UV-Vis spectroscopy — Beer-Lambert law, conjugation and λ_max

4.8.2 · Chemistry › Spectroscopy & Analysis (Intro)

1. Asal mein kya ho raha hai — electronic transitions

Photon energy orbital gap se match karni chahiye:

Common transition types (energy order, large gap → small λ):

Transition	Gap	Typical λ	Seen in
$σ \to σ^{*}$	bahut badi	<150 nm (vacuum UV)	C–C, C–H
$n \to σ^{*}$	badi	~150–250 nm	C–O, C–N (lone pairs)
$π \to π^{*}$	moderate	~180–700 nm	C=C, C=O, aromatics
$n \to π^{*}$	chhoti	~250–600 nm	C=O carbonyls

2. Conjugation aur λ_max — iska dil

Molecule	Conjugated C=C	λ_max (approx)
Ethene	1	~170 nm (UV)
Buta-1,3-diene	2	~217 nm
Hexa-1,3,5-triene	3	~258 nm
β-carotene	11	~450 nm (visible!)

Figure — UV-Vis spectroscopy — Beer-Lambert law, conjugation and λ_max

3. Beer-Lambert Law — kitna hai yeh measure karna

4. Common mistakes (Steel-manned)

5. Active recall

Recall Quick self-test (answers cover karo)

Organic molecules ki UV-Vis mein kaun sa transition dominate karta hai? → == $π \to π^{*}$ == (aur $n \to π^{*}$ )
Conjugation badhne par λ_max ka direction? → red-shift (λ_max increases)
Kyun? → bada "box" → chhota $Δ E$ → bada $λ = h c /Δ E$
Beer-Lambert batao. → $A = ε c l$
A aur T ka relation? → $A = - lo g_{10} T$

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

Socho molecules chhote stretchy springs of electrons hain. Light chhote energy ke packets hain. Ek molecule tabhi ek light packet ko "nigalta" hai jab uska size exactly woh jump fit kare jo electrons kar sakte hain. Zyada double bonds wali badi molecules ek lambi slide ki tarah hain — electrons ek chhota, aasaan jump kar sakte hain, toh woh low-energy (longer-wavelength, zyada colourful) light nigate hain. Isliye gajar blue light pakad sakta hai aur orange dikhta hai! Aur agar tumhein pata karna ho ki tumhare paani mein kitna dye hai, toh bas measure karo ki woh kitni light khaata hai: mota glass ya gehra dye zyada khaata hai, ek steady, predictable tarike se.

6. Flashcards

UV-Vis spectroscopy physically kya measure karta hai?

UV/visible photons ka absorption jo electrons ko molecular orbitals ke beech promote karta hai (HOMO→LUMO type transitions).

Beer-Lambert law likho aur har term define karo.

A = ε c l

;

A

=absorbance,

ε

=molar absorptivity (L mol⁻¹ cm⁻¹),

c

=concentration (mol L⁻¹),

l

=path length (cm).

Absorbance aur transmittance ka relation batao.

A = - lo g_{10} T = lo g_{10} (I_{0} / I)

Zyada conjugation λ_max kyun badhata hai?

Bada delocalisation "box" → energy levels closer → chhota ΔE → bada λ via

λ = h c /Δ E

(red shift).

Organic UV-Vis spectra mein kaun sa electronic transition dominate karta hai?

π \to π^{*}

(aur lower-energy

n \to π^{*}

carbonyls ke liye).

Chromophore vs auxochrome define karo.

Chromophore = woh group jo absorb karta hai (C=C, C=O, ring); auxochrome = lone-pair group (–OH, –NH₂) jo λ_max shift karta hai.

Bathochromic shift kya hai?

λ_max ka longer wavelength ki taraf shift (red shift), jaise added conjugation se.

Agar T = 0.10 hai, toh A kya hai?

A = - lo g_{10} (0.10) = 1.0

Ek solution red dikhta hai. Roughly yeh kya absorb karta hai?

Iska complement — green light (~500 nm).

Standard UV-Vis par

σ \to σ^{*}

rarely kyun dikhta hai?

Iska ΔE bahut bada hai → λ < 150 nm vacuum UV mein, normal instrument range se bahar.

Beer-Lambert kab fail karta hai?

High concentrations par (solute interactions, stray light, refractive effects) → curvature/underestimation.

Connections

Planck relation E = hν — energy ↔ wavelength ka foundation
Particle in a box — conjugated π-systems ka model
Conjugation and resonance — kyun delocalisation ΔE kum karta hai
HOMO and LUMO orbitals — transition mein involved levels
Complementary colours — kyun absorbed ≠ observed colour
IR spectroscopy — sister technique jo vibrations probe karti hai, electrons nahi
Quantitative analysis & calibration curves — A = εcl ko practice mein use karna