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CHAPTER OVERVIEW

- (7.1-7.2) Electromagnetic radiation, solving for wavelength and frequency, quantized energy, Debroglie relationship for calculating wavelength of a particle, particle wave duality and continuous vs. discrete line spectrum.
- (7.3-7.4) The Bohr model of the atom, energy calculations for electron transitions. (see Bohr lab)
- (7.5) Quantum mechanical view of the atom, Heisenberg uncertainty principle, electron probability distributions.
- (7.6-7.7) Quantum numbers n, l, ml and ms and orbital shapes and energies.
- (7.8-7.11) Pauli exclusion, Hund’s rule and aufbau principle.
- (7.12) Shielding effect, Z effective (eff. Nuclear charge), ionization energy, orbital filling across a period.
- (7.13) Trends of the first and second ionization energy, electron affinity, electronegativity, and atomic radius.

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

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

106hz = 1 Megahertz

SPEED of LIGHT

- All EMR travels at the speed of light.
- c = 2.9979 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 Hz? Is this visible?

- Ex. What is the frequency of blue light with a wavelength of 484 nm?

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 = 6.626 x 10-34 Joule seconds
- is frequency

Ex. What is the energy associated with light with a frequency of 6.65 x 108 / second?

EINSTEIN

- Who? Einstein
- What? Said electromagnetic radiation is quantized in particles called photons.
- When? 1905
- Each photon has energy E = h = hc/
- Combining this with E = mc2

Yields:

- m = h / (c )

Used to find the apparent mass of a photon

or

- = h/ mv

(careful – velocity, for things not travelling at the speed of light)

Used to find the apparent wavelength of a massive object

DeBROGLIE WAVELENGTH

- Which is it? Particle Wave Duality
- Is energy a wave like light, or a particle ? both
- Does matter a wavelength? Yes. It is imperceptible.
- Treating matter as a wave:
- Use the velocity v to find wavelength

DeBroglie’s equation: = h/ mv

- Ex. Sodium atoms have a characteristic color when excited in a flame. The color comes from the emission of light of 589.0 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?
- What is the wavelength of an electron travelling at 1.0 x 107 m/s?

Mass of e-1 = 9.11 x 10-31 kg

- What is the wavelength of a softball with a mass of 0.10 kg moving at 99 mi/hr?

EMISSION of LIGHT

- Continuous Spectrum
- The range of frequencies present in light.
- White light has a continuous spectrum.
- All the colors are possible.
- A rainbow can be seen through a spectroscope or prism.

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

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 it was moving around.
- 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.

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 = -2.178 x 10-18 J (Z2 / n2)
- When the electron is removed, n = , E = 0
- We are worried about the change when the electron moves from one energy level to another.
- ΔE = E final – E initial
- ΔE = -2.178 x 10-18J Z2 (1/ nf2 - 1/ ni2)

BOHR MODEL CALCULATIONS

- Ex. Calculate the energy need to move an electron from its ground state to the third energy level.
- 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.
- When is it true?
- Only for hydrogen atoms and other monoelectronic species.
- Why the negative sign?
- To decrease the energy of the electron you make it closer to the nucleus.
- The maximum energy an electron can have is zero, at an infinite distance.

QUANTUM MECHANICS

- The mathematical relationships predicted by BOHR (and demonstrated in our investigation) 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.
- 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.

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.

QUANTUM MECHANICS

- Let’s look at a wave pattern between two fixed points (like an electron traveling between two walls) or a guitar string. This is known as a standing wave.
- There are only certain frequencies at which the wave can travel because the ends are fixed. Set frequencies mean set wavelengths and set energy values.
- When a wave is set up, it can be defined by it’s number of nodes These are areas when the wave goes from + to – in value.
- 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.

QUANTUM MECHANICS

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…

- So, both the wavelength and the frequency of the trapped electron are discrete or quantized: meaning there are only certain allowable energy states and nothing in between.

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 2d2= E

2 m dx2

(the Hamiltonian operator)

where h is a modification of Planck’s constant = h / 2 = 1.05457 x 10-34 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.

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.

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.

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.

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 (m-1)

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

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

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

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

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:
- Ti = [Ar] 4s2 3d2
- V = [Ar] 4s23d3
- Cr = [Ar] 4s13d5
- Cu=[Ar] 4s13d10
- Mn = [Ar] 4s23d5
- Cu=
- These have half filled orbitals.
- Scientists aren’t sure of why it happens. Leads to stability due to minimizing electron repulsions.

Z effective and Ionization based on position on the periodic table

- We can use Zeff to predict properties, if we determine its pattern on the periodic table. 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 = -2.18 x 10-18 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 10-18 J(Z2/n2)
- E= 1.13 x 106 J/mol(Z2/n2)
- E= 1310 kJ/mol(Z2/n2)

IONIZATION ENERGY

- Example
- Calculate the ionization energy of B+4
- Ionization energy =1310 kJ/mol(Zeff2/n2)
- So we can measure Zeff
- 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?

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

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.
- How do orbitals differ?

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 as well.
- This provides for better shielding.

PERIODIC TRENDS

- Ionization energy
- Atomic radius
- Electron affinity
- Electronegativity

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

IONIZATION ENERGY

- Across a Period
- Generally from left to right, IE increases because there is a greater nuclear charge with the same shielding.
- Down a Group
- As you go down a group IE decreases because electrons are farther away.
- It is not that simple
- Zeff changes as you go across a period, so will IE
- Half filled and filled orbitals are harder to remove electrons from.

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.

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.
- Anions: always larger than the parent atom since electrons are gained. Inner electrons shield the added e and the size of the cloud increases.
- Isoelectronic species: atoms or ions with the same number of electrons.
- Ex. Compare the size of elements that are isoelectronic with argon

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.

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 nuclear shielding.

PLACE THE FOLLOWING IN ORDER of INCREASING AR, IE, EA, and EN

K Ca Cr Kr

- AR:
- IE:
- EA:
- EN:

Cs Ag Si F

- AR:
- IE:
- EA:
- EN:

O S Se Te

- AR:
- IE:
- EA:
- EN:

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