IR spectroscopy — characteristic group frequencies (O-H, N-H, C=O, C≡N, C=C, etc.); fingerprint region

4.8.3 · Chemistry › Spectroscopy & Analysis (Intro)

IR KAAM KARTA KAISE HAI

Dipole rule kyun? Light ek oscillating electric field hai. Usase energy lene ke liye, molecule ko ek oscillating "handle" present karna padta hai — ek changing dipole. $O_{2}$ ka symmetric stretch zero dipole change deta hai, isliye $O_{2}$ IR mein invisible hai. $C = O$ jaisa polar bond ek bada dipole swing deta hai, isliye woh strongly absorb karta hai.

FREQUENCY PREDICT KARNA — ek spring se derive karo

Bond = harmonic oscillator. Do masses $m_{1}, m_{2}$ ek spring se jude hain jiska stiffness $k$ hai (the force constant, units N/m).

Step 1 — Newton + Hooke. Ek single mass ke liye spring par, $F = - k x$ aur $F = ma = m \overset{x}{¨}$ : $m \overset{x}{¨} = - k x \Rightarrow \overset{x}{¨} = - \frac{k}{m} x$ Yeh SHM hai jiska angular frequency $ω = k / m$ hai. Yeh step kyun? $\overset{x}{¨} = - ω^{2} x$ ka solution $x = A cos ω t$ hai — $ω$ par oscillation.

Step 2 — ek nahi, do atoms. Dono atoms move karte hain, isliye $m$ ki jagah reduced mass use karo: $μ = \frac{m _{1} m _{2}}{m _{1} + m _{2}}$ Kyun? Centre-of-mass frame mein relative coordinate ek single particle ki tarah behave karta hai jiska mass $μ$ hai spring par.

Step 3 — frequency. $ν = \frac{1}{2 π} \frac{k}{μ}$

Step 4 — chemists wavenumber use karte hain $\tilde{ν} = 1/ λ = ν / c$ (units cm⁻¹): $\tilde{ν} = \frac{1}{2 π c} \frac{k}{μ}$

Characteristic group frequencies (80/20 table)

Yeh yaad kar lo — yeh ~80% IR problems solve kar deta hai.

Group	$\tilde{ν}$ (cm⁻¹)	Shape / note	Kyun wahan hai
O–H (alcohol)	3200–3550	broad, rounded	H-bonding isse smear kar deti hai
O–H (carboxylic acid)	2500–3300	bahut broad	strong H-bonding
N–H	3300–3500	1–2 sharper spikes	NH₂ mein do dikhte hain
≡C–H	~3300	sharp	high $k$ region
=C–H / C–H	2850–3100	sharp	light H
C≡N	2200–2260	sharp, medium	triple-ish, stiff
C≡C	2100–2260	weak (low dipole)	symmetric ⇒ weak
C=O	1670–1750	strong, sharp	bada dipole → tall peak
C=C	1620–1680	weak–medium	small dipole
C–O	1000–1300	strong	fingerprint edge

Fingerprint region

Worked examples

Common mistakes

Flashcards

IR wavenumber set karne wale do molecular factors kaun se hain?

Force constant

k

(stiffness) aur reduced mass

μ

— via

\tilde{ν} = \frac{1}{2 π c} k / μ

IR selection rule kya hai?

Vibration molecule ka dipole moment change kare; dipole change nahi ⇒ IR-inactive.

Reduced mass define karo.

μ = \frac{m _{1} m _{2}}{m _{1} + m _{2}}

, spring par do atoms ke liye effective single mass.

C–H ~3000 cm⁻¹ ke paas kyun absorb karta hai?

H bahut light hai ⇒ small

μ

⇒ large

k / μ

C=O ka typical wavenumber aur yeh strong kyun hai?

~1700 cm⁻¹; strong hai kyunki polar carbonyl ek large dipole change deta hai.

Alcohol O–H aur carboxylic-acid O–H mein fark karo.

Alcohol: broad 3200–3550. Acid: bahut broad 2500–3300 + saath mein C=O ~1710.

C=C IR mein aksar weak kyun hota hai?

Stretching par small dipole change (often near-symmetric) ⇒ weak/absent peak.

Fingerprint region kya hai aur iska use kya hai?

~1500 cm⁻¹ se neeche; tangled skeletal/bending bands jinka unique pattern matching se molecular identity confirm karta hai.

O–H, C–H, C≡N, C=O, C=C ko decreasing wavenumber mein order karo.

O–H (3300) > C–H (3000) > C≡N (2250) > C=O (1700) > C=C (1650).

Bond order peak position set karta hai ya peak height?

Position (via

k

). Height dipole change (polarity) se set hoti hai.

C≡N vs C=N — kaun sa higher hai aur kyun?

C≡N higher; same

μ

par larger

k

⇒ higher

\tilde{ν}

Recall Feynman: ek 12-saal ke bacche ko samjhao

Socho ki molecule mein har bond ek choti si spring hai jo do balls ko pakde hue hai. Agar tum use dhakelo, woh apni special speed par aage-peeche bounce karta hai. Tighter springs aur halki balls fast bounce karti hain; loose springs aur bhaari balls slow bounce karti hain. Ab molecule par invisible "heat light" (infrared) daalo. Har spring sirf woh light pakadta hai jiska flicker uski apni bounce se match kare. Yeh dekh kar ki kaun si lights swallow ho gayi, hum figure out kar lete hain ki molecule mein kaun si springs (bonds) hain. Jo springs lop-sided hain (ek end zyada electrons kheenchta hai) woh sabse zyada light pakadti hain — isliye C=O spring ek badi dark line deti hai. Neeche wali tiny springs ki messy bheed itni unique hoti hai ki woh exact molecule ka naam batane ke liye fingerprint ki tarah kaam karti hai.

Connections

Molecular dipole moment — set karta hai kaun si vibrations IR-active hain aur kitni intense.
Simple harmonic oscillator — master equation ke peeche physics model.
Hydrogen bonding — O–H aur N–H bands ki broadening explain karta hai.
Bond order and bond strength — $k$ ko single/double/triple bonds se link karta hai.
Mass spectrometry & NMR spectroscopy — complementary structure-elucidation tools.
Electromagnetic spectrum — IR kahan hota hai (visible aur microwave ke beech).