Atomic radius — covalent, metallic, van der Waals; trends across period and group

2.2.2 · Chemistry › Periodic Trends

"Atomic radius" ko teen definitions ki zarurat kyun padti hai?

KIYA problem hai? Ek atom ek nucleus hai jo ek fuzzy electron cloud se ghira hota hai jiska density kabhi exactly zero nahi hota. Koi sharp boundary nahi hoti jis par ruler rakh sako.

HOW hum ise fix karte hain: do atoms ke beech internuclear distance $d$ measure karo aur har atom ko uska ek hissa do. Jo hissa tum dete ho woh depend karta hai contact ki nature par:

WHY alag-alag sizes hoti hain? Nuclei ke beech jitna strong pull hoga, woh utna paas aayenge, aur tumhe utna chhota radius milega:

$r_{co v} < r_{m e t} < r_{v d W}$

Covalent bond = shared electrons → strong attraction → nuclei paas khiinche jaate hain → chhota radius.
Metallic bond = har atom electrons bahut saare neighbours ke saath share karta hai (delocalised "sea"), isliye bond per neighbour thoda loose hota hai → thoda bada.
vdW = koi bond nahi, sirf weak induced-dipole attraction jo full electron clouds ke repulsion ka virodh karta hai → atoms door rehte hain → sabse bada radius.

Figure — Atomic radius — covalent, metallic, van der Waals; trends across period and group

PERIOD ke across trend (left → right): radius DECREASES

First principles se derivation. Atom ki size is baat se set hoti hai ki outermost electrons kitni tightly pakde hue hain. Yeh effective nuclear charge se govern hota hai:

$Z_{e f f} = Z - S$

jahan $Z$ = protons ki sankhya aur $S$ = inner electrons dwara shielding (screening).

Ek period ke across:

KIYA change hota hai: har step mein ek proton ( $Z ↑$ by 1) aur same shell mein ek electron add hota hai (same principal quantum number $n$ ).
WHY radius shrink hota hai: same shell mein electrons ek doosre ko poorly shield karte hain (woh nucleus se same distance par hote hain). Isliye $S$ thoda hi badhta hai jabki $Z$ ek puri unit se badhta hai.
HOW yeh hota hai: $Z_{e f f} = Z - S$ badhta hai → outer electrons stronger net pull feel karte hain → pura cloud contract hota hai → radius decrease hota hai.

GROUP ke neeche trend (top → bottom): radius INCREASES

KIYA change hota hai: har step neeche ek naya electron shell add hota hai → $n$ 1 se badhta hai.
WHY radius badhta hai: added shell aur bahar hoti hai, aur bhari hui inner shells outer electron ko achhi tarah shield karti hain, $Z_{e f f}$ ko roughly modest rakhti hain. $n$ mein jump dominate karta hai.
HOW yeh hota hai: $r \propto n^{2} / Z_{e f f}$ mein, $n$ har period mein ek puri unit badhta hai → $n^{2}$ jump karta hai → radius badhta hai halanki $Z$ bhi badhta hai.

Worked comparison: size predict karna

Flashcards

Covalent radius kya hota hai?

Do atoms ke beech internuclear distance ka aadha hissa jo ek single covalent bond se jude hain,

r_{co v} = d_{A - A} /2

Hum atomic radius directly kyun measure nahi kar sakte?

Electron cloud ki koi sharp boundary nahi hoti; density dheere-dheere zero tak fade hoti hai, isliye hum internuclear distance measure karte hain aur use split karte hain.

Ek element ke teen radii ka order kya hai?

r_{co v} < r_{m e t} < r_{v d W}

vdW radius sabse bada kyun hota hai?

Yeh non-bonded atoms ke beech measure kiya jaata hai jo sirf weak forces se hold hote hain, isliye nuclei door rehte hain (koi bond unhe andar nahi kheenchta).

Effective nuclear charge define karo.

Z_{e f f} = Z - S

, ek outer electron dwara feel ki jaane wali net positive charge, inner-electron shielding

S

ke baad.

Period ke across radius kyun decrease hota hai?

Z

har step mein 1 badhta hai lekin added electron same shell mein enter karta hai aur poorly shield karta hai, isliye

Z_{e f f}

badhta hai → outer electrons tighter kheenche jaate hain → chhota.

Group ke neeche radius kyun badhta hai?

Ek naya shell (n↑) add hota hai;

n^{2}

ki growth extra, well-shielded nuclear charge ko haraati hai → bada.

Noble gases kaun sa radius use karte hain, aur kyun?

van der Waals radius, kyunki woh bonds nahi banate; non-bonded neighbours tak measure kiya jaata hai.

Hydrogen-like model mein

r

kaise scale karta hai?

r \propto n^{2} / Z_{e f f}

Al, Mg, Na, K ko size ke hisaab se rank karo.

A l < M g < N a < K

Recall Feynman: ek 12-saal ke bachche ko explain karo

Imagine karo ki har atom ek fuzzy cotton ball hai jiska koi clear edge nahi hai, toh tum sirf ek ka measure nahi kar sakte. Iske badle tum do ko ek saath push karte ho aur unke centres ke beech ki distance measure karte ho, phir kehte ho ki har ek us ka aadha hai. Agar woh tightly glued hain (ek bond), toh woh paas squish hote hain → chhota radius. Agar woh sirf gently touch kar rahe hain (koi glue nahi), toh woh door rehte hain → bada radius. Table ki row ke across jaane par, centre (nucleus) mein zyada "grip" aa jaati hai aur fuzz ko tight kheench leti hai → atoms shrink hote hain. Column ke neeche jaane par, har atom ko fuzz ki ek brand-new outer layer milti hai → atoms bade hote jaate hain.

Connections

Effective Nuclear Charge — har radius trend ke peeche ka engine.
Shielding and Penetration — kyun inner electrons $Z$ ko screen karte hain.
Ionic Radius — cations shrink hote hain, anions atom ke relative swell hote hain.
Ionisation Energy — chhota radius ⇒ generally zyada IE.
Electronegativity — table ke across $Z_{e f f}$ aur radius ko track karta hai.
Metallic Bonding — metallic-radius geometry set karta hai.
Van der Waals Forces — woh weak forces jo vdW radius define karte hain.