Chemistry 1AChapter 7

Atomic Theory

• To see a World in a Grain of SandAnd a Heaven in a Wild FlowerHold Infinity in the palm of your handAnd Eternity in an hour

William Blake Auguries of Innocence• Thus, the task is not so much to see what no

one has yet seen, but to think what nobody has yet thought, about that which everybody sees.

Erwin Schrodinger

Ways to deal with Complexity and Uncertainty

• Analogies In order to communicate something of the nature of the electron, scientists often use analogies. For example, in some ways, electrons are like vibrating guitar strings.

• Probabilities In order to accommodate the uncertainty of the electron’s position and motion, we refer to where the electron probably is within the atom instead of where it definitely is.

Electron like Light• Dual Nature

– Particle• Massless photons of varying energy for

light.• Negatively charged particles with a mass of

9.1096 × 10−28 g for the electron.– Wave – related to the effect on the

space around them• Oscillating electric and magnetic fields for

light.• 3-D Wave of varying negative charge for

electron.

Guitar String Waveform

Allowed Vibrations for a Guitar String

Determination of the Allowed Guitar String Waveforms

• Set up the general form of the wave equation that describes the vibrating string.

• Determine the forms of the general equation that fit the boundary conditions.

• Each possible equation is solved over and over again for the amplitude at many different positions.

• We plot the values determined in Step 3 and get an image of the possible wave forms.

• Steps 3 and 4 can be repeated for other equations that meet the boundary conditions.

Equation for Guitar String

• AX = the amplitude at position x• AO = the maximum amplitude at any

point on the string• n = 1, 2, 3, ...• x = the position along the string• a = the total length of the string

X On xA = A sin

aπ

Guitar String Amplitudes

A1 A0 A2

Guitar String Waveform 1

X OxA = A sin

aπ

Guitar String Waveform 2

X O2 xA = A sin

aπ

Guitar String Waveform 3

X O3 xA = A sin

aπ

Determination of the Allowed Electron Waveforms

• Set up the general form of the wave equation that describes the electron in a hydrogen atom. Ψx,y,z = f(x,y,z)

• Determine the forms of the general equation that fit the boundary conditions. Each equation has its own set of three quantum numbers: n, l, and ml.Ψ1s = f1s(x,y,z) with 1,0,0 for quantum numbers Ψ2s = f2s(x,y,z) with 2,0,0 for quantum numbers Ψ2p = f2p(x,y,z) with 2,1,1 or 2,1,0

or 2,1, −1 for quantum numbers Etc.

Determination of the Allowed Electron Waveforms (cont.)

• Each allowed equation is solved to get the values for the wave function for many different positions.

• When we plot the solutions for one of the possible wave functions on a three-dimensional coordinate system, we get an image of one of the possible waveforms.

Waveform for 1s Electron (with quantum numbers 1,0,0)

Other Allowed Waveforms

1s Orbital

Particle Interpretation of 1s Orbital

Wave Character of the Electron

• Just as the intensity of the movement of a guitar string can vary, so can the intensity of the negative charge of the electron vary at different positions outside the nucleus.

• The variation in the intensity of the electron charge can be described in terms of a three-dimensional standing wave like the standing wave of the guitar string.

Wave Character of the Electron

• Although both the electron and the guitar string can have an infinite number of possible waveforms, only certain waveforms are possible.

• We can focus our attention on the waveform of varying charge intensity without having to think about the actual physical nature of the electron.

Summary• The electron in a H atom can be described

with a 3-dimensional wave equation.• This equation has 3 quantum numbers

associated with it. • Each unique set of 3 quantum numbers

(e.g. 1,0,0 for the 1s orbital) yields an equation that when calculations are done using this equation for various positions outside the nucleus and when the results of these calculations are plotted on a 3-dimensional coordinate system, we get an image of the variation in the intensity of negative charge generated by the electron.

• This image is called an orbital.

Electron-Wave Quantum Numbers for the Hydrogen Electron

• Principal quantum number – n– Describes the PE and relative size of orbital.

• Angular momentum quantum number (orbital shape quantum number) – l

– Describes the general shape of orbital.• Magnetic quantum number (orbital

orientation quantum number) – ml– Describes the direction the orbital points

relative to other orbitals of the same energy.• Magnetic spin quantum number – ms

– Necessary for describing electrons, not orbitals.

Electron-Wave Quantum Numbers for the Hydrogen Electron (cont.)• Possible values

n = 1, 2, 3,…l = 0, 1, 2,…, (n − 1)ml = +l,…, 0,…, −l

ms = +1/2 and −1/2• What they describe

n – principle energy level (shell)n, l – sublevel (subshell)n, l, ml – orbitaln, l, ml, ms - electron

Possible Sublevels for the First 4 Principal Energy Levels of the Hydrogen Electron

1,0 1s

2,0 2s2,1 2p

3,0 3s3,1 3p3,2 3d

4,0 4s

4,1 4p

4,2 4d

4,3 4f

Orbitals Within Sublevels

• Any “s” sublevel – one orbitaln,0,0

• Any “p” sublevel – three orbitalsn,1,+1 n,1,0 n,1,−1

• Any “d” sublevel – five orbitalsn,2,+2 n,2,+1 n,2,0 n,2,−1 n,2,−2

• Any “f” sublevel – seven orbitalsn,3,+3 n,3,+2 n,3,+1 n,3,0 n,3,−1 n,3,−2 n,3,−3

Cutaway of 1s and 2s Orbitals (with quantum numbers 2,0,0)

Realistic and Stylized 2py Orbital

2px, 2py, and 2pz Orbitals

3d Orbitals

Other Allowed Waveforms

Grand Orbital Table

• The website below, created by David Manthey, shows many more orbitals.

http://www.orbitals.com/orb/orbtable.htm

Orbitals for Ground States of Known Elements

Orbital Energies for Hydrogen

Calculating Frequencies for Hydrogen Spectrum

ν

ν

⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

⎛ ⎞⎜⎜⎝

15high2 2

high

152 2

high

1 1frequency = = 3.289 x 10 1/s - n = 2, 3,

Lyman (UV portion of hydrogen spectrum)

Balmer (visible portion of

4, ...1 n

1 1 = 3.289 x 10 1/s

hydrogen spectr

- 2 n

um)

ν

⎟⎟⎠

⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

high

15high2 2

high

Paschen (IR portion of hydrogen spectrum

n = 3, 4, 5, ...

1 1 = 3.289 x 10 1/s - n = 4, 5, 6n

)

, ...3

Line Spectrum of Hydrogen

Continuous and Line Spectrum

Frequency, Wavelength, and the Speed of Light

8

speed of light (c) = wavelength( ) frequency( )distance cycles distancec = = =

cycle time timem cycles mor c = = = 2.9979 10

cycle s s

λ ν

λν

λν

•

×

Lab

• Goal – to determine wavelengths of lines in the visible portion of the hydrogen spectrum–From Calculation

–From Experiment

ν

λν

⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

⎛ ⎞×⎜ ⎟⎝ ⎠

15high2

high

8 9

1 1frequency = = 3.289 x 10 1/s - n = 3, 4, 5, 6, and 74 n

2.9979 10 m/s 10 nmwavelength = = 1 m

Wave Interference

Wave Diffraction Patterns

Lab – With He Spectrum

• View lines and measure angle of diffraction for each.

• Assign to wavelengths on table based on color, intensity and relative position.

• Graph angle of diffraction vs. wavelength on graph paper provided.

Calibration Curve

When Graphing• Label graph and axes.• Set scale to

– use as much of the graph paper as possible. (Do not start numbering the scale at 0.)

– Make each box a value that makes the graph easy to read, e.g. 3 nm per box, not 2.4356 nm.

• Indicate each data point with a clear x. • Draw the best straight line that

averages the points.

Lab – for H Spectrum

• View lines and measure angle of diffraction for each.

• Use the graph created from the helium data to determine the wavelength for each line.

Electron Spin

Pauli Exclusion Principle

• No two electrons in an atom can be the same in all ways. (No two electrons in an atom can have the same set of four quantum numbers, n, l, ml, and ms.)

• There are four ways that electrons can be the same:

• Electrons can be in the same principal energy level (same n).

• They can be in the same sublevel (same n and l).

• They can be in the same orbital (same n, l, and ml).• They can have the same spin (same ms).

• Leads to the conclusion that there can only be 2 e−/orbital…2 e−/s sublevel, 6 e−/p sublevel, 10 e−/d sublevel, and 14 e−/f sublevel.

Electron Configurations

• The sublevels are filled in such a way as to yield the lowest overall potential energy for the atom.

• No two electrons in an atom can be the same in all ways. This is one statement of the Pauli Exclusion Principle.

• When electrons are filling orbitals of the same energy, they prefer to enter empty orbitals first, and all electrons in half-filled orbitals have the same spin. This is called Hund’s Rule.

Orbitals for Ground States of Known Elements

Why is 1s before 2s?

Electron Configurations (cont.)

Why 2s before 2p?

Electron Configurations through Neon

• H - 1s1

• He - 1s2

• Li - 1s2 2s1

• Be - 1s2 2s2

• B - 1s2 2s2 2p1

• C - 1s2 2s2 2p2

• N - 1s2 2s2 2p3

• O - 1s2 2s2 2p4

• F - 1s2 2s2 2p5

• Ne - 1s2 2s2 2p6

Orbital Overlap

Why 4s before 3d?

1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f 6d 7p

Order of Orbital Filling

Writing Electron Configurations

• Determine the number of electrons in the atom from its atomic number.

• Add electrons to the sublevels in the correct order of filling.

• Add two electrons to each s sublevel, 6 to each p sublevel, 10 to each d sublevel, and 14 to each f sublevel.

• To check your complete electron configuration, look to see whether the location of the last electron added corresponds to the element’s position on the periodic table.

Order of Filling from the Periodic Table

Long Periodic Table

Drawing Orbital Diagrams

• Draw a line for each orbital of each sublevel mentioned in the complete electron configuration. Draw one line for each s sublevel, three lines for each psublevel, five lines for each d sublevel, and seven lines for each f sublevel.

• Label each sublevel. • For orbitals containing two electrons,

draw one arrow up and one arrow down to indicate the electrons’ opposite spin.

• For unfilled sublevels, follow Hund’s Rule.

Abbreviated Electron Configurations

• The highest energy electron are most important for chemical bonding.

• The noble gas configurations of electrons are especially stable and, therefore, not important for chemical bonding.

• We often describe electron configurations to reflect this representing the noble gas electrons with a noble gas symbol in brackets.

• For example, for sodium1s2 2s2 2p6 3s1 goes to [Ne] 3s1

Writing Abbreviated Electron Configurations

• Find the symbol for the element on a periodic table.

• Write the symbol in brackets for the noble gas located at the far right of the preceding horizontal row on the table.

• Move back down a row (to the row containing the element you wish to describe) and to the far left. Following the elements in the row from left to right, write the outer-electron configuration associated with each column until you reach the element you are describing.

Abbreviated Electron Configurations – Optional Step

• Rewrite the abbreviated electron configuration, listing the sublevels in the order of increasing principal energy level (all of the 3’s before the 4’s, all of the 4’s before the 5’s, etc.)

Group 1 Abbreviated Electron Configurations

Abbreviated Electron Configuration Steps for Zinc

Common Mistakes• Complete electron configurations –

miscounting electrons (Use the periodic table to determine order of filling.)

• Orbital diagrams – forgetting to leave electrons unpaired with the same spin when adding electrons to the p, d, or fsublevels (Hund’s Rule)

• Abbreviated electron configurations– Forgetting to put 4f14 after [Xe]– Forgetting to list sublevels in the order of

increasing principal quantum number – For cations, forgetting to remove highest

energy level electrons first

Anomalies

• Cu [Ar] 3d10 4s1

• Ag [Kr] 4d10 5s1

• Au [Xe] 4f14 5d10 6s1

• Cr [Ar] 3d5 4s1

• Mo [Kr] 4d5 5s1

• Pd [Kr] 4d10

Paramagnetic and Diamagnetic Atoms

• Diamagnetic atoms have no permanent net magnetic field because all of their electrons are paired. – Uncharged palladium atoms and the

uncharged atoms that are in columns that end either the s, p, d, or f blocks are diamagnetic.

• Paramagnetic atoms have a permanent net magnetic field due to having at least one unpaired electron. – All uncharged atoms are paramagnetic except

palladium atoms and the uncharged atoms that are in columns that end either the s, p, d, or f blocks.

Writing Abbreviated Electron Configurations for Transition Metal Monatomic Cations

• Draw the abbreviated electron configuration for the uncharged atom, listing the sublevels in the order of increasing principal quantum number.

• Remove the number of electrons equal to the charge, removing them from the right to left in the electron configuration.

Factors that Affect Ionic Charge (1)

• Ions form in such a way as to yield the most stable, lowest potential energy ionic compound.

• Ions are less stable than their neutral counterparts. Therefore, it takes energy to form ions.

• The higher the charges are, the less stable they are and the more energy it takes to form them.

• Therefore, this factor favors low charges.

Factors that Affect Ionic Charge (2)

• The formation of ionic bonds stabilizes the ions, so energy is released when the cations and anions form ionic bonds.

• The higher the charges are, the stronger the bonds and the more energy is released when they form.

• Therefore, this factor favors higher charges.

Factors that Affect IonicCharge (3)

• Ions form the charges that yield the best balance between (1) the tendency to keep charges low to minimize the energy necessary to form ions and (2) the tendency to maximize charge to yield the strongest, most stable ionic bond.

• The best balance is often reached when the ions form stable electron configurations, which require the least energy to form.

Very Rough PE Diagram for NaCl Formation

Very Rough PE Diagram for AlN Formation

Stable Configurations

• 1s2 (2 electrons)– H−, Li+, Be2+

• ns2np6 (10, 18, 36, 54, and 86 electrons) – All monatomic anions, except H−

– Cations from Group 1, 2, or 3 and Al3+

• nd10(n+1)s2 (30, 48, and 80 electrons)– Ga+, In+, Tl+, Sn2+, Pb2+, and Bi3+

• nd10 (28, 46, and 78 electrons)– Cu+, Ag+, Au+, Zn2+, Cd2+, Hg2+, Ga3+, In3+, and

Tl3+

Monatomic Ion Charges

Trends on the Periodic TableChemistry 1A

Atomic Size• Covalent Radius for Covalently Bonded

Atoms– F-F bond length is 144 pm, so F covalent

radius is 72 pm.– H-F bond length is 109 pm, so H covalent

radius is 37 nm.• Atomic Radius for Elements like the

Noble Gases– Ar atomic radius is 131 pm

• Metallic Radius for Metals– Al metallic radius is 143 pm.

Trends in Atomic Size (1)

Trends in Atomic Size (2)

Ionization Energy, ΔHi.e.

• First Ionization EnergyA(g) → A+(g) + e−

• Second Ionization EnergyA+(g) → A2+(g) + e−

• Third Ionization EnergyA2+(g) → A3+(g) + e−

Ionization Energy Trends (1)

Ionization Energy Trends (2)

Electron Affinity, ΔHe.a.

• First Electron AffinityA(g) + e− → A−(g)

• Second Electron AffinityA−(g) + e− → A2−(g)

• Third Electron AffinityA2−(g) + e− → A3−(g)

Electron Affinity Trends

Trends – Representative Elements

AtomicSize

ΔHi.e. ΔHe.a. EN

Increases to left and down

Increases to right and up

Morefavorable to right and up

Increases to right and up

Two Factors Used to Explain Trends

• The principal energy level reflects the size of orbitals and potential energy of the electrons in those orbitals.

• All other factors being equal, increased nfor the orbitals in which electrons are found means increased size of orbitals, which leads to decreased attraction for electrons and increased potential energy of those electrons.

Effective Charge• Effective charge is the approximate nuclear

charge felt by the highest energy electrons. – nuclear charge minus #e− in lower energy levels – The effective charge on the highest energy

electrons of the representative elements is equal to their A-group number.

– The effective charge on the highest energy electron of the transition metals (other than the anomalies) is +2.

• All other factors being equal, increased effective charge means increased attraction for electrons, which leads to decreased size of orbitals and decreased potential energy of electrons.

Explanation of Trends (1)

Explanation of Trends (2)

Explanation of Trends (3)

Ionic or Molecular?• Is aluminum iodide, AlI3, ionic or

molecular?• If you are told that aluminum iodide’s

formula was better described as Al2I6, would it change your prediction?

• Many metal and nonmetal combinations are better described as forming molecular compounds rather than ionic compounds.

• To see why, a new classification of chemical bonds is added to our list…ionic bonds with covalent character.

Ionic Bonds with Covalent Character

• The attraction for the anion’s negative charge cloud from the cation draws the anion’s charge cloud toward the cation and distorts the anion electron cloud.

• This distortion is described as covalent character, that is, sharing of electrons.

Bond Types

Degree of Covalent Character

• Greater distortion of anion electron cloud (more covalent character) in an ionic bond comes from– More highly charged cation…more attraction

for anion electron cloud.– Smaller cation…more focused attraction for

anion electron cloud.– Larger anion…electron cloud less strongly

attracted, so anion is more easily distorted.– More highly charged anion…more repulsion

between electrons, so anion is more easily distorted.

Ionic Size

• Cations are much smaller than the uncharged atoms they come from.– Fewer electrons means less repulsion

between electrons, allowing the electron cloud to be pulled closer to the nucleus.

• Anions are much larger than the uncharged atoms they come from.– More electrons means more repulsion

between electrons, causing the electron cloud to expand to minimize this increased repulsion.

Ionic and Atomic Size

Isoelectronic Series

• A collection of ions and an uncharged atom with the same number of electrons is called an isoelectronic series.

• For isoelectronic atoms or ions, higher nuclear charge leads to smaller size.

Predicting Degree of Covalent Character

• CsF…low covalent character– Large, low charge cation-low attraction and unfocused

attraction.– Small, low charge anion…electrons strongly

attracted…hard to distort

• AlI3…high covalent character– Small, highly charged cation…strong attraction and

focused attraction.– Large anion…electrons weakly attracted…easy to distort

• Li3P…high covalent character– Small cation…focused attraction.– Large anion, highly charged anion…electrons weakly

attracted…easy to distort