Effective nuclear charge Z_eff — Slater's rules

2.2.1 · Chemistry › Periodic Trends

$Z_{e f f}$ HAI KYA?

YEH EXIST KYO KARTA HAI? Har electron ek saath do cheezein feel karta hai:

Attraction $+ Z$ nucleus ki taraf.
Repulsion har doosre electron se.

Doosre electrons, khaas taur par jo nucleus ke zyada kareeb hain, effectively kuch nuclear charge "block" kar dete hain. Isliye electron aisa behave karta hai jaise nucleus ka charge $Z_{e f f} < Z$ ho.

SLATER'S RULES KI ZAROORAT KYO HAI

Real atoms many-electron systems hote hain — inhe exactly solve nahi kar sakte. Slater's rules ek simple recipe hai jo sirf electron configuration use karke $S$ (aur isliye $Z_{e f f}$ ) ko estimate karti hai. Ye empirical hain (real data se fit ki gayi hain), Schrödinger's equation se derive nahi hui hain, lekin physics ko capture karti hain: inner electrons same-shell electrons se zyada screen karte hain, aur $s, p$ vs $d, f$ alag tarah se screen karte hain.

SLATER'S RULES KAISE APPLY KAREIN (recipe)

Step 1 — Configuration ko Slater groups mein likho (special grouping note karo): $(1 s) (2 s, 2 p) (3 s, 3 p) (3 d) (4 s, 4 p) (4 d) (4 f) (5 s, 5 p) \dots$ Key points: $s$ aur $p$ same $n$ ke saath jaate hain; $d$ aur $f$ alag groups hain.

Step 2 — Interest ka electron chuno. $S$ mein contributions add karo:

YE NUMBERS KYO?

$0.35$ : same-shell electrons roughly same distance par hote hain, isliye ye poorly screen karte hain (ye truly "aapke aur nucleus ke beech" nahi hain).
$0.85$ : $n - 1$ shell aapke andar hai lekin perfectly nahi, isliye ye strongly screen karta hai par poora nahi.
$1.00$ : $\leq n - 2$ wale shells itne deep hain ki har ek charge ka almost ek poora unit screen karta hai.
$d, f$ electrons apne left ki har cheez se full screening ( $1.00$ ) feel karte hain kyunki woh orbitals zyada penetrating hain / $d, f$ electron baahir ki taraf zyada hota hai.

Figure — Effective nuclear charge Z_eff — Slater's rules

Worked examples

Common mistake Classic errors ko steel-man karna

Mistake A: "Har inner electron poora 1.0 screen karta hai." Kyon sahi lagta hai: Inner electrons aapke aur nucleus ke "beech" hain, toh kya inhe ek poora proton cancel nahi karna chahiye? Fix: sirf $\leq n - 2$ wale shells (1.00) karte hain. $n - 1$ shell aapke apne region se partially overlap karta hai → sirf $0.85$ ; same-shell electrons aapke paas hain → sirf $0.35$ .

Mistake B: "Electron ko apne hi group mein count karo." Kyon sahi lagta hai: woh us group mein hai. Fix: $S$ doosre electrons se shielding measure karta hai; electron khud ko kabhi shield nahi karta. Same group ke liye hamesha (group population $- 1$ ) use karo.

Mistake C: " $3 d$ electron ke liye, $3 s, 3 p$ $0.85$ par screen karte hain (same $n$ )." Kyon sahi lagta hai: ye $n = 3$ share karte hain. Fix: $d$ / $f$ electron ke liye, uske left ki saari cheez (same- $n$ $s, p$ bhi shamil) 1.00 par screen karti hai, 0.85 nahi. Special $0.85$ / $0.35$ split sirf $s, p$ target rules ke liye hai.

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

Socho nucleus ek warm campfire hai ( $+$ charge) aur electrons uske paas baithna chahte hain. Jo bachche fire ke bilkul paas baithe hain (inner electrons) woh peeche khade bachche ke liye garmahat block kar dete hain. Woh door wala bachcha kamzor fire feel karta hai jaisi woh actually hai. $Z_{e f f}$ hai "jahaan tum baithe ho wahaan se fire kitni warm lagti hai." Tumhare paas wale bachche (same shell) zyada block nahi karte; fire ke paas wale bachche (inner shells) bahut zyada block karte hain. Slater's rules bas ek scorecard hai ki har blocker kitni garmahat chura leta hai.

Trend consequences (80/20 payoff)

Flashcards

Effective nuclear charge

Z_{e f f}

define karo

Woh net positive charge jo ek electron feel karta hai,

Z_{e f f} = Z - S

, doosre electrons ki shielding

S

subtract karne ke baad.

Slater's rules mein, SAME group ka ek electron

S

mein kya contribute karta hai?

Har ek

0.35

(lekin

0.30

agar group

1 s

hai); electron khud ko kabhi shield nahi karta.

n s / n p

target ke liye

(n - 1)

shell ka ek electron kya contribute karta hai?

Har ek

0.85

\leq n - 2

wale shells ke electrons kya contribute karte hain?

Har ek

1.00

n d

n f

target ke liye, saare LEFT wale groups kitna contribute karte hain?

Har ek

1.00

(full screening), same

n

hone se farq nahi padta.

Slater's rules mein

s, p, d, f

kaise group kiye jaate hain?

(1 s) (2 s, 2 p) (3 s, 3 p) (3 d) (4 s, 4 p) (4 d) (4 f) \dots

— same

n

s

aur

p

saath;

d

aur

f

har ek alag.

Na ke

3 s

valence electron ke liye

Z_{e f f}

kya hai?

11 - 8.80 = 2.20

(S = 8×0.85 + 2×1.00).

Transition-metal ions mein

3 d

se pehle

4 s

kyon remove hota hai?

Ek baar fill hone ke baad,

3 d

Z_{e f f}

zyada hota hai (nucleus zyada feel karta hai)

4 s

se, isliye

4 s

zyada loosely held hai aur pehle nikalta hai.

Ek period mein left-to-right

Z_{e f f}

kyon badhta hai?

Z

1 se badhta hai lekin same-shell shielding sirf ~0.35 badhti hai, isliye net

Z_{e f f}

har step mein ~0.65 badhta hai.

Connections

Atomic Radius — zyada $Z_{e f f}$ electrons ko andar kheenchti hai → chhota radius.
Ionization Energy — zyada $Z_{e f f}$ → electron nikaalna mushkil.
Electronegativity — zyada $Z_{e f f}$ → bonding electrons par zyada pull.
Shielding and Penetration — $0.35/0.85/1.00$ numbers ki physical basis.
Aufbau and 4s vs 3d filling — Slater $Z_{e f f}$ removal order explain karta hai.
Periodic Trends — parent chapter.