108 m/s
 we will use 3.00 x 108 m/s
 Relationship between c, , and 
 c = 
 Ex. What is the wavelength of light that has a frequency of 5.0 Hz? Is this visible?
Ex. What is the frequency of blue light with a wavelength of 484 nm?   

7. PLANCK
PRIOR to DeBROGLIE: Matter and energy were seen as different from each other in fundamental ways. Matter was treated as a particle. Energy could come in waves, with any frequency. Until,
Who? Max Planck
What? Found that the colors of light emitted from hot objects (heated to incandescence) couldn’t be explained by viewing energy as a wave.
Instead, he proposed that light was given off in the form of photons with a discrete amount of energy called quanta.
When? 1900
How? can the energy of a photon can be calculated?
E = h
Where:
E is energy
h is Planck’s constant = x Joule seconds
 is frequency
Ex. What is the energy associated with light with a frequency of 6.65 x 108 ­/ second?

8. EINSTEIN
Who? Einstein
What? Said electromagnetic radiation is quantized in particles called photons after witnessing the photoelectric effect.
When? 1905
Each photon has energy E = h = hc/
Combining this with E = mc2
Yields two rearrangements:
m = h / (c )
Used to find the apparent mass of a photon
 = h/ mc and therefore,  = h/ mv
(careful – velocity, for things not travelling at the speed of light)
Used to find the apparent wavelength of a massive object

9. DeBroglie’s equation:  = h/ mv
DeBROGLIE WAVELENGTH
Does matter a wavelength?
Yes. It is imperceptible.
Does light energy have mass?
Yes, the apparent mass which is also imperceptible.
Treating matter as a wave:
Use the velocity v to find wavelength
This  is known as the apparent wavelength or the DeBroglie wavelength
DeBroglie’s equation:  = h/ mv

10. Sample Calculations:
Ex. Sodium atoms have a characteristic color when excited in a flame. The color comes from the emission of light of nm.
What is the frequency of this light ?
What is the energy of a photon of this light ?
What is the apparent mass of a photon of this light ?
What is the energy of a mole of these photons?

11. Sample calculations DeBroglie’s equation.
What is the wavelength of an electron travelling at 1.0 x 107 m/s?
  Mass of e-1 = 9.11 x kg
What is the wavelength of a softball with a mass of 0.10 kg moving at 99 mi/hr?

12. SPECTROSCOPY
The study of electromagnetic radiation as it interacts with matter.
Initial spectroscopy experiments provided evidence about the early atomic model.
Ex. Bohr model based on Geissler tube analysis and AES
Ex. Photoelectron/ Photoemission spectroscopy (PES) leading to the Shell/ Subshell mode
Types of spectroscopy used in analytical chemistry:
AAS spectroscopy
AES spectroscopy
IR spectroscopy
NMR spectroscopy
Raman Spectroscopy
UV/VIS spectroscopy
X-Ray spectroscopy

13. EMISSION of LIGHT Continuous Spectrum
Shows the range of frequencies present in light.
White light has a continuous spectrum.
All the colors are possible. ROY G BIV
A rainbow can be seen through a spectroscope or prism.

14. DISCRETE LINE SPECTRUM
Hydrogen spectrum
Emission spectrum because these are the colors it gives off or emits.
Called a line spectrum.
There are just a few discrete lines showing. What this means:
Only certain energies are allowed for the hydrogen atom.
Can only give off certain energies.
Energy in the in the atom is quantized.
Use E = h = hc / 
410nm, 434nm, 486nm, 656 nm = the Balmer Series
Also lines in the UV (Lyman Series) and the IR (Paschen Series)

15. NIELS BOHR Who? Niels Bohr
What? Developed the quantum model of the hydrogen atom.
He said the atom was like a solar system.
The electrons were attracted to the nucleus because of opposite charges.
Didn’t fall in to the nucleus because the e- was constantly moving.
The Bohr Ring Atom
He didn’t know why but only certain energies were allowed.
He called these allowed energies energy levels.
Putting Energy into the atom moved the electron away from the nucleus from ground state to excited state.
When it returns to ground state it gives off light of a certain energy.

16. BOHR RING MODEL of the ATOM

17. THE BOHR MODEL n is the energy level n = 1 is called the ground state
Z is the nuclear charge, which is +1 for hydrogen.
For each energy level the energy is: 
E = x J (Z2 / n2)
When the electron is removed, n =  , E = 0
n≠0 mathematically undefined.
We are worried about the change when the electron moves from one energy level to another.
ΔE = E final – E initial
ΔE = x 10-18J Z2 (1/ nf2 - 1/ ni2)

18. When is it true?
Only for the hydrogen atom and other monoelectronic species (ex. He+1, Li+2, etc.)
Why the negative sign?
To decrease the energy of the electron you make it closer to the nucleus. The – represents a binding energy. To overcome the binding energy you must put in
x J of energy / proton binding the e-.
The maximum energy an electron can have is zero, at an infinite distance from the nucleus.

19. BOHR MODEL CALCULATIONS
Ex. Calculate the energy need to move an electron from its ground state to the third energy level. Would visible light be energetic enough to cause this transition?
Ex. Calculate the energy released when an electron moves from n= 4 to n=2 in a hydrogen atom.
Ex. Calculate the wavelength of light given the last transition.
Ex. Calculate the energy released when an electron moves from n= 5 to n=3 in a He+1 ion.

20. QUANTUM MECHANICS
The mathematical relationships predicted by BOHR successfully predict wavelengths of light emitted for an electron transitioning between two energy levels within the hydrogen atom and predict the most probable radius of the energy levels from nucleus.
BUT
This model fails when applied to POLYELECTRONIC systems (atoms with more than one e-). e- interactions and Z (the nuclear charge) make it impossible to apply BOHR’s relationship.

21. QUANTUM MECHANICS QUANTUM MECHANICAL VIEW OF THE ATOM
Also known as the wave mechanical view.
Predicted by:
Heisenberg
DeBroglie
Schrodinger
Premises:
e- is a particle that can travel as a wave (DeBroglie relationship = h/mv)
waves have only some allowable energy levels (corresponding to n= 1, 2, etc. in the H atom)…these allowable energy levels are called quantum levels.

22. WAVE THEORY
A standing wave exists between two fixed points like an electron traveling between two walls or a guitar string.
There are only certain frequencies at which the wave can travel because the ends are fixed. Set frequencies lead to set wavelengths and quantized energy values.
Waves can be defined by their number of nodes These are areas when the wave goes from + to – in value.

23. 

24. QUANTUM MECHANICS
0 nodes = the first harmonic. It has the lowest frequency and the longest wavelength. This is known as the ground state in the atom. This is the n=1 level. Sometimes called the fundamental frequency.
All other frequencies will be a multiple of the fundamental frequency.
1 node = the second harmonic. The n=2 energy level (1 central node, 2 fixed nodes)
2 nodes = the third harmonic. The n = 3 energy level (2 central nodes, 2 fixed nodes)
And so on…

25. PREDICTING THE ELECTON’s POSITION
HOW CAN THE ELECTRON’s POSTION or MOTION BE DESCRIBED?
 = the wave function which tells the 3-D coordinates of the e- position.
 is part of the SCHRODINGER equation.
- h 2 d2 = E 
2 m dx2
(the Hamiltonian operator)
where h is a modification of Planck’s constant = h / 2 = x Js
m = the mass of the particle
E is the energy of the wave function  which has three dimensions built in.
and the d2 term means to take the 2nd derivative of the function
The solution of the calculus based equation results in 4 QUANTUM numbers, which tell us something about the electron’s behavior. More on these later.

26. PROBABILITY PLOTS
2 = the probability of finding an electron in a particular point in space called an orbital.
Can be shown as a radial distribution. Where the highest point is the most likely distance from the nucleus to find the electron. When n= 1 this distance also coincides with the first “orbit” predicted by BOHR.
.529 angstroms from the nucleus = most probable location of H’s electron.

27. PREDICTING the ELECTRON’s POSITION
Unfortunately, the electron’s position and momentum cannot be known at the same time.
This is the Heisenberg uncertainty principle.
 x   mv = h / 4
Where x is the uncertainty about the position.
 mv is the uncertainty about the momentum.
So, the more you know about the electron’s position, the less you can know about its movement (momentum). In macroscopic systems, this uncertainty is negligible.

28. QUANTUM NUMBERS Principle quantum number Symbol: n
What does it tell about the electron?
The distance from the nucleus
Energy level
Values:
1 to 
Cannot be 0 since it would be undefined mathematically since n is in the denominator of the Schrodinger equation.

29. QUANTUM NUMBERS Angular quantum number Symbol: l
What does it tell about the electron?
The shape of the orbital with the most probability of finding the e-
Values:
0 to (n-1)

30. QUANTUM NUMBERS Magnetic Symbol: ml
What does it tell about the electron?
The orientation of the orbital in 3D space
Values:
- L to l including 0

31. QUANTUM NUMBERS Spin Symbol: ms What does it tell about the electron?
The direction of electron spin about its own axis
Values:
+1/2 clockwise
-1/2 counter clockwise

32. ENERGY LEVEL DIAGRAMS

33. RULES for FILLING the DIAGRAM
Aufbau – fill orbitals in lower energy levels before proceeding to the next level.
Hund’s Rule- Place electrons in separate orbitals before pairing them within the same energy level.
Pauli exclusion principle – every electron must have a different set of quantum numbers. Electrons in the same orbital must have opposite spins.
Examples:
Phosphorus, strontium, nickel, krypton
Fill energy level diagram, determine quantum set, valence electrons, and electron configurations

34. Practice 67-70 from HW packet.

35. ELECTRON CONFIGURATION
Shows the filled orbitals in short hand notation.
Ex. Mg   
Ex. Cl 
NOBLE GAS electron configuration: shows the noble gas core to simplify electron configuration.
Focuses on valence electrons - the electrons in the outermost energy levels (not including d).
Ex. O
Ex. Br
Ex. U

36. ELECTRON CONFIGURATION
How is electron configuration related to the periodic table?.
Elements in the same column have the same electron configuration.
Put in columns because of similar properties.
Similar properties because of electron configuration.
Noble gases have filled energy levels.
Transition metals are filling the d orbitals
Exceptions to filling rules: Cr Cu
These have half filled orbitals.
Scientists aren’t sure of why it happens. Leads to stability due to minimizing electron repulsions.

37. Z effective and Ionization Energy
Zeffective - is the net positive charge experienced by an electron in a multi-electron atom. The term "effective" is used because the shielding effect of negatively charged electrons prevents higher orbital electrons from experiencing the full nuclear charge by the repelling effect of inner-layer electrons.
We can use Zeff to predict properties, if we determine its pattern on the periodic table. We can use the amount of energy it takes to remove an electron for this.
Ionization Energy- The energy necessary to remove an electron from a gaseous atom.
Remember this: 
E = x J(Z2/n2) was true for Bohr atom.
Can be derived from quantum mechanical model as well for a mole of electrons being removed
E =(6.02 x 1023/mol) x 2.18 x J(Z2/n2) 
E= 1.13 x 106 J/mol(Z2/n2)
E= 1310 kJ/mol(Z2/n2)

38. IONIZATION ENERGY Example Calculate the ionization energy of B+4
Ionization energy = 1310 kJ/mol (Zeff 2/n2) 
The ionization energy for a 1s electron from sodium is
1.39 x 105 kJ/mol .
The ionization energy for a 3s electron from sodium is
4.95 x 102 kJ/mol .
Why?

39. SHIELDING
Electrons on the higher energy levels tend to be farther out.
Have to “look through” the other electrons to see the nucleus.
They are less affected by the nucleus.
Lower effective nuclear charge (Z eff).
If shielding were completely effective,
Zeff = 1
Why isn’t it?
Penetration effect

40. s>p>d>f

41. ns > np > nd > nf (within the same energy level)
PENETRATION EFFECT
The outer energy levels penetrate the inner levels so the shielding of the core electrons is not totally effective.
From most penetration to least penetration the order is 
ns > np > nd > nf (within the same energy level)
This is what gives us our order of filling, electrons prefer s and p.   

42. ORBITAL SIZE
 The more positive the nucleus, the smaller the orbital. 
A sodium 1s orbital is the same shape as a hydrogen 1s orbital, but it is smaller because the electron is more strongly attracted to the nucleus.
The helium 1s is smaller than the H 1s as well.
This provides for better shielding in atoms with higher nuclear charge.
How do we know? PES data.

43. PERIODIC TRENDS Ionization energy Atomic radius Electron affinity
Electronegativity

44. IONIZATION ENERGY
Defined as: The energy required to remove an electron form a gaseous atom.
Highest energy electron removed first.
First ionization energy (I1) is that required to remove the first electron.
Second ionization energy (I2) – the second electron 
Trends in ionization energy
 For Mg
I1 = 735 kJ/mole
I2 = 1445 kJ/mole
I3 = 7730 kJ/mole
The effective nuclear charge increases as you remove electrons.
It takes much more energy to remove a core electron than a valence electron because there is less shielding.
Ex. Explain this trend
For Al
I1 = 580 kJ/mole
I2 = 1815 kJ/mole
I3 = 2740 kJ/mole
I4 = 11,600 kJ/mole

45. IONIZATION ENERGY Across a Period
Generally from left to right, IE increases because there is a greater nuclear charge with the same shielding.
It is not that simple
Zeff changes as you go across a period, so will IE
Down a Group
As you go down a group IE decreases because electrons are farther away and inner electrons shield the outer electons.

46. IONIZATION ENERGY

47. IONIZATION ENERGY What are the exceptions to this trend?
Look at graph. Choose examples.
Explain why an np1 electron is easier to remove than an ns2 electron.
Explain why an np4 electron is easier to remove than an np3 electron.

48. ATOMIC RADIUS Defined as:
½ the distance between nuclei of 2 identical atoms
Across a Period
Decreases due to electrons being added in the same energy level and the number of protons increasing. Shielding is not as effective and higher Zeff causes e to be pulled closer to the nucleus resulting in a smaller atomic radius.
Down a Group
Increases. Electrons are added in higher energy levels farther from the nucleus. Core electrons shield the nuclear charge so a lower Zeff is not as effective at pulling the electrons, so the atomic radius increases.

49. IONIC RADIUS Measured relative to the parent atom.
Cations: always smaller than the parent atom since electrons are lost. Higher p+ to e- ratio causes the remaining e to be pulled closer. Zeffective increases.
Anions: always larger than the parent atom since electrons are gained. Inner electrons shield the added e and the size of the cloud increases. Zeffective decreases.
Isoelectronic species: atoms or ions with the same number of electrons.
Ex. Compare the size of elements that are isoelectronic with argon

50. ELECTRON AFFINITY ELECTRON AFFINITY
Defined as: the amount of energy needed to add an electron to a gaseous atom (usually in kj/mole)
(+) EA – metals – hard to add an e-, energy is required, endothermic
(-) EA – non-metals –easy to add an e-, energy is released, exothermic
(0) EA – noble gases – no reason to test their affinity, as they have no reason to gain an e.
Across a period:
(+) to (-) becomes more favorable (except for noble gases)
Down a group:
becomes less favorable. It is more difficult to add an electron to a larger atom due to shielding.

51. ELECTRONEGATIVITY Defined as:
The ability of a bonded atom to attract an electron pair
Highest electronegativity: F 4.0 on the Pauling scale
Across a period: increases
Smaller atoms with higher nuclear charge are better at attracting e- pairs.
Metals always have a lower eneg. than non-metals because they are less likely to be sharing e- pairs.
Down a group: decreases
Larger atoms are less able to attract the e- pair due to shielding.

52. PLACE THE FOLLOWING IN ORDER of INCREASING AR, IE, EA, and EN
K Ca Cr Kr
AR:
IE:
EA:
EN:
Cs Ag Si F
O S Se Te