Diagonal relationship — Li - Mg, Be - Al, B - Si

WHAT is a diagonal relationship?

$\text{Li}\;\searrow\;\text{Mg}, \qquad \text{Be}\;\searrow\;\text{Al}, \qquad \text{B}\;\searrow\;\text{Si}$

Figure — Diagonal relationship — Li - Mg, Be - Al, B - Si

WHY does it happen? (Derivation from first principles)

The single quantity that controls this chemistry is polarising power — how strongly a cation distorts (pulls) the electron cloud of a neighbouring anion. Fajans captured this as the charge-to-size ratio, the ionic potential:

Now watch what the two periodic trends do to the two inputs of $\phi$ :

Across a period (→): charge $z$ ↑ and radius $r$ ↓, so $\phi = \frac{z\uparrow}{r\downarrow} \;\Rightarrow\; \phi \text{ increases strongly.}$

Down a group (↓): charge $z$ stays same but radius $r$ ↑, so $\phi = \frac{z}{r\uparrow} \;\Rightarrow\; \phi \text{ decreases.}$

Diagonally (↘) = do both: the increase from moving right is partly offset by the decrease from moving down. The two trends do not cancel exactly (see numbers below), but they push in opposite directions, so a diagonal partner is closer in polarising behaviour than a straight group neighbour. Crucially, the radius — one of the two inputs — often ends up nearly matched diagonally, and that is what makes the chemistry track.

Check it with real numbers (ionic radii, pm)

Ion	$z$	$r$ (pm)	$\phi = z/r$ (charge/pm)
Li⁺	1	76	0.013
Na⁺	1	102	0.010
Mg²⁺	2	72	0.028
Be²⁺	2	45	0.044
Al³⁺	3	53	0.057

HOW it shows up chemically (the evidence)

Worked example Li resembles Mg (not the other alkali metals)

Li₂CO₃, Li₃PO₄ and LiF are sparingly soluble — and the corresponding Mg salts (MgCO₃, Mg₃(PO₄)₂, MgF₂) are also insoluble/sparingly soluble. (Note: this is specific to these salts; MgCl₂, Mg(NO₃)₂, MgSO₄ are quite soluble, and so are LiCl, LiNO₃.) Why? For carbonate/phosphate/fluoride, the small, high- $\phi$ Li⁺ and Mg²⁺ give large lattice energy relative to hydration ⇒ low solubility. Other alkali metal carbonates (Na, K) are soluble.
Li and Mg form nitrides directly: $6\text{Li}+\text{N}_2\to 2\text{Li}_3\text{N}$ ; $3\text{Mg}+\text{N}_2\to\text{Mg}_3\text{N}_2$ . Na does not.
Carbonates decompose on heating to oxide: $\text{Li}_2\text{CO}_3\to\text{Li}_2\text{O}+\text{CO}_2$ , like $\text{MgCO}_3$ . Na₂CO₃ is thermally stable.
Both form mainly normal oxides (Li₂O, MgO); Na forms peroxide, K forms superoxide.

Worked example B resembles Si

Note: B and Si chemistry is covalent, not ionic — the $z/r$ argument here is only a qualitative size/electronegativity analogy (a hypothetical B³⁺ never actually exists), so we compare covalent radii and electronegativity instead: B (covalent r ≈ 84 pm, $\chi$ ≈ 2.0) vs Si (r ≈ 111 pm, $\chi$ ≈ 1.9). Both are small, comparably electronegative non-metals ⇒ similar bonding.
Both are metalloids with covalent network/molecular structures; both form acidic oxides (B₂O₃, SiO₂).
Hydrides are volatile, flammable, and hydrolysed by water (boranes ~ silanes), unlike stable alkane analogues of C.
Both form hard, refractory solids; halides (BF₃, SiF₄) are covalent and hydrolyse. Why? Similar small size and electronegativity ⇒ strong tendency to covalent multi-centre bonding.

Common mistakes (Steel-man → Fix)

Flashcards

What are the three classic diagonal pairs?

Li/Mg, Be/Al, B/Si

Which property controls the diagonal relationship?

Polarising power via ionic potential

\phi = z/r

— through a matched input (size for Li/Mg, φ itself for Be/Al)

Why do diagonal partners resemble each other?

Moving right ↑ φ and moving down ↓ φ are opposing trends; a diagonal step leaves either the radius or φ nearly matched, so chemistry tracks

Does φ cancel exactly for Li→Mg?

No — φ roughly doubles (0.013→0.028); it is the ionic radius (76 vs 72 pm) that matches

Give one property showing Li is like Mg not Na.

Li₂CO₃ (and LiF, Li₃PO₄) insoluble and Li₂CO₃ decomposes on heating; Li forms Li₃N with N₂ (Na does neither)

Which Mg salts are insoluble (like Li)?

Carbonate, phosphate, fluoride — but MgCl₂, Mg(NO₃)₂, MgSO₄ are soluble

Which oxide behaviour links Be and Al?

Both BeO and Al₂O₃ are amphoteric

Why are BeCl₂ and AlCl₃ covalent?

Be²⁺/Al³⁺ have high, closely matched ionic potential → strongly polarise Cl⁻ (Fajans) → covalent

Why is B like Si and not like C?

B and Si have similar small covalent radius and electronegativity → metalloid, acidic oxides, hydrolysable volatile hydrides (covalent, not ionic)

Formula for ionic potential and meaning?

\phi=z/r

; field strength at ion surface / polarising power

Recall Explain to a 12-year-old (Feynman)

Imagine every atom has a "grip strength" for grabbing other atoms' electrons. Going right in the table makes the grip stronger; going down makes it weaker. If you take one step down AND one step to the right, those two changes push against each other — you don't fully undo the grip, but you land near an atom with a similar size and similar behaviour. That's why tiny Lithium acts like Magnesium, Beryllium like Aluminium, and Boron like Silicon — same personality, even though they're in different families.

Connections

Fajans' Rules — polarising power → covalent character (same $\phi$ logic)
Periodic Trends — Atomic and Ionic Radii — the size half of $z/r$ (the matched input for Li/Mg)
Anomalous Behaviour of First Element — small size of Li, Be, B causes both anomaly and diagonal likeness
Amphoterism — BeO/Al₂O₃ shared behaviour
Lattice Energy vs Hydration Energy — why high- $\phi$ salts (carbonate/phosphate/fluoride) are insoluble
Effective Nuclear Charge (Zeff) — why $r$ shrinks across a period

Concept Map

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Dekho, periodic table mein do simple trends hain. Jab tum right ki taraf jaate ho (period mein aage), ion chhota aur zyada "polarising" ho jaata hai — matlab uski charge/size ratio ( $\phi = z/r$ ) badhti hai. Aur jab tum neeche jaate ho (group mein), ion bada ho jaata hai, toh $\phi$ ghatti hai. Ab diagonal (↘) step mein yeh dono trends ek dusre ko oppose karte hain — poori tarah cancel nahi hote, par kaam-se-kaam ek input match ho jaata hai. Isi se diagonal partner ki chemistry milti-julti nikalti hai.

Ek honest baat: Li→Mg mein $\phi$ actually double ho jaata hai (0.013 se 0.028), toh perfect cancellation ka claim galat hai. Yahan asli match ionic radius ka hai (76 vs 72 pm) — isi wajah se Li salts ka lattice/hydration balance Mg jaisa behave karta hai. Lekin Be→Al mein $\phi$ khud close hai (0.044 vs 0.057) aur dono high hai, isliye dono strongly covalent. Aur B→Si ionic bilkul nahi hai — yeh sirf size aur electronegativity ki similarity hai (B³⁺ toh exist hi nahi karta).

Isi wajah se Li, Mg jaisa behave karta hai: Li₂CO₃, LiF, Li₃PO₄ insoluble aur MgCO₃, MgF₂ bhi insoluble — par dhyan rakhna, saare Mg salts insoluble nahi (MgCl₂, MgSO₄, Mg(NO₃)₂ toh khoob soluble hain). Be, Al jaisa: dono amphoteric oxide, covalent chloride. B, Si jaisa: dono metalloid, acidic oxide, hydrolysable volatile hydrides.

Exam ke liye 80/20: logic yaad rakho ki trends oppose karte hain (cancel nahi), phir Li/Mg = size match, Be/Al = φ match, B/Si = covalent analogy. Har pair ke 2-2 examples yaad kar lo — topic cover.

Diagonal relationship — Li - Mg, Be - Al, B - Si

WHAT is a diagonal relationship?

WHY does it happen? (Derivation from first principles)

Check it with real numbers (ionic radii, pm)

HOW it shows up chemically (the evidence)

Common mistakes (Steel-man → Fix)

Flashcards

Connections

Concept Map

Hinglish (regional understanding)

Go deeper — visual, from zero

Test yourself — Periodic Trends

Connections