Electronic configuration of elements (Z = 1 to 30) — exceptions Cr, Cu

2.1.10 · Chemistry › Quantum Atomic Structure

1. Electronic configuration KYA hoti hai?

KYUN zaroori hai? Configuration ek element ki chemistry decide karti hai — valency, magnetism, color, reactivity. Periodic table ke saare patterns yahan se aate hain.

2. TEEN rules (filling order ko first principles se derive karo)

Rule 1 — Aufbau principle (KYA + KYUN)

KYUN energy order set karti hai? Ek system minimum energy par sabse stable hota hai. Lower-energy orbital mein electron zyada tightly bound hota hai → lower total energy → zyada stable atom. Nature yeh "apne aap" choose karta hai.

KAISE pata chalta hai kaunsa subshell lower hai? (n + l) rule (Madelung rule) use karo:

Chalo $(n + l)$ compute karke order derive karte hain:

Subshell	$n$	$l$	$n + l$
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

Increasing $(n + l)$ ke order mein padhne par, ties lower $n$ se todke: $1 s < 2 s < 2 p < 3 s < 3 p < 4 s < 3 d < 4 p$

Key surprise: $4 s (n + l = 4)$ $3 d (n + l = 5)$ se pehle fill hota hai. Yahi ek fact neeche Cr aur Cu ko explain karta hai.

Rule 2 — Pauli exclusion principle

Toh capacities hain: $s = 2$ , $p = 6$ , $d = 10$ .

Rule 3 — Hund's rule of maximum multiplicity

KYUN? Ek hi orbital mein do electrons bahut zyada repel karte hain (space ka same region). Unhe alag orbitals mein spread karna electron–electron repulsion ghataata hai (exchange energy stabilization). Parallel spins aur extra quantum-mechanical stability add karte hain (exchange).

Figure — Electronic configuration of elements (Z = 1 to 30) — exceptions Cr, Cu

3. Z = 1 se 30 banana (worked, har jump par KYUN ke saath)

Main noble-gas shorthand use karunga jab shells close ho jaayein.

Z	Element	Configuration
1	H	$1 s^{1}$
2	He	$1 s^{2}$
3	Li	$[He] 2 s^{1}$
4	Be	$[He] 2 s^{2}$
5	B	$[He] 2 s^{2} 2 p^{1}$
6	C	$[He] 2 s^{2} 2 p^{2}$
7	N	$[He] 2 s^{2} 2 p^{3}$
8	O	$[He] 2 s^{2} 2 p^{4}$
9	F	$[He] 2 s^{2} 2 p^{5}$
10	Ne	$[He] 2 s^{2} 2 p^{6}$
11	Na	$[Ne] 3 s^{1}$
12	Mg	$[Ne] 3 s^{2}$
13	Al	$[Ne] 3 s^{2} 3 p^{1}$
14	Si	$[Ne] 3 s^{2} 3 p^{2}$
15	P	$[Ne] 3 s^{2} 3 p^{3}$
16	S	$[Ne] 3 s^{2} 3 p^{4}$
17	Cl	$[Ne] 3 s^{2} 3 p^{5}$
18	Ar	$[Ne] 3 s^{2} 3 p^{6}$
19	K	$[Ar] 4 s^{1}$
20	Ca	$[Ar] 4 s^{2}$
21	Sc	$[Ar] 3 d^{1} 4 s^{2}$
22	Ti	$[Ar] 3 d^{2} 4 s^{2}$
23	V	$[Ar] 3 d^{3} 4 s^{2}$
24	Cr	$[Ar] 3 d^{5} 4 s^{1}$ ⚠️
25	Mn	$[Ar] 3 d^{5} 4 s^{2}$
26	Fe	$[Ar] 3 d^{6} 4 s^{2}$
27	Co	$[Ar] 3 d^{7} 4 s^{2}$
28	Ni	$[Ar] 3 d^{8} 4 s^{2}$
29	Cu	$[Ar] 3 d^{10} 4 s^{1}$ ⚠️
30	Zn	$[Ar] 3 d^{10} 4 s^{2}$

4. EXCEPTIONS: Cr aur Cu (note ka dil)

Naive prediction (sirf Aufbau blindly follow karne par):

Cr (24): $[Ar] 3 d^{4} 4 s^{2}$
Cu (29): $[Ar] 3 d^{9} 4 s^{2}$

Reality:

Cr (24): $[Ar] 3 d^{5} 4 s^{1}$
Cu (29): $[Ar] 3 d^{10} 4 s^{1}$

Exchange bonus kaise count hota hai (derivation)

Exchange energy $\propto$ ek subshell mein parallel-spin electrons ke pairs ki sankhya. Agar ek subshell mein $k$ parallel electrons hain, toh aise pairs ki sankhya hai: $(2 k) = \frac{k ( k - 1 )}{2}$

Chromium comparison:

Configuration A $3 d^{4}$ : 4 parallel $d$ -electrons → $(2 4) = 6$ exchange pairs (plus $4 s^{2}$ pair, lekin $4 s$ single orbital hai — koi parallel bonus nahi).
Configuration B $3 d^{5} 4 s^{1}$ : 5 parallel $d$ -electrons → $(2 5) = 10$ exchange pairs.

$A \to B$ jaane par $10 - 6 = 4$ extra exchange pairs milte hain — ek badi stabilization jo ek electron ko $4 s$ se thodi-si-higher $3 d$ mein move karne ki chhoti energy cost ko outweigh karti hai. Isliye Cr = $3 d^{5} 4 s^{1}$ .

Copper comparison: $3 d^{10}$ ek completely filled subshell hai — maximum symmetry, saare orbitals filled — dramatically stable. Isliye atom $3 d^{9} 4 s^{2}$ ke bajay $3 d^{10} 4 s^{1}$ prefer karta hai.

5. Configuration se extra info padhna

Flashcards

(n+l) rule aur uska tie-breaker batao.

Lower

(n + l)

pehle fill hota hai; agar equal ho toh lower

n

pehle fill hota hai.

4s, 3d se pehle kyun fill hota hai?

4s ka

(n + l) = 4

hai jo 3d ke

(n + l) = 5

se kam hai, isliye yeh lower energy par hai.

Cr (Z=24) ki configuration?

[Ar] 3 d^{5} 4 s^{1}

Cu (Z=29) ki configuration?

[Ar] 3 d^{10} 4 s^{1}

Cr ki naive (galat) config aur real one kyun prefer ki jaati hai?

Naive

3 d^{4} 4 s^{2}

; real

3 d^{5} 4 s^{1}

kyunki half-filled

d^{5}

extra symmetry + exchange stabilization deta hai.

k parallel electrons mein exchange pairs ki sankhya?

(2 k) = k (k - 1) /2

Cr ke liye

3 d^{4} \to 3 d^{5}

jaane par exchange-pair gain?

6 se 10 pairs → gain of 4.

Hund's rule aur uski physical reason batao.

Degenerate orbitals mein pehle parallel spins ke saath singly fill karo; electron repulsion ghatti hai aur exchange stabilization milti hai.

Orbital capacity ke liye Pauli ka consequence?

Ek orbital mein max 2 electrons opposite spins ke saath (s=2, p=6, d=10).

Fe (

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

) mein unpaired electrons?

4 unpaired.

Ions banate waqt Sc–Zn mein electrons pehle kahan se jaate hain?

4s electrons (highest n) pehle, 3d se pehle.

Mn (Z=25) ki config?

[Ar] 3 d^{5} 4 s^{2}

Zn (Z=30) ki config?

[Ar] 3 d^{10} 4 s^{2}

Aufbau exact law kyun nahi hai?

Z=24,29 ke paas 3d aur 4s energies almost equal ho jaati hain; total-energy minimization simple ordering ko override kar sakta hai.

Recall Feynman: ek 12-saal ke bachche ko samjhao

Socho electrons woh bachche hain jo theatre mein seats le rahe hain, sabse sasti seats pehle (yahi Aufbau hai). Har seat mein sirf 2 bachche aa sakte hain, aur unhe opposite direction mein face karna hota hai (Pauli). Agar equal-price seats ki poori row khaali ho, toh har bachcha apni seat leta hai pehle, koi double up nahi karta (Hund) — bachche sharing nahi karna chahte! Ab, bachche sabse khush hote hain jab ek poori special row ya exactly half-full ho ya completely full — yeh "neat aur balanced" lagta hai. Isliye Chromium aur Copper mein se har ek EK bachche ko thodi-si-sasti seat se special row mein move karta hai taaki woh perfectly half-full ( $3 d^{5}$ ) ya completely full ( $3 d^{10}$ ) ho jaaye. Isliye yeh normal seating pattern todte hain.

Connections

Aufbau principle — base filling order jo yeh note refine karta hai.
Pauli exclusion principle — orbital capacities set karta hai.
Hund's rule of maximum multiplicity — pairing aur unpaired-electron counts govern karta hai.
Quantum numbers (n, l, m, s) — orbitals aur $(n + l)$ energy trick define karte hain.
Shielding and penetration effect — $4 s$ < $3 d$ ke peeche deeper WHY.
Exchange energy and stability — Cr/Cu exceptions ka quantitative basis.
Magnetic properties of transition metals — unpaired-electron counts use karta hai.
Periodic trends — configurations s-, p-, d-block structure explain karti hain.