Photochemistry — Stark-Einstein law, quantum yield, Jablonski diagram, fluorescence vs phosphorescence

5.1.9 · Chemistry › Physical Chemistry (Advanced)

1. Stark–Einstein Law (Law of Photochemical Equivalence)

WHY does this law exist? Light absorption ek quantum event hai. Ek molecule "aadha photon" absorb nahi kar sakti; absorption matlab ek poore photon ka disappear hona aur ek molecule ka simultaneously excited state mein jump karna hai. Isliye primary event strictly 1:1 hai.

WHAT it does NOT say: Yeh yeh nahi kehta ki kitne product molecules banenge. Primary act ke baad, secondary (chemical) steps result ko multiply ya quench kar sakte hain — isliye quantum yields bahut badi ya bahut chhoti ho sakti hain (agla section).

2. Quantum Yield ( $Φ$ )

WHY define it? Stark–Einstein law primary step ko 1:1 fix karta hai, lekin real reactions mein secondary chemistry hoti hai. $Φ$ overall efficiency measure karta hai — ek absorbed photon aakhirkar kitni chemistry produce karta hai.

HOW to read the value:

$Φ$ value	Matlab	Cause
$Φ = 1$	ideal primary act, koi extra steps nahi	har excited molecule ek baar react karti hai
$Φ < 1$	inefficient	excited molecules react karne se pehle de-excite ho jaati hain (fluorescence, heat, collisional quenching)
$Φ ≫ 1$	chain reaction	ek photon ek chain shuru karta hai jo kaafi saari molecules consume karta hai

3. Jablonski Diagram — fates ka map

Figure — Photochemistry — Stark-Einstein law, quantum yield, Jablonski diagram, fluorescence vs phosphorescence

The processes (WHAT each arrow means):

Absorption ( $S_{0} \to S_{1}$ ): photon molecule ko upar kick karta hai. Femtoseconds.
Vibrational relaxation / Internal Conversion (IC): molecule heat ke roop mein (wavy) $S_{1}$ ke lowest vibrational level par drop karti hai. Fast.
Fluorescence ( $S_{1} \to S_{0}$ ): radiative emission, spin preserved (singlet→singlet). Allowed → fast ( $1 0^{- 9}$ – $1 0^{- 7}$ s).
Intersystem Crossing (ISC) ( $S_{1} \to T_{1}$ ): non-radiative, spin flips to triplet (wavy). Spin-forbidden lekin spin–orbit coupling ke through hota hai.
Phosphorescence ( $T_{1} \to S_{0}$ ): radiative, spin wapas flip hona chahiye (triplet→singlet). Spin-forbidden → slow ( $1 0^{- 3}$ s to minutes).

4. Fluorescence vs Phosphorescence

Property	Fluorescence	Phosphorescence
Transition	$S_{1} \to S_{0}$	$T_{1} \to S_{0}$
Spin change	koi nahi (allowed)	haan (forbidden)
Lifetime	$1 0^{- 9}$ – $1 0^{- 7}$ s	$1 0^{- 3}$ s – minutes
Afterglow	turant band	persist karta hai ("glow-in-dark")
Emitted photon ki energy	zyada	kam (kyunki $T_{1} < S_{1}$ )

5. Common Mistakes (Steel-manned)

6. Active Recall

Recall Fluorescence vs phosphorescence kya decide karta hai, aur woh lifetime kaise decide karta hai?

Whether a spin flip ki zaroorat hai ya nahi. Fluorescence ( $S_{1} \to S_{0}$ , no flip) spin-allowed hai → fast ( $1 0^{- 9}$ s). Phosphorescence ( $T_{1} \to S_{0}$ , flip needed) spin-forbidden hai → slow (ms–min, afterglow).

Recall Ek reaction ka

$Φ = 2 \times 1 0^{5}$ hai. Yeh mechanistically kya batata hai? Ek absorbed photon ~ $2 \times 1 0^{5}$ product molecules produce karta hai ⇒ ek chain reaction (e.g. radical chain). Primary act tab bhi 1 photon → 1 activated molecule hai (Stark–Einstein intact).

Recall Stokes shift ko ek saansh mein explain karo.

Vibrational relaxation/IC emit karne se pehle absorbed energy ka kuch hissa heat ke roop mein dump karta hai, toh emitted photons absorbed photons ki tulna mein lower energy (longer wavelength) ke hote hain.

Recall (Feynman, ek 12-saal ke bacche ko explain karo)

Socho ek ball jise tum ek staircase par upar throw karte ho. Light woh throw hai — iske paas ek step par land karne ke liye bilkul sahi push honi chahiye, kabhi half step nahi (yahi photon rule hai). Ek high step par pahunchne ke baad, ball: light ki quick flash dete hue seedhi wapas neeche aa sakti hai (fluorescence), ya ek secret slow ramp par slip ho sakti hai jahan woh bahut der tak dheere dheere neeche aati hai, softly glowing karti hai chahe aap throw karna band kar do (phosphorescence) — yahi glow-in-the-dark toy hai. Aur kabhi kabhi ek push dominoes ki row shuru kar deta hai (chain reaction), ek se bahut zyada balls knock down karta hai.

Flashcards

State the Stark–Einstein law of photochemical equivalence.

Primary photochemical act mein, har absorbing molecule exactly ek photon (quantum) of radiation absorb karti hai; ek photon → ek excited molecule.

What is an "einstein" and its energy?

Ek mole photons; energy

E = N_{A} h ν = N_{A} h c / λ

Energy per einstein at 400 nm (approx)?

~299 kJ/mol.

Define quantum yield

Φ

Φ

= (number of molecules reacting / events) ÷ (number of photons absorbed).

Why can

Φ ≫ 1

Ek chain (e.g. radical) reaction: ek photon ek chain initiate karta hai jo kaafi saari molecules consume karta hai; sirf primary act 1:1 hai.

Why can

Φ < 1

Competing de-excitation: fluorescence, internal conversion (heat), ya collisional quenching excitation ko reaction se pehle remove kar dete hain.

Φ

for H₂ + Cl₂ → HCl, and why?

1 0^{6}

; Cl• aur H• propagation se lamba radical chain.

What does a Jablonski diagram show?

Electronic/vibrational states (

S_{0}, S_{1}, T_{1}

) aur saare radiative (straight) aur non-radiative (wavy) transitions.

Difference between singlet and triplet state?

Singlet: paired (antiparallel) spins; triplet: parallel spins.

Define internal conversion (IC).

Same multiplicity wali states ke beech non-radiative transition (e.g.

S_{1} \to S_{0}

), energy heat ke roop mein khatam hoti hai.

Define intersystem crossing (ISC).

Spin-flipping non-radiative transition

S_{1} \to T_{1}

(singlet to triplet) spin–orbit coupling ke through.

Fluorescence: transition, spin, lifetime?

S_{1} \to S_{0}

, koi spin change nahi (allowed),

1 0^{- 9}

–

1 0^{- 7}

Phosphorescence: transition, spin, lifetime?

T_{1} \to S_{0}

, spin change required (forbidden),

1 0^{- 3}

s to minutes (afterglow).

Why does phosphorescence persist after light is removed?

T_{1} \to S_{0}

spin-forbidden hai, isliye de-excitation slow hoti hai, energy kaafi der tak slowly leak hoti hai.

State Kasha's rule.

Emission ek given multiplicity (

S_{1}

T_{1}

) ki lowest excited state se hoti hai, chahe koi bhi higher state excite kiya ho.

What causes the Stokes shift?

Vibrational relaxation/IC emission se pehle energy heat ke roop mein lose kar deta hai, isliye emitted light absorbed light ki tulna mein lower-energy (redder) hoti hai.

Why is phosphorescence light redder than fluorescence?

T_{1}

S_{1}

ke neeche hoti hai, isliye

T_{1} \to S_{0}

ek chhota energy gap (longer wavelength) emit karta hai.

Connections

Planck's Quantum Theory & E=hν
Electronic Spectra & Selection Rules (spin-allowed/forbidden)
Spin Multiplicity & Singlet–Triplet States
Chain Reactions & Radical Mechanisms
Beer–Lambert Law (photons absorbed)
Fluorescence Spectroscopy / LASERs
Thermal vs Photochemical Reactions