Atomic Structure, Electron Configuration, and Periodic Trends: Study Notes

Atomic Structure and Electron Configuration

Ground State Electron Configuration

Electron configuration describes the arrangement of electrons in an atom's orbitals. The ground state configuration is the lowest energy arrangement of electrons.

• Full Electron Configuration: Lists all occupied orbitals in order of increasing energy.

• Condensed Electron Configuration: Uses noble gas notation to simplify the configuration.

• Example: For fluorine (F): Full: $1s^2 2s^2 2p^5$ Condensed: [He] $2s^2 2p^5$

Box Diagrams (Valence Shell Only)

Box diagrams visually represent electron pairing and orbital filling in the valence shell.

• Each box: Represents an orbital; arrows indicate electrons and their spins.

• Example: For F: [He] 2s (two paired electrons), 2p (five electrons: two paired, one unpaired).

Quantum Numbers and Atomic Orbitals

Quantum Numbers

Quantum numbers describe the properties of atomic orbitals and the electrons in them:

• Principal quantum number (n): Energy level (shell)

• Angular momentum quantum number (l): Subshell (s, p, d, f)

• Magnetic quantum number (ml): Orientation of orbital

• Spin quantum number (ms): Electron spin (+1/2 or -1/2)

Atomic Orbital Sketches

Orbitals are regions in space where electrons are likely to be found. For fluorine, the 2p orbitals are shown as three perpendicular dumbbell shapes centered on the nucleus.

• Each orbital: Assigned quantum numbers (n, l, ml, ms).

Effective Nuclear Charge (Zeff) and Periodic Trends

Effective Nuclear Charge (Zeff)

Zeff is the net positive charge experienced by valence electrons, accounting for shielding by inner electrons.

• Formula: $Z_{eff} = Z - S$ Where Z is the atomic number and S is the number of shielding electrons.

• Trend: Zeff increases across a period (left to right) and decreases down a group.

• Example: For P, Cl, As, Br (all with 2p electrons):

  • P: $Z_{eff} = 15 - 2 = 13$

  • Cl: $Z_{eff} = 17 - 2 = 15$

  • As: $Z_{eff} = 33 - 2 = 31$

  • Br: $Z_{eff} = 35 - 2 = 33$

  Bromine's 2p electrons feel the largest Zeff.

Atomic Radius and Periodic Trends

Atomic radius generally decreases across a period due to increasing Zeff, pulling electrons closer to the nucleus. Down a group, radius increases as additional shells are added.

• Additional info: Oxygen is smaller than sulfur, selenium, and tellurium due to higher Zeff and less electron repulsion in the same group.

Transition Metals and Oxidation States

Variable Oxidation States

Transition metals can have multiple oxidation states due to the similar energies of their s and d orbitals.

• Example: Vanadium ([Ar] $4s^2 3d^3$) can form ions with +1 or +2 charge by removing electrons from the 4s orbital.

• Higher charges: Require removal of electrons from inner shells, which needs much more energy due to increased Zeff.

Ionization Energy and Electron Removal

Comparing Ionization Energies

Ionization energy is the energy required to remove an electron from an atom or ion.

• Trend: Higher Zeff and smaller atomic radius make it harder to remove electrons.

• Example: For Ti+, K+, Mg+, Na+:

  • Ti: $Z_{eff} = 22 - 18 = 4$

  • K: $Z_{eff} = 19 - 10 = 9$

  • Mg: $Z_{eff} = 12 - 10 = 2$

  • Na: $Z_{eff} = 11 - 10 = 1$

  K+ has its valence electrons closer to the nucleus, so it is hardest to remove an additional electron from Na+ due to its low Zeff and small radius.

Excited State Electron Configurations

Identifying Elements from Electron Configuration

Excited state configurations occur when electrons occupy higher energy orbitals than in the ground state.

• Example: $1s^2 2s^2 2p^6 3p^1$ corresponds to sodium (Na) in an excited state.

• Energy Absorption: Electrons absorb energy to move to higher orbitals; emission occurs when electrons drop to lower energy levels.

HTML Table: Effective Nuclear Charge Comparison

Element	Atomic Number (Z)	Shielding Electrons (S)	Zeff
P	15	2	13
Cl	17	2	15
As	33	2	31
Br	35	2	33

Summary

• Electron configuration and quantum numbers are foundational for understanding atomic structure.

• Effective nuclear charge (Zeff) explains many periodic trends, including atomic radius and ionization energy.

• Transition metals exhibit variable oxidation states due to their electron configurations.

• Excited state configurations involve energy absorption and can be used to identify elements.