General Chemistry I

Chapter 6

Electronic Structure of Atoms

The Wave Nature of Light

n    Leads to understanding of electronic structure of atoms

n    Electromagnetic radiation

n    Visible light

n    Radio waves

n    X-rays

n    Microwaves

n    Others…

The Nature of Waves

n    Wavelength

n    Distance for one complete cycle

n    Units are length (m)

n    Frequency

n    Number of cycles for given time (n)

n    Units are cycles per second or s-1 (Hz)

n    Amplitude

n    Height of peak from baseline

Electromagnetic Radiation

n    Sinusoidal in nature

n    Both electric and magnetic components

n   Orthogonal to each other

n   Look at the electric component

n    All electromagnetic radiation moves at the same speed in a vacuum

n    Speed of light (c)

n    3.00 x 108 m/s

n    Wavelength(8) x Frequency (n) = ???

n     m x s-1 = m/s

n    Speed

n   OF LIGHT!

n    For EMR, c = 8n

n    EMR properties related to wavelength

n    More properly to frequency!

n    Wavelengths cover a wide range of values!

n    Often more appropriate to express wavelengths in units other than meters.

Problems:  1 – 9 odd

Quantized Energy and Photons

n    Temperature can be judged by color of light emitted from an object

n    Red hot cooler than white hot

n    Could not explain using known laws of physics

n    Max Planck

n    Assumed energy could only be given off in ‘chunks’

n    Planck’s Constant used for energy of single ‘quantum’ of energy

n    h = 6.626 x 10-34 J s

n   Equantum = hn

n     v is the frequency of the emitted light.

The Photoelectric Effect

n    Explained by Einstein

n    Quantized energy packets of light called photons.

n    Ephoton = hn

n    Is light a particle or a wave?

n    Behaves as both

n    Called ‘Dual Nature of Light’

Problems:  11 – 21 odd

Bohr’s Model of the Hydrogen Atom

n    Light Spectra

n    Continuous

n    From ‘Black Body’ radiation

Hydrogen Line Spectrum

n    Balmer Series

n    Discovered in 1885

n    Explained presence of visible lines

The Bohr Atom

n    Balmer’s observation was pre-nuclear atom.

n    With Rutherford’s discovery, electrons were pictured as small solar system.

n    Classical physics – electron will spiral into the nucleus.

n    Bohr – used Planck’s idea of quantized energy

n    Only certain orbits are ‘permitted.’

n     Energy transitions from the Bohr model

n     Only these energy transitions are allowed

n    Quantized!

n    Explains why lines are observed.

n    Energy when n = 4 is 0

n    Electron loses energy as it approaches the nucleus (n gets smaller).

n    Energies for electrons in orbits are less than zero!

n   Negative sign before Rydberg constant

n    Bohr assumed electrons could ‘jump’ orbits.

n    Light was energy associated with ‘jump.’

n    To calculate the energy difference

n    Use Bohr’s equation

n    What is RH / h?

n    3.29 x 1015 s-1

n    Same as Balmer constant!

n   Balmer series is for electrons ‘falling’ to the n=2 level

n    Sign convention

n    Positive value means photon is absorbed.

n   Electron moves to a higher energy level.

n    Negative sign means photon emitted.

n   Electron moves to a lower energy level.

n     When an electron is promoted it requires energy.

n    Fraunhofer lines

n     When an electron is ‘demoted’ (returns to a lower energy state it emits energy

n    Line spectra

The Bohr Atom - Limitations

n    Only applies to single-atom species

n    He+, Li2+, …

n    When applied to multi-electrons problems arose.

n   Still have line spectra, but not where predicted.

n    Why???

Problems:  23 – 29 odd

The Wave Behavior of Matter

n    If light can act like particles, can matter act like waves?

n    YES IT CAN!

n    Louis de Broglie

n    Proposed ‘matter waves’

n     l = h/mv

n   h = Planck’s constant; m = mass (g), v = velocity (m/s)

n    Leads to uncertainty in position!

n    As mass increases, wavelength decreases

n    Doesn’t explain why I can’t hit a curve ball!

n    Only significant for very small particles

n    Electrons!

n    Principle behind electron microscopes

n   Shorter the wavelength, the better the resolution

n   For an electron, l = 0.122 nm

Uncertainty

n    Classical physics

n    Can calculate exactly the position and momentum of an object

n    Wave mechanics

n    Because of the significant wave properties of electrons, cannot determine both the position and momentum of an electron

n    Heisenberg Uncertainty Principle

n   Eliminates the ‘mini solar system’ picture for the atom

Problems:  33 – 37 odd

Quantum Mechanics and Atomic Orbitals

n    If electrons behave as waves, then wave equations should be able to predict electron behavior.

n    Quantum Mechanics or Wave Mechanics

n    Erwin Schrodinger

n    Derived a set of equations to describe electrons based on wave properties

n    Wave functions (y)

Schrodinger Wave Equation

n    Electron properties a function of y2

n    Predicts allowed energies

n    For hydrogen, values match what Bohr determined

n   Difference is we don’t know the location of the electron using the wave function.

n    y2 is a ‘probability density function.’

n    Equation yields 3 quantum numbers to describe electrons.

n    Principal quantum number (n)

n   Corresponds to a Bohr ‘orbit.’

n   Shell (City)

n    Azimuthal quantum number (l)

n   Subshell (Hotel)

n    Magnetic quantum number (ml)

n   Orbital (Room)

Assigning Quantum Numbers

n     n

n    Can have any integral value from 1 to 4.

n     l

n    Integral values range from 0 to n – 1.

n    When l = 0 (s);  l = 1 (p); l = 2 (d); l = 3 (f)

n     ml

n    Integral values range from -l to +l.

Quantum Number Principles

n    A n shell will have n subshells

n    When n = 3 there are 3 subshells

n    An l subshell will have 2l + 1 orbitals

n    When l = 2 (d) there are 5 orbitals

n    Total number of orbitals for a shell = n2

n    The 4th shell will have 16 orbitals

n    Very significant for the periodic table!

n     Relative energy levels for the hydrogen atom

n    All orbitals in a shell have the same energy (degenerate)

n    Explains Bohr atom.

THIS IS TRUE ONLY FOR SINGLE ELECTRON SPECIES!

 

Representation of Orbitals

n     s orbitals

n    Shaped like a ball

n    Spherical symmetry

n     Nodes

n    Areas with a low probability of finding an electron

n    Nucleus (all)

n    Other nodes when n>1.

n     p orbitals

n    2 lobes with node at nucleus

n    All p orbitals are shaped the same with a different orientation in space

n    Also increase in size as we increase value of n.

n    d orbitals

n    4 lobes for most of the orbitals

n    3 sets of orbitals with the lobes between the x/y/z axes

n    1 orbital with the 4 lobes on the x/y axes

n    1 orbital with 2 lobes (z axis) and a ‘doughnut’!

n    f orbitals

n    4 sets with 8 lobes

n    3 sets with 2 lobes and ‘double doughnut’

Problems:  39 – 49 odd

Orbitals in Many-Electron Atoms

n    Good News

n    Orbital descriptions (shapes) for the hydrogen atom orbitals are the same as for other multi-electron atoms.

n    Bad News

n    If you have more than one electron, the interaction between the electrons becomes important!

Effective Nuclear Charge

n    2 forces on electrons

n    Attraction to the nucleus

n    Repulsion by other electrons

n    Too complex to treat in detail, but can make some simplifying assumptions

n    ‘Average’ electronic environment

n    Effective nuclear charge

n   Zeff = Z – S

n   S= average # electrons between electron and nucleus

Orbital Energies

n    Amount of screening dependent on distance from the nucleus

n    More electrons between the nucleus and electron of interest.

n   Distance from nucleus increases with n value for a given subshell

n   Distance from nucleus increases for increasing l value in a given shell

n    s closer than p closer than d closer than f
n    Zeff decreases as l increases

Energy Relationships

n     For the s (or p, d, f) orbitals

n    As n increases, energy increases

n     For the 2nd (or 3rd, 4th,…) shell

n    As l increases, energy increases

n    All orbitals are degenerate in a given subshell.

Electron Spin

n    Multi electron atoms

n    Noticed what was thought to be a single line were two closely spaced lines

n    Attributed to ‘electron spin’

n    4th quantum number (ms)

n   Values of + ½

n   Bed in hotel room.

Pauli Exclusion Principle

n    No two atoms can have the same set of 4 quantum numbers.

n    Each electron has a unique address!

n    Shows the maximum number of electrons in an orbital must be 2

n    Leads to understanding why the periodic table works.

Problems:  51 – 61 odd

Electron Configurations

n    Arrangement of electrons in an atom.

n    Aufbau principle

n    Electrons will enter lowest available energy level

n    Pauli Exclusion Principle

n    Orbitals can hold at most 2 electrons

n    Hund’s Rule

n    Degenerate orbitals will ½ fill with electrons of parallel spin before any fill with anti-parallel spin.

Notation

n    Show shell (n) and subshell (letter designating the value for l) with superscript indicating the number of electrons in each.

n    For Li; 1s2 2s1

n   Indicates 2 electrons in the 1s subshell (filling it) and 1 electron in the 2s shell (not full)

n     Argon

n    1s2 2s2 2p6 3s2 3p6

n     Where does the next electron go (K)?

n    We know that 3d is greater than 3s

n    We know that 4s is greater than 3s

n    Is 4s < 3d???

n    K – [Ar] 4s1

n    4s subshell will fill completely (Ca) before the 3d subshell starts to fill (Sc)

n    We can use the periodic table to help predict where the electrons go.

n    Groups and regions on periodic table defined by their electronic structure!!!

Valence Electrons

n      Electrons in the outermost shell

n     For elements in a group, the valence shell configuration is the same

n     Chemical and physical properties are driven by valence electrons

n     Families have similar chemical and physical properties

n    Inner electrons are ‘core’ electrons

Predicting Electronic Configurations

n    Learn to use the periodic table to predict these structures

n    Not always right!

n    Anomalies usually occur when atom can have a more stable arrangement using ½ filled or completely filled orbitals

n   Ag – predict [Kr] 5s2 4d9

n   Ag – actual [Kr] 5s1 4d10

n   WHY??

Anomalies

n     Ag – [Kr] 5s1 4d10

n    Energy levels are dynamic, not static

n    Above electronic structure has only ½ filled and completely filled subshells.

n     HOW THE &%## AM I SUPPOSED TO KNOW THAT!

n    I expect you to be able to predict using the periodic table (Ag would be [Kr] 5s2 4d9)

n    I expect you to be able to explain why an anomaly would occur GIVEN THE CORRECT CONFIGURATION!

Problems:  63 – 69 odd