Colour and spectra — d-d transitions, charge transfer; selection rules

3.4.11 · Chemistry › Coordination Chemistry

1. Coordination compounds coloured KYUN hote hain?

Energy aur colour ko kya link karta hai? Photon ko yeh satisfy karna hoga: $Δ E = h ν = \frac{h c}{λ}$

Yeh exact equation KYUN? Energy quantised hoti hai. Sirf wahi photon jo exactly gap energy carry kare, electron ko promote kar sakta hai. Kam energy → koi jump nahi; zyada energy → koi jump nahi (isko ek actual level difference se match karna hoga).

Absorbed λ (nm)	Absorbed colour	Seen colour
400–450	violet	yellow-green
490–500	green	red/purple
580–600	yellow	blue
650–700	red	green

2. d–d transitions — sabse common colour source

Colour wavelength predict KAISE karein? Absorbed energy gap ke barabar hoti hai: $Δ_{o} = h ν_{abs} = \frac{h c}{λ _{abs}}$

Spectroscopists ise wavenumber $\overset{ν}{ˉ} = 1/ λ$ (cm⁻¹ mein) mein report karte hain kyunki $\overset{ν}{ˉ} \propto E$ directly hota hai: $Δ_{o} = h c \overset{ν}{ˉ}$

3. Charge Transfer (CT) bands — intense colours

Feature	d–d band	Charge-transfer band
Electron move karta hai	d-orbitals ke andar	metal ↔ ligand
$ε$ (intensity)	chhota (1–100)	bahut bada (10³–10⁴)
Selection rules	aksar forbidden	aksar allowed
Example	$[Cu (H_{2} O)_{6}]^{2 +}$ pale blue	$MnO_{4}^{-}$ deep purple

4. Selection rules — kuch transitions weak KYUN hoti hain

d–d bands forbidden hone ke bawajood dikhte KAISE hain?

Forbidden by	$ε$ par effect	Example
Sirf Laporte	$ε \sim 10$	$[Ti (H_{2} O)_{6}]^{3 +}$
Laporte + spin	$ε \sim 0.1$	$[Mn (H_{2} O)_{6}]^{2 +}$
Koi nahi (CT)	$ε \sim 1 0^{4}$	$MnO_{4}^{-}$
Bilkul bhi d-electron nahi	colourless	$[Zn (H_{2} O)_{6}]^{2 +}$ ( $d^{10}$ )

Figure — Colour and spectra — d-d transitions, charge transfer; selection rules

5. Steel-manned mistakes

6. Active recall

Recall Quick self-test (chhupao aur jawab do)

$[Sc (H_{2} O)_{6}]^{3 +}$ colourless kyun hai? → $d^{0}$ , excite karne ke liye koi electron nahi.
CT band d–d band se ~1000× stronger kyun hoti hai? → CT Laporte-allowed hai; d–d Laporte-forbidden hai.
Octahedral complexes mein Laporte rule ko kya relax karta hai? → asymmetric vibrations (vibronic coupling).
$Δ_{o} = 20000 cm^{- 1}$ kis wavelength par absorb karta hai? → $λ = 1/20000 cm = 500 nm$ .

Recall Feynman: 12-saal ke bachche ko explain karo

Socho metal atom ke electrons ek neeche wali shelf aur ek upar wali shelf par baithe hain. Light ka ek photon bilkul sahi value ke ek sikke jaisa hai — tabhi ek electron upar wali shelf par jaane ka ticket kharid sakta hai. Jis colour ki light woh "kharche" woh bahar aane wali light mein missing hoti hai, isliye hum bache hue colours dekhte hain. Agar dono shelves khali hain ya dono full hain, to koi jumping nahi hoti, aur cheez colourless lagti hai. Kabhi kabhi electron sharminda hota hai (jump "forbidden" hai), isliye woh sirf thoda sa tab jump karta hai jab atom wiggle kare — isse pale colours milte hain. Lekin jab ek electron ligand se metal par poori tarah se leap karta hai (charge transfer), to yeh ek bada bold jump hai → super bright colour, jaise purple potassium permanganate mein.

Connections

Crystal Field Theory — $Δ_{o}$ aur $t_{2 g} / e_{g}$ splitting ka origin
Spectrochemical Series — ligands $Δ_{o}$ aur isliye colour kaise tune karte hain
Magnetic Properties of Complexes — high/low spin ka spin selection rule se link
Beer–Lambert Law — $ε$ transition allowedness measure karta hai
Oxidation States of Transition Metals — high state ⇒ LMCT
Electronic Spectra & Term Symbols — multiplet transitions ( $d^{n}$ states)

Zyaadatar coordination compounds coloured KYUN hote hain?

Ek d-electron ek visible photon absorb karta hai aur

t_{2 g}

e_{g}

tak jump karta hai (gap

Δ_{o}

); hum absorbed colour ki complementary colour dekhte hain.

Absorbed energy aur wavelength ka relation?

Δ E = h c / λ = h c \overset{ν}{ˉ}

; bada gap ⇒ chhoti wavelength (bluer) absorb hoti hai.

d^{0}

aur

d^{10}

ions colourless KYUN hote hain?

d^{0}

mein excite karne ke liye koi electron nahi;

d^{10}

mein use receive karne ke liye koi empty d-level nahi ⇒ koi d–d transition nahi.

Laporte selection rule batao.

Centrosymmetric molecules mein transitions parity change karni chahiye (

g \leftrightarrow u

);

d \to d

hai

g \to g

⇒ forbidden.

Spin selection rule batao.

Δ S = 0

; unpaired electrons ki sankhya badalne wali transitions spin-forbidden hoti hain (bahut weak).

d–d bands Laporte-forbidden hone ke bawajood kaise dikhte hain?

Asymmetric molecular vibrations momentarily centre of symmetry todo karti hain (vibronic coupling), unhe weakly allowed banati hain.

LMCT vs MLCT kya hai?

LMCT: ligand→metal electron jump (high oxidation-state metal); MLCT: metal→ligand

π^{*}

jump (π-acceptor ligands).

MnO_{4}^{-}

d^{0}

hone ke bawajood intensely purple KYUN hai?

Colour ek Laporte-allowed LMCT (O lone pair → Mn) se hai, jisse huge

ε

(~10³–10⁴) milta hai.

[Mn (H_{2} O)_{6}]^{2 +}

sirf pale pink KYUN hai?

High-spin

d^{5}

: har d–d transition Laporte- aur spin-forbidden dono hai ⇒

ε \sim 0.01

Typical molar absorptivity: d–d vs charge transfer?

d–d: 1–100; charge transfer: 10³–10⁴ (kyunki CT fully allowed hai).

Agar

Δ_{o} = 20000 cm^{- 1}

ho, to kaunsi wavelength absorb hoti hai?

λ = 1/ (20000 cm^{- 1}) = 5 \times 1 0^{- 5} cm = 500 nm

Kya "forbidden" matlab

ε = 0

hai?

Nahi — symmetry-breaking aur spin-orbit coupling rules relax karte hain; forbidden matlab weak hai, zero nahi.