CHAPTER 7

ATOMIC STRUCTURE

and

PERIODICITY

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

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/ second106 hz = 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 photonor = 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.

BOHR MODEL

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/ nf

2 - 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:HeisenbergDeBroglieSchrodinger  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 MECHANICSAll 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 POSITIONHOW 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 = 1.05457 x 10-34 Js

m = the mass of the particleE 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 nucleusEnergy 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 

ENERGY LEVEL DIAGRAMS

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, kryptonFill energy level diagram, determine quantum set,

valence electrons, and electron configurations

Practice 67-70 from HW packet.

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] 4s2 3d3

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(Zeff 2/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

s>p>d>f

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.

IONIZATION ENERGY

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 AFFINITYELECTRON 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 ENK Ca Cr Kr AR: IE: EA: EN:

Cs Ag Si F AR: IE: EA: EN:

O S Se Te AR: IE: EA: EN: