Aufbau principle — order of filling (Madelung rule, n + l)

2.1.7 · Chemistry › Quantum Atomic Structure

Filling ke liye rule ki zaroorat kyun hai?

Sirf $n$ ke hisaab se kyun nahin bharte (1s, 2s, 2p, 3s, 3p, 3d, 4s...)? Kyunki multi-electron atoms mein orbital energies sirf $n$ se set nahin hoti. Electrons ek doosre ko shield karte hain, aur koi electron nucleus ki taraf kitna penetrate karta hai yeh uski shape ( $l$ ) par depend karta hai. Ek 4s electron nucleus ke paas ghusta hai, zyada positive charge feel karta hai, isliye woh 3d se zyada neeche — yaani kam energy par — baith sakta hai. Sirf- $n$ wali ordering yahan fail ho jaati hai — hume kuch aisa chahiye jo $n$ aur $l$ dono capture kare.

Madelung ( $n + l$ ) rule — ek ranking ki tarah samjho

Scratch se order kaise banayein (snake diagram yaad karne ki zaroorat nahin):

Orbital	$n$	$l$	$K = n + l$
1s	1	0	1
2s	2	0	2
2p	2	1	3
3s	3	0	3
3p	3	1	4
4s	4	0	4
3d	3	2	5
4p	4	1	5
5s	5	0	5
4d	4	2	6
5p	5	1	6
6s	6	0	6

Increasing $K$ ke saath neeche padho; equal $K$ mein increasing $n$ ke saath:

$1 s < 2 s < 2 p < 3 s < 3 p < 4 s < 3 d < 4 p < 5 s < 4 d < 5 p < 6 s < 4 f < 5 d < 6 p < 7 s < 5 f < 6 d$

Figure — Aufbau principle — order of filling (Madelung rule, n + l)

Worked examples

Common mistakes (Steel-man + fix)

Flashcards

Madelung rule mein orbital filling kis quantity se rank hoti hai?

Sum

n + l

se; chhota pehle bharta hai.

Jab do orbitals ka

n + l

equal ho toh tie-breaker kya hai?

Jis orbital ka

n

chhota ho woh pehle bharta hai.

4s aur 3d ka

n + l

compute karo aur batao kaun pehle bharta hai.

4s: 4+0=4; 3d: 3+2=5; 4s pehle bharta hai.

4s, 3d se pehle kyun bharta hai jab

n

zyada hai?

Kyunki

n + l

(energy) matter karta hai, sirf

n

nahin; 4s zyada penetrate karta hai aur energy mein neeche baith ta hai.

4p tak filling order string do.

1s 2s 2p 3s 3p 4s 3d 4p.

Fe (Z=26) ki ground-state configuration?

1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{6} 4 s^{2}

Ionization par pehle kaun sa orbital electrons khota hai, 4s ya 3d?

4s (sabse zyada

n

wala pehle jaata hai).

[A r] 3 d^{5} 4 s^{1}

kyun hai?

Half-filled 3d subshell extra stable hoti hai, jo plain Aufbau ko override karta hai.

s, p, d, f ke liye

l

values kya hain?

0, 1, 2, 3.

Quantum number

l

wale subshell mein maximum electrons kitne?

2 (2 l + 1)

Recall Feynman: 12 saal ke bacche ko samjhao

Socho ek stadium hai jahan sabse saste seats pehle bharte hain. Har seat ka price tag hota hai jo $n + l$ ke barabar hai. Bacche (electrons) hamesha sabse sasta khaali seat pakad lete hain. Agar do seats ki price same ho, toh woh field ke paas wali seat choose karte hain (chhota $n$ ). Isliye "4s seat" (price 4) "3d seat" (price 5) se pehle le li jaati hai, chahe 3d ki row number chhoti ho. Simple: sabse sasta pehle, tie mein woh seat jo action ke zyada paas ho.

Connections

Quantum Numbers (n, l, m, s) — yahan $l$ azimuthal quantum number hai.
Penetration and Shielding — physical reason ki Madelung kyun kaam karta hai.
Pauli Exclusion Principle — subshell capacity $2 (2 l + 1)$ set karta hai.
Hund's Rule — electrons kisi chosen subshell ke andar kaise arrange hote hain.
Electron Configuration Exceptions (Cr, Cu) — jahan Aufbau bend karta hai.
Ionization and Electron Removal Order — kyun 4s pehle jaata hai.
Periodic Table Blocks (s, p, d, f) — Aufbau order literally table banata hai.