Periodic Trends of the Elements

Purpose: To understand where electrons ( $e^-$ -) reside and how their location impacts atomic behavior. This requires identifying which electrons occupy which orbitals.
Significance of Orbital Occupation: The specific orbital an $e^-$ - occupies indicates its relative energy.
- Previously, only the principal quantum number $(n)$ was needed to determine relative energy. Now, the azimuthal or angular momentum quantum number $(l)$ is also crucial.
Determining Relative Energy:
- Higher $n$ means higher energy: A $3d$ $e^-$ - has higher energy than a $2p$ $e^-$ - because $(n=3)$ is greater than $(n=2)$ .
- Higher $l$ means higher energy (for the same $n$ ): A $3d$ $e^-$ - has higher energy than a $3p$ $e^-$ - because $(l=2)$ (for $d$ ) is higher than $(l=1)$ (for $p$ ).
Electron Configuration: A systematic and easier approach to determine the energy of various orbitals in an atom.

$e^-$ - are placed in orbitals one at a time.
Order of Filling: Orbitals are filled in order of increasing energy.
- Generally, as $(n)$ and $(l)$ increase, energy increases.
- The magnetic quantum number ( $m<em>l$ ) does not affect energy; orbitals with the same $(n)$ and $(l)$ (e.g., three $2p$ orbitals like $2p</em>x$ , $2p<em>y$ , $2p</em>z$ ) are degenerate, meaning they have the same energy level.
- If multiple $e^-$ - need to be placed in degenerate orbitals, they are dispersed across these orbitals (Hund's Rule, implicitly).

Diagrammatic Aid: A useful diagram (often depicted as a series of diagonal arrows through organized $(s, p, d, f)$ subshells) helps remember the filling order.
- Start from the top right and follow the diagonal arrows down.
Order of Filling (List):
$1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p$
Examples of Electron Configurations:
- Fluorine (F): $1s^2 2s^2 2p^5$
- Sodium (Na): $1s^2 2s^2 2p^6 3s^1$
- Copper (Cu): $1s^2 2s^2 2p^6 3s^2 3p^6 4s^1 3d^{10}$
  - Note: Copper is an exception where an electron is promoted from $4s$ to $3d$ to achieve a full $3d$ subshell, which is more stable.
Using the Periodic Table: The periodic table can also be used as a guide for determining electron configurations based on blocks ( $s, p, d, f$ ).

Illustration with F and C:
- Fluorine (F): $1s^2 2s^2 2p^5$ (9 protons, 1 unpaired $e^-$ - in $2p$ )
- Carbon (C): $1s^2 2s^2 2p^2$ (6 protons, 2 unpaired $e^-$ - in $2p$ )
Concept: The valence electrons in F experience a greater