Rationale of trends in the Periodic table

Basis of periodic trends:

1) z_eff = z - s

2) F = k Z_eff Qe / r² ;  attractive force between the nucleus & outermost electron; r = distance between the nucleus & outermost electron

3) F = k Q_e Q_e / r² ;  repulsive force between electron - electron

4) electron energy level profile & basis of E_{minimum to eject electron} in the photoelectric effect; IE = Δ energy between n = ∞ & occupied highest energy electron level

n = ∞ ___ ← electron is ejected

.

.

                       ___ ___ ___ 2p

n = 2   ___ 2s

 

n = 1   ____ 1s

atomic size

* left → right in the periodic table (ignore transition metals):

  ± s  & ↑ z → ↑ z_eff → ↑ F_{nucleus-electron attraction} → ↓ size

* top → bottom in the periodic table

↑ s & ↑ z →  ± z_eff

but ↑ # electron shell  → ↑ size

atom / ion size

* anion versus (corresponding) atom

add electron (to atom to form anion) → ↑ electron - electron repulsion→ ↑ size (of anion relative to atom); i.e. size of anion > size of corresponding atom

*cation versus (corresponding) atom

remove electron (from atom to form cation) → ↓ electron - electron repulsion→ ↓ size (of cation relative to atom); i.e. size of cation < size of corresponding atom

* ions (cations or anions)

[left → right] or [top → bottom] of periodic table

have the same trend as atomic size for similar reasons

Ionization energy (IE) trends

* 1^st IE < 2^nd IE < 3^rd IE < . . .

remove electron →

↓ electron - electron repulsion→ ↓ size → ↑ F_{nucleus-electron attraction} → ↑ energy to remove electron = ↑ IE

* there is a "big" jump in IE between electron subshells, e.g. 2^nd IE of Na & 3^rd IE of Mg (Re. table 7.2 in the textbook); because, to remove the electron from the next lower subshell, there is a decrease in shielding

       i.e.   ↓ s & ± z → ↑ z_eff → ↑ F_{nucleus- electron attraction} → ↑ energy to remove electron = ↑ IE

* left → right in periodic table

     ↑ z & ± s → ↑ z_eff → ↓ size [ & ↑ z_eff ] → ↑ F_{nucleus-electron attraction} → ↑ energy to remove electron = ↑ IE

     * while going left → right in the periodic table, IE drops between Be & B; Mg & Al

     electron configuration in above pair of atoms corresponds to going from a full s-orbital to a higher energy p-orbital

           i.e.   ↑ energy of electron orbital → ↓ energy needed to eject electron → ↓ IE

     * while going left → right in the periodic table, IE drops between N & O; P & S; As& Se

       electron configuration of these atoms:   ↑ ↑ ↑ → ↑ ↓ ↑ ↑

np³ orbital electrons are in separate orbitals, while an electron in np⁴ orbital is paired with another electron in the same orbital → there is electron - electron repulsion in np⁴ orbital (while there is no such interaction in np³ orbital) → becomes easier to remove electron = ↓ IE

* top → bottom in the periodic table

      ↑ r & ± z_eff → ↓ F_{nucleus-electron attraction} → ↓ energy to remove electron → ↓ IE

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EA trends

* left → right in the periodic table (ignore Noble gases)

      ↑ z & ± s → ↑ z_eff (& ↓ size) → ↑ F _{nucleus-electron attraction} [ → easier for electron to be attracted to the atom] → ↑ [magnitude of] EA (for process, where EA < 0).

* while going left → right in the periodic table, the magnitude of EA drops between C & N; Si & P; Ge & As; Sn & Sb

   electron configuration:   n p²   versus   n p³

when add electron to above atom, its's easier to add an electron to np² [since there is an empty p-orbital] than np³ [since it means that the electron would be added to an occupied p-orbital] → there is electron - electron repulsion→ "harder" to add electron → ↓ energy release due to adding electron to the atom → ↓ magnitude of EA (for process, where EA < 0)

* top → bottom in the periodic table

   no clear trend:  there are opposing factors / influences that cancel each others' effect

     e.g.   ± z_eff → ± F_{attraction . . .} → ± EA

         [coulomb's law consideration]:   ↑ size → ↓ F_{attraction . . .} → ↓ EA

[geometry consideration]:   ↑ size → ↓ electron - electron repulsion→ ↑ EA