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

2.2.7 · Chemistry › Periodic Trends

KIYA hai diagonal relationship?

$Li ↘ Mg, Be ↘ Al, B ↘ Si$

KYUN hota hai? (First principles se derivation)

Woh ek quantity jo is chemistry ko control karti hai woh hai polarising power — yani ek cation kitni strongly kisi neighbouring anion ke electron cloud ko distort (pull) karta hai. Fajans ne ise charge-to-size ratio, yaani ionic potential ke roop mein capture kiya:

Ab dekho ki dono periodic trends $ϕ$ ke dono inputs ke saath kya karte hain:

Ek period mein across (→): charge $z$ ↑ aur radius $r$ ↓, toh $ϕ = \frac{z ↑}{r ↓} \Rightarrow ϕ strongly badhta hai.$

Ek group mein down (↓): charge $z$ same rehta hai lekin radius $r$ ↑, toh $ϕ = \frac{z}{r ↑} \Rightarrow ϕ ghatta hai.$

Diagonally (↘) = dono karo: right jaane se jo increase hoti hai woh down jaane se decrease se partly offset ho jaati hai. Dono trends exactly cancel nahi hote (neeche numbers dekho), lekin yeh opposite directions mein push karte hain, isliye ek diagonal partner seedhe group neighbour se polarising behaviour mein zyada close hota hai. Sabse important baat, radius — dono inputs mein se ek — aksar diagonally nearly matched ho jaata hai, aur yahi chemistry ko track karaata hai.

Real numbers se check karo (ionic radii, pm)

Ion	$z$	$r$ (pm)	$ϕ = z / r$ (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

CHEMICALLY kaise dikhta hai (evidence)

Worked example Li, Mg se milta hai (baaki alkali metals se nahi)

Li₂CO₃, Li₃PO₄ aur LiF sparingly soluble hain — aur corresponding Mg salts (MgCO₃, Mg₃(PO₄)₂, MgF₂) bhi insoluble/sparingly soluble hain. (Note: yeh specifically inhi salts ke liye hai; MgCl₂, Mg(NO₃)₂, MgSO₄ quite soluble hain, aur LiCl, LiNO₃ bhi.) Kyun? Carbonate/phosphate/fluoride ke liye, chhota, high- $ϕ$ Li⁺ aur Mg²⁺ hydration ke relative badi lattice energy dete hain ⇒ low solubility. Doosre alkali metal carbonates (Na, K) soluble hain.
Li aur Mg directly nitrides banaate hain: $6 Li + N_{2} \to 2 Li_{3} N$ ; $3 Mg + N_{2} \to Mg_{3} N_{2}$ . Na nahi karta.
Carbonates heating par oxide mein decompose hote hain: $Li_{2} CO_{3} \to Li_{2} O + CO_{2}$ , $MgCO_{3}$ ki tarah. Na₂CO₃ thermally stable hai.
Dono mainly normal oxides banate hain (Li₂O, MgO); Na peroxide banata hai, K superoxide.

Worked example B, Si se milta hai

Note: B aur Si ki chemistry covalent hai, ionic nahi — yahan $z / r$ argument sirf ek qualitative size/electronegativity analogy hai (hypothetical B³⁺ actually kabhi exist nahi karta), isliye hum covalent radii aur electronegativity compare karte hain: B (covalent r ≈ 84 pm, $χ$ ≈ 2.0) vs Si (r ≈ 111 pm, $χ$ ≈ 1.9). Dono chhote, comparably electronegative non-metals hain ⇒ similar bonding.
Dono metalloids hain covalent network/molecular structures ke saath; dono acidic oxides banate hain (B₂O₃, SiO₂).
Hydrides volatile, flammable, aur paani se hydrolyse hote hain (boranes ~ silanes), C ke stable alkane analogues ke unlike.
Dono hard, refractory solids banate hain; halides (BF₃, SiF₄) covalent hain aur hydrolyse karte hain. Kyun? Similar small size aur electronegativity ⇒ covalent multi-centre bonding ki strong tendency.

Common mistakes (Steel-man → Fix)

Flashcards

Teen classic diagonal pairs kaunse hain?

Li/Mg, Be/Al, B/Si

Diagonal relationship ko kaunsi property control karti hai?

Polarising power via ionic potential

ϕ = z / r

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

Diagonal partners ek doosre se kyun milte-julte hain?

Right jaana ↑ φ aur down jaana ↓ φ opposing trends hain; ek diagonal step radius ya φ ko nearly matched chhod deta hai, isliye chemistry track karti hai

Kya φ, Li→Mg ke liye exactly cancel hota hai?

Nahi — φ roughly double ho jaata hai (0.013→0.028); jo match karta hai woh ionic radius hai (76 vs 72 pm)

Ek property batao jo dikhaye ki Li, Na se nahi balki Mg se milta hai.

Li₂CO₃ (aur LiF, Li₃PO₄) insoluble hai aur Li₂CO₃ heating par decompose hota hai; Li, N₂ ke saath Li₃N banata hai (Na dono nahi karta)

Kaun se Mg salts insoluble hain (Li ki tarah)?

Carbonate, phosphate, fluoride — lekin MgCl₂, Mg(NO₃)₂, MgSO₄ soluble hain

Kaunsa oxide behaviour Be aur Al ko jodata hai?

BeO aur Al₂O₃ dono amphoteric hain

BeCl₂ aur AlCl₃ covalent kyun hain?

Be²⁺/Al³⁺ ke paas high, closely matched ionic potential hai → Cl⁻ ko strongly polarise karta hai (Fajans) → covalent

B, C se nahi balki Si se kyun milta hai?

B aur Si ki similar small covalent radius aur electronegativity hain → metalloid, acidic oxides, hydrolysable volatile hydrides (covalent, ionic nahi)

Ionic potential ka formula aur matlab?

ϕ = z / r

; ion surface par field strength / polarising power

Recall Ek 12-saal ke bachche ko explain karo (Feynman)

Socho har atom ki ek "grip strength" hoti hai doosre atoms ke electrons ko pakadne ki. Table mein right jaane par grip stronger hoti hai; down jaane par weaker hoti hai. Agar tum ek step down AND ek step right lete ho, toh yeh dono changes ek doosre ke against push karte hain — tum grip ko poori tarah undo nahi karte, lekin tum ek aisi atom ke paas pahunchte ho jo similar size aur similar behaviour wali hoti hai. Isliye chhota Lithium Magnesium ki tarah behave karta hai, Beryllium Aluminium ki tarah, aur Boron Silicon ki tarah — same personality, chahe woh alag families mein hain.

Connections

Fajans' Rules — polarising power → covalent character (same $ϕ$ logic)
Periodic Trends — Atomic and Ionic Radii — $z / r$ ka size wala half (Li/Mg ke liye matched input)
Anomalous Behaviour of First Element — Li, Be, B ki small size dono anomaly aur diagonal likeness karaati hai
Amphoterism — BeO/Al₂O₃ shared behaviour
Lattice Energy vs Hydration Energy — kyun high- $ϕ$ salts (carbonate/phosphate/fluoride) insoluble hain
Effective Nuclear Charge (Zeff) — kyun ek period mein across $r$ shrink karta hai