Electronic Structure

• Electronic structure: the arrangement and energy of electrons.

Waves

• Electromagnetic radiation moves as waves through space at the speed of light.

• Wavelength (\lambda): the distance between corresponding points on adjacent waves.

• Frequency (v): the number of waves passing a given point per unit of time.

• The longer the wavelength, the smaller the frequency.

• Example:

  • Top wave = low frequency, long wavelength

  • Bottom wave = high frequency, short wavelength

Electromagnetic Radiation

• All electromagnetic radiation travels at the same velocity.

• The speed of light (\:c\:) is 3.00\times 10^{8} m/s

  • c=\lambda v

  • 3.00\times 10^{8} m/s = (wavelength)(frequency)

The Photoelectric Effect

• Each metal has a different energy at which it ejects electrons.

• Are lower energy, electrons are not emitted.

• Energy is proportional to frequency

  • E=hv

  • Plank’s constant (h) is 6.626\times 10^{-34} J\sdot s

Quantum Mechanics

• Quantum mechanics: describes the movement of electrons.

• The square of the wave function gives the electron density, or probability of where an electron is likely to be at any given time.

Quantum Numbers

• Orbitals: describes a spatial distribution of electron density.

• An orbital is described by a set of four quantum numbers.

Principal Quantum Number (n)

• The principle quantum number, n, describes the energy level on which the orbital resides.

• n provides the size

• The values of n are integers greater or equal to 1.

  • n = 1, 2, 3, … \infty \geq 1

• These correspond to the values in the Bohr model.

Angular Momentum Quantum Numbers (l)

• This quantum number defines the shape of the orbital.

• Allowed values of l are integers ranging from 0 to n-1

• Letter designate the different values of l.

  Value of l	Orbital letter used
  0	s
  1	p
  2	d
  3	f

Magnetic Quantum Number (m_l)

• The magnetic quantum numbers described the three-dimensional orientation of the orbital.

• Allowed values of m_l are integers ranging from -l to l including 0.

  • -l\leq m_{l}\leq l

• There can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, and 7 f orbitals.

• Orbitals with the same value of n form an electron shell.

• Different orbitals types within a shell are subshells.

Orbital orientations (m_l)

• s Orbitals

  • The value of l for s orbitals is 0.

  • Spherical in shape.

  • Radius of sphere increase with the value n.

• p Orbitals

  • The value of l for p orbitals is 1.

  • They have two lobes with a node between them.

• d Orbitals

  • The value of l for a d orbital is 2.

  • Four of five d orbitals have four orbitals; the other resembles a p orbital with a doughnut around the center.

• f Orbitals

  • The value of l for f orbitals is 3.

  • Complex shape.

Spin Quantum Number (m_s)

• Two electrons in the same orbital do not have exactly the same energy.

• The “spin” of an electron describes its magnetic field, which affects its energy.

• The spin of the quantum number has only two allowed values: +1/2 and -1/2

• Only one can spin up, other other spins down.

Summary

Orbital Diagrams

• Each box in the diagram represents one orbital.

• Half arrows represent the electrons.

• The direction of the arrow represents the relative spin of an electron.

Energies of Orbitals

• Degenerates: systems or orbitals that have the same energy.

• As the number of electrons increases, so does the repulsion.

• In atoms with more than one electron, not all orbitals on the same energy level are degenerate.

• Energy levels start to overlap in energy (ex: 4s must be filled before 3p because its lower.

• Hund’s Rule: For a set of orbitals in the same sublevel, there must be one electron in each orbital before pairing and the electrons have the same spin.

• Pauli Exclusion Principle: No two electrons in the same atom can have the same set of four quantum numbers.

• Therefore, no two electrons in the same atom can have the exact same energy.

• This means that every electron in an atom must differ by at least one of the four quantum number values. They will have OPPOSITE SPINS.

Electron Configurations

• Electron configuration: the way electrons are distributed in an atom.

• Ground state: the most stable organization is the lowest possible energy.

• Each component consists of:

  • a number denoting the energy level

  • a letter denoting the type of orbital

  • a superscript denoting the number of electrons in those orbitals

• Describes where electrons are located around the nucleus of an atom.

• Moves diagonally

• 1s² → 2s² → 2p⁶ → 3s² → 3p⁶ → 4s² → 3d¹⁰ → 4p⁶ → 5s² → 4d¹⁰ → and so on

Electron Configuration Examples

• H: 1s¹

  • Has 1 total electron

• He: 1s²

  • Has 2 total electrons

• Li: 1s²2s¹

  • Has 3 total electrons

• Be: 1s²2s²

  • Has 4 total electrons

• B: 1s²2s²2p¹

  • Has 5 total electrons

• C: 1s²2s²2p²

  • Has 6 total electrons

• N: 1s²2s²2p³

  • Has 7 total electrons

• O: 1s²2s²2p⁴

  • Has 8 total electrons

• F: 1s²2s²2p⁵

  • Has 9 total electrons

• Ne: 1s²2s²2p⁶

  • Has 10 total electrons

Row and Energy Levels

• The periodic table is broken up into four blocks: s, p, d, and f.

  • Columns 1-2 and He are a part of the s block

  • The transition metals (columns 3-12) are the d block

  • Columns 13-18 make up the p block

  • The lower elements are part of the f block

• The row indicates the highest occupied electron level.

• The columns gives the outermost electron configuration (the superscript)

Condensed Electron Configurations

• Elements in the same group of the periodic table have the same number of electrons in the outer most shell. These are the valence electrons.

• The filled inner shell electrons are called core electrons.

• The shortened version is written by using brackets around a noble gas symbol and listing only valence electrons.

• Condensed Electron Configuration Examples:

  • Na = [Ne]3s¹

  • Ne = [He]2s²2p⁶

  • Cl = [Ne]3s²3p⁵

  • O = [He]2s²2p⁴

  • Ca = [Ar]4s²

Reference: Chemistry The Central Science (14th Edition)