How unit 6 is examined
Covers spectroscopy basics with the Beer-Lambert law, UV-visible (electronic) spectroscopy, and IR and microwave spectroscopy of diatomic molecules; all three topics carry high marks (7 to 14 each).
Principle, Instrumentation & Applications
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Definition. <mark>Spectroscopy is the study of the interaction of electromagnetic radiation with matter, in which the matter absorbs or emits radiation of particular frequencies and moves between quantised energy levels.</mark>
Key points.
- A molecule absorbs a photon only when its energy matches the gap between two levels, so $\Delta E = h\nu = hc/\lambda$.
- The absorbed region decides the type: microwave gives rotational, infrared gives vibrational, and UV-visible gives electronic transitions.
- Every spectrometer has the same parts: a source, a wavelength selector (monochromator), a sample cell, a detector and a recorder.
- Lambert's law: the fraction of light absorbed by a medium is independent of the incident intensity, so absorbance is directly proportional to the path length $l$.
- Beer's law: for a dilute solution, absorbance is directly proportional to the concentration $c$ of the absorbing solute.
- Combining the two laws gives the Beer-Lambert law, $A$ is proportional to $cl$.
- Limitations: it holds only for dilute solutions (below about 0.01 M), monochromatic light and a non-associating, non-dissociating, non-fluorescent solute.
- Uses of the law: finding unknown concentration from a calibration line, and studying reaction rates.
Formula. $$A=\log_{10}\frac{I_0}{I}=\epsilon\,c\,l,\qquad T=\frac{I}{I_0},\qquad A=-\log_{10}T$$ Here $A$ is absorbance (no unit), $\epsilon$ is the molar absorptivity (L mol$^{-1}$ cm$^{-1}$), $c$ is the concentration (mol L$^{-1}$) and $l$ is the path length (cm).
Derivation. Let a thin layer $dx$ absorb a fraction of the intensity: $-dI/I = k'c\,dx$. Integrating from $x=0$ ($I=I_0$) to $x=l$ ($I$) gives $\ln(I_0/I)=k'cl$. Converting to base 10 gives $\log_{10}(I_0/I)=\epsilon cl$, which is $A=\epsilon cl$.
UV and IR together for an unknown compound.
| Step | UV spectroscopy | IR spectroscopy |
|---|---|---|
| Tells | Conjugation, chromophores, auxochromes | Functional groups |
| Transition | $\pi\to\pi^*$, $n\to\pi^*$ | Bond stretching and bending |
| Data | $\lambda_{\max}$ and $\epsilon_{\max}$ | Bands in cm$^{-1}$ |
Example. A compound of formula C$_3$H$_6$O shows a strong IR band at about 1715 cm$^{-1}$ (C=O) and no band near 3300 cm$^{-1}$ (no O-H), so it is acetone. Its UV spectrum shows only a weak $n\to\pi^*$ band near 270 nm, so there is no conjugation. Allyl alcohol instead shows a broad O-H band near 3300 cm$^{-1}$ and no 1715 cm$^{-1}$ band. An $\alpha,\beta$-unsaturated ketone shows C=O nearer 1680 cm$^{-1}$ and a UV $\pi\to\pi^*$ band above 220 nm, showing conjugation.
Answer frame. For Beer-Lambert: open with the definition of spectroscopy in one line; state Lambert's law, then Beer's law; write the combined law with the meaning of each symbol; give the short derivation; close with the limitations. For UV plus IR: state what each technique reveals, use the table, then work the acetone versus allyl alcohol example and end with one line that IR fixes the groups and UV fixes the conjugation.
Pitfall: Absorbance has no unit; do not confuse it with percentage absorbed, and write $\epsilon$ with its unit.
Asked: [7 marks] (Nov 2022, Jun 2023, Dec 2023) Explain about Lambert and Beer's law; state and explain the Beer-Lambert law. Asked: [7 marks] (Jun 2025) How can a combination of UV and IR spectroscopy be used to determine the structure of an unknown organic compound? Illustrate with an example.
Electronic spectroscopy (UV-visible)
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Definition. <mark>Electronic spectroscopy is the absorption of UV-visible radiation (200-800 nm) by a molecule, which raises its electrons from a ground-state orbital to a higher-energy orbital.</mark>
Key points.
- Four transitions occur, in order of decreasing energy: $\sigma\to\sigma^*$ (alkanes, below 150 nm), $n\to\sigma^*$ (alcohols, amines, halides, 150-250 nm), $\pi\to\pi^*$ (alkenes, aromatics, 170-250 nm, strong) and $n\to\pi^*$ (C=O, N=O, above 270 nm, weak).
- Conjugation lowers the $\pi\to\pi^*$ gap, so $\lambda_{\max}$ moves to longer wavelength.
- A chromophore is a covalently unsaturated group responsible for absorption, such as C=C, C=O or NO$_2$.
- An auxochrome is a saturated group with lone pairs (-OH, -NH$_2$) that, attached to a chromophore, shifts and intensifies absorption.
- Bathochromic (red) shift is a shift of $\lambda_{\max}$ to longer wavelength; hypsochromic (blue) shift is a shift to shorter wavelength.
- Hyperchromic shift is an increase in $\epsilon_{\max}$ (intensity); hypochromic shift is a decrease.
- Applications: detecting chromophores and conjugation, distinguishing isomers, quantitative analysis by Beer-Lambert law, and checking purity.
Diagram.
Energy: sigma* (highest)
pi*
n
pi
sigma (lowest)
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Instrumentation. The source gives UV (deuterium) or visible (tungsten) light; the monochromator selects one wavelength; a beam splitter sends it through the reference and sample cells (quartz for UV); the detector compares the two beams and the recorder plots absorbance against wavelength.
Example. Given $A_1$ from 40% absorbed, $l=2$ cm, $c_1=20$ g L$^{-1}$, $c_2=40$ g L$^{-1}$; find % absorbed at $c_2$ (wavelength printed as 43.5 nm in the paper).
| Step | Working |
|---|---|
| $T_1$ | $1-0.40=0.60$ |
| $A_1$ | $-\log_{10}0.60=0.2218$ |
| $A_2$ | $A\propto c$, so $A_2=A_1\times 40/20=0.4437$ |
| $T_2$ | $10^{-0.4437}=0.36$ |
Percentage absorbed $=(1-0.36)\times100=$ 64%.
Answer frame. Open with the definition of spectroscopy and electronic spectroscopy; draw the energy-level diagram and name the four transitions with examples; then the block diagram with the function of each part; then the applications; close with the shift definitions. For the numerical, define the term in one line, then use the table above and end with the bold answer.
Pitfall: Do not put the light absorbed directly into $A=\epsilon cl$; convert to transmittance first, then take the log.
Asked: [14 marks] (Jun 2022, Dec 2024) What is electronic spectroscopy? Discuss electronic transitions and applications of UV spectroscopy; discuss UV spectroscopy principle, instrumentation and applications. Asked: [7 marks] (Dec 2023) Define bathochromic shift, hypsochromic shift, hyperchromic shift and chromophore. Asked: [7 marks] (Jun 2025) What is electronic spectroscopy? A substance absorbs 40% of light in a 2 cm cell at 20 g L$^{-1}$; find the percentage absorbed at 40 g L$^{-1}$.
Vibrational & Rotational Spectroscopy of diatomic molecules
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Definition. <mark>Rotational (microwave) spectroscopy studies transitions between rotational levels of a molecule, and vibrational (infrared) spectroscopy studies transitions between its vibrational levels; both need a change in dipole moment.</mark>
Key points.
- Rotational principle: in the microwave region a molecule with a permanent dipole moment (HCl, CO) absorbs and rotates faster, while homonuclear molecules (H$_2$, N$_2$) are inactive.
- Rotational energy is $E_J=BJ(J+1)$ with $B=h/(8\pi^2Ic)$, moment of inertia $I=\mu r^2$ and reduced mass $\mu=m_1m_2/(m_1+m_2)$.
- The selection rule is $\Delta J=\pm1$, so the lines are equally spaced by $2B$; measuring $B$ gives the moment of inertia and the bond length $r$.
- Vibrational principle: in the infrared region a bond absorbs only if its dipole moment changes during vibration, so HCl and CO are active and H$_2$ and N$_2$ are not.
- Treated as a harmonic oscillator, $E_v=(v+\tfrac12)h\nu$ with $\nu=\frac{1}{2\pi}\sqrt{k/\mu}$, and the selection rule is $\Delta v=\pm1$.
- A diatomic molecule has only one fundamental mode, the stretch; a stronger bond (larger $k$) absorbs at higher wavenumber, so C=O appears near 1715 cm$^{-1}$.
- Applications: bond length and force constant, identifying functional groups, and checking purity.
Diagram. <figure class="ds-fig" style="margin:1.4rem 0;overflow-x:auto"><svg xmlns="http://www.w3.org/2000/svg" id="dsfig-u6-02" viewBox="0 0 596 80" width="596" height="80" role="img" aria-label="IR or microwave spectrometer. S source (Nernst glower or globar for IR, klystron for microwave), M monochromator (grating), C sample cell (NaCl windows), D detector with amplifier (thermocouple), R recorder. An IR instrument splits the source into sample and reference beams"><style>#dsfig-u6-02 .e{stroke:#454C5A;stroke-width:1.4;fill:none}#dsfig-u6-02 .e.hi{stroke:#2340B8;stroke-width:2.6}#dsfig-u6-02 .n{fill:#FFFFFF;stroke:#16181D;stroke-width:1.4}#dsfig-u6-02 .n.hi{fill:#E3E9FC;stroke:#2340B8;stroke-width:2.2}#dsfig-u6-02 .n.rb-b{fill:#16181D;stroke:#16181D}#dsfig-u6-02 .n.rb-r{fill:#BD3227;stroke:#BD3227}#dsfig-u6-02 text{font-family:"JetBrains Mono",ui-monospace,Menlo,Consolas,monospace;font-size:13px}#dsfig-u6-02 .t{fill:#16181D;font-weight:500}#dsfig-u6-02 .t.inv{fill:#FFFFFF;font-weight:700}#dsfig-u6-02 .kd{stroke:#16181D;stroke-width:1.2}#dsfig-u6-02 .dot{fill:#16181D}#dsfig-u6-02 .ann{fill:#2340B8;font-size:11px;font-weight:700}#dsfig-u6-02 .lbl{fill:#6F7787;font-family:system-ui,-apple-system,sans-serif;font-size:12px;font-weight:700}#dsfig-u6-02 .ptr{fill:#2340B8;font-size:12px;font-weight:700}#dsfig-u6-02 .ah{fill:#454C5A}#dsfig-u6-02 .ah.hi{fill:#2340B8}#dsfig-u6-02 .wl rect{fill:#FFFFFF;stroke:#DCE0E7}#dsfig-u6-02 .wl .t{font-size:12px;font-weight:700}#dsfig-u6-02 .wl.hi rect{fill:#2340B8;stroke:#2340B8}#dsfig-u6-02 .wl.hi .t{fill:#FFFFFF}html.dark #dsfig-u6-02 .e{stroke:#B1B7C3}html.dark #dsfig-u6-02 .e.hi{stroke:#8FA3FF}html.dark #dsfig-u6-02 .n{fill:#161920;stroke:#E6E8ED}html.dark #dsfig-u6-02 .n.hi{fill:#1E2748;stroke:#8FA3FF}html.dark #dsfig-u6-02 .n.rb-b{fill:#E6E8ED;stroke:#E6E8ED}html.dark #dsfig-u6-02 .n.rb-r{fill:#FF7E71;stroke:#FF7E71}html.dark #dsfig-u6-02 .t{fill:#E6E8ED}html.dark #dsfig-u6-02 .t.inv{fill:#0F1115}html.dark #dsfig-u6-02 .kd{stroke:#E6E8ED}html.dark #dsfig-u6-02 .dot{fill:#E6E8ED}html.dark #dsfig-u6-02 .ann{fill:#8FA3FF}html.dark #dsfig-u6-02 .lbl{fill:#858D9C}html.dark #dsfig-u6-02 .ptr{fill:#8FA3FF}html.dark #dsfig-u6-02 .ah{fill:#B1B7C3}html.dark #dsfig-u6-02 .ah.hi{fill:#8FA3FF}html.dark #dsfig-u6-02 .wl rect{fill:#161920;stroke:#2A2E37}html.dark #dsfig-u6-02 .wl.hi rect{fill:#8FA3FF;stroke:#8FA3FF}html.dark #dsfig-u6-02 .wl.hi .t{fill:#0F1115}</style><defs><marker id="ah10" viewBox="0 0 10 10" refX="9" refY="5" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path class="ah" d="M0,1 L9,5 L0,9 z"/></marker><marker id="ahh10" viewBox="0 0 10 10" refX="9" refY="5" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path class="ah hi" d="M0,1 L9,5 L0,9 z"/></marker></defs><path class="e" d="M59,40 L148,40" marker-end="url(#ah10)"/><path class="e" d="M188,40 L277,40" marker-end="url(#ah10)"/><path class="e" d="M317,40 L406,40" marker-end="url(#ah10)"/><path class="e" d="M446,40 L535,40" marker-end="url(#ah10)"/><circle class="n" cx="40" cy="40" r="18"/><text class="t" x="40" y="40" dy=".35em" text-anchor="middle">S</text><circle class="n" cx="169" cy="40" r="18"/><text class="t" x="169" y="40" dy=".35em" text-anchor="middle">M</text><circle class="n" cx="298" cy="40" r="18"/><text class="t" x="298" y="40" dy=".35em" text-anchor="middle">C</text><circle class="n" cx="427" cy="40" r="18"/><text class="t" x="427" y="40" dy=".35em" text-anchor="middle">D</text><circle class="n" cx="556" cy="40" r="18"/><text class="t" x="556" y="40" dy=".35em" text-anchor="middle">R</text></svg><figcaption style="font-size:.82em;opacity:.72;margin-top:.45rem">IR or microwave spectrometer. S source (Nernst glower or globar for IR, klystron for microwave), M monochromator (grating), C sample cell (NaCl windows), D detector with amplifier (thermocouple), R recorder. An IR instrument splits the source into sample and reference beams</figcaption></figure>
Instrumentation. The source gives a continuous band; the monochromator picks each frequency; the sample cell holds the gas or liquid; the detector converts intensity to a signal, which is amplified and recorded against wavenumber.
Answer frame. Open with the definition of spectroscopy; draw the block diagram; then develop the rotational principle, energy and selection rule; then the vibrational principle, energy and selection rule; then the instrument parts in order; close with applications (bond length, functional groups).
Pitfall: Homonuclear diatomic molecules show no rotational or IR spectrum because they have no dipole moment change.
Asked: [14 marks] (Nov 2022, Jun 2023) What is spectroscopy? Describe the principle and instrumentation of vibrational and rotational spectroscopy; discuss principle, instrumentation and applications.
Last-minute revision
- Spectroscopy: interaction of electromagnetic radiation with matter, $\Delta E=h\nu$.
- Beer-Lambert law: $A=\log(I_0/I)=\epsilon cl$, and $A=-\log T$.
- The law fails for concentrated solutions and non-monochromatic light.
- UV transitions, high to low energy: $\sigma\to\sigma^*$, $n\to\sigma^*$, $\pi\to\pi^*$, $n\to\pi^*$.
- Red shift is longer $\lambda_{\max}$; blue shift is shorter; hyperchromic means higher $\epsilon$.
- 40% absorbed at 20 g/L gives 64% absorbed at 40 g/L ($T=0.36$).
- Rotational: microwave, $\Delta J=\pm1$, $E_J=BJ(J+1)$, gives bond length.
- Vibrational: IR, $\Delta v=\pm1$, $\nu=\frac{1}{2\pi}\sqrt{k/\mu}$.
- Both need a dipole moment change; H$_2$ and N$_2$ are inactive.
- IR: C=O near 1715 cm$^{-1}$, O-H near 3300 cm$^{-1}$; UV shows conjugation.
Memory hooks
- Red = Bathochromic = longer wavelength; Hypso means lower, so blue and shorter.
- Transition order by energy: "S N P N" for $\sigma\sigma^*$, $n\sigma^*$, $\pi\pi^*$, $n\pi^*$.
- Microwave rotates, infrared vibrates, UV excites electrons.
- Absorbed % to $T$ to $A$ to scale by concentration to $T$ to absorbed %.
Coverage checklist
- Principle, Instrumentation & Applications: Lambert and Beer's law (Nov 2022, Jun 2023, Dec 2023); UV plus IR structure determination (Jun 2025).
- electronics spectroscopy: UV transitions, instrumentation and applications (Jun 2022, Dec 2024); shift and chromophore definitions (Dec 2023); absorbance numerical (Jun 2025).
- Vibrational & Rotational Spectroscopy of diatomic molecules: principle and instrumentation (Nov 2022, Jun 2023).