Atomic - ionic size trends; lanthanide contraction

3.3.3 · Chemistry › d-Block (Transition Metals) & f-Block

KYA explain kar rahe hain hum

Hum trends samajhna chahte hain atomic radius aur ionic radius mein, in cases ke liye:

d-block: ek 3d/4d/5d series mein left→right aur group mein neeche.
f-block (lanthanides): woh steady shrink jo lanthanide contraction kehlati hai.
Iska bada consequence: same group ke 4d aur 5d elements size mein almost equal ho jaate hain.

SIZE $Z_{eff}$ par kyun depend karti hai (first principles)

Ek one-electron-like picture ke liye, shell $n$ mein ek electron ki most-probable radius is tarah scale hoti hai: $r \propto \frac{n ^{2}}{Z _{eff}} .$

Toh poora subject do competing knobs par aa jaata hai:

+1 proton har step → $Z$ badhata hai → size shrink hoti hai.
+1 electron har step → $S$ (shielding) badhati hai → size grow hoti hai.

Kaun jeetta hai yeh depend karta hai ki naya electron kis subshell mein jaata hai.

Har step mein 1 proton ( $Z ↑$ ) aur 1 electron inner (n−1)d mein add hota hai. Kyunki d-electrons poorly shield karte hain, $Z_{eff}$ thoda badhta hai → size pehle decrease hoti hai, phir almost flat ho jaati hai, aur end ke paas thodi upar aa sakti hai (Cu, Zn). Metallic radii mein yeh late bump do effects se aata hai: (i) filling shell mein badh raha $d$ – $d$ electron–electron repulsion, aur (ii) ab (lagbhag) filled d-shell metallic bonding mein bahut kam contribute karti hai, isliye metallic bonds kamzor pad jaate hain aur atoms thoda door ho jaate hain.

Net result: series mein chhhoti si decrease, phir levelling. Main-group period se bahut gentle.

2. Ek d-group mein neeche

3d → 4d jaane par, $n$ badhta hai, isliye size badhti hai (4d > 3d). Lekin 5d ≈ 4d size mein! Kyun? Aage padho — yeh lanthanide contraction ka tohfa hai.

3. Lanthanides mein across (La→Lu): lanthanide contraction

Har step mein ek proton aur ek electron deeply buried 4f mein add hota hai. 4f bahut buri tarah shield karta hai, isliye outer (5s5p6s) electrons par $Z_{eff}$ badhta rehta hai → radius saare 14 lanthanides mein steadily shrink hoti rehti hai.

Total shrink (Shannon ionic radii, coordination number 6) ≈ $\sim 1.032$ Å (La³⁺) se $\sim 0.861$ Å (Lu³⁺) tak: per step chhoti lekin 14 elements mein accumulate ho jaati hai. (Agar CN badle toh values shift hongi — hamesha coordination number bolo.)

Figure — Atomic - ionic size trends; lanthanide contraction

Consequences (woh 80/20 jo tumhe zaroor pata hona chahiye)

Common mistakes (Steel-manned)

Flashcards

Atomic radius ek ratio mein kis par depend karta hai?

r \propto n^{2} / Z_{eff}

— bada shell use badhata hai, bada effective charge use shrink karta hai.

Subshell ke hisaab se shielding power ka order?

s > p > d > f

(s sabse zyada penetrate karta hai aur best shield karta hai; f worst shield karta hai).

3d series mein sizes thodi hi kyun decrease hoti hain?

Added electrons inner 3d mein jaate hain (poor shielding), isliye added proton dominate karta hai lekin mildly.

Lanthanide contraction define karo.

Poorely-shielding 4f subshell fill hone par La se Lu tak Ln/Ln³⁺ ki size mein steady decrease.

Per-step lanthanide shrink chhoti kyun hai lekin effect bada kyun hai?

Har step ~1 pm, lekin 14 elements mein accumulate ho jaata hai.

4d vs 5d ke liye lanthanide contraction ka main consequence?

5d sizes ≈ 4d (Zr≈Hf, Nb≈Ta, Mo≈W) → bahut similar chemistry.

Identical size ki wajah se alag karna sabse mushkil pair kaun sa hai?

Zr aur Hf.

Os aur Ir itne dense kyun hain?

Contraction volume shrink karta hai jabki mass badhta hai ⇒ huge mass/volume.

Ln(OH)₃ ki basicity La→Lu mein kya trend hai?

Decrease hoti hai (La(OH)₃ sabse basic, Lu(OH)₃ sabse kam) kyunki charge density badhti hai.

Fe³⁺, Fe²⁺ se chhota kyun hai?

Kam electrons lekin same protons ⇒ higher

Z_{eff}

per electron ⇒ tighter pull.

Effective nuclear charge define karo.

Z_{eff} = Z - S

, woh net positive charge jo ek electron ko shielding

S

ke baad feel hota hai.

Cu, Zn par metallic radius thoda kyun badhti hai?

d

–

d

repulsion badhti hai AUR filled d-shell metallic bonding mein barely contribute karti hai, bonds kamzor ho jaate hain.

Recall Feynman: 12-saal ke bacche ko samjhao

Socho nucleus ek magnet hai jo chhoti electron-balls ko kheenchta hai, aur inner electrons bodyguards hain jo magnet aur outer balls ke beech khade hain, kuch pull ko block karte hue. Transition metals mein hum ek zyada strong magnet (proton) aur ek aalsi bodyguard (ek d-electron jo achhe se block nahi karta) dono add karte rehte hain. Isliye magnet jeetta hai aur atom thoda shrink hota rehta hai. Lanthanides mein bodyguards (f-electrons) sabse zyada aalsi hote hain, isliye 14 ke baad atom bahut zyada shrink ho jaata hai — isliye alag rows ke do metals (jaise Zr aur Hf) same size ke ho jaate hain aur twins ki tarah behave karte hain.

Connections

d-Block Overview & Electronic Configuration
f-Block (Lanthanides & Actinides)
Effective Nuclear Charge & Slater's Rules
Periodic Trends — Atomic & Ionic Radii
Density, Melting Point Trends in Transition Metals
Basic Character of Oxides & Hydroxides
Separation of Lanthanides (Ion-exchange)