Electronic Transitions and UV-Visible Absorption

Introduction

Infrared radiation makes bonds vibrate, but it does not carry enough energy to disturb the electrons that hold a molecule together. Move to shorter wavelengths, into the ultraviolet and visible regions (roughly 200–800 nm), and each photon carries enough energy to lift an electron from one molecular orbital into another. This process, an electronic transition , is the basis of UV-visible spectroscopy. It explains why some compounds are colourless, why others are brightly coloured, and why sunscreens can absorb harmful ultraviolet light.

Core explanation

Molecular orbitals and electron configuration. When atoms bond, their atomic orbitals combine to form molecular orbitals. Bonding orbitals (σ and π) are lower in energy than the original atomic orbitals, antibonding orbitals (σ and π ) are higher, and lone pairs occupy non-bonding orbitals (n) at roughly their original energy. In the ground state, electrons fill the lowest-energy orbitals first, two per orbital.

HOMO and LUMO. The most important pair of orbitals is the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) . The smallest energy needed to excite the molecule is usually the gap between them, ΔE = E(LUMO) − E(HOMO).

Absorption of a photon. A photon is absorbed only if its energy matches an allowed gap between two orbitals:

ΔE = hf = hc/λ

where h is the Planck constant (6.63 × 10⁻³⁴ J s), c is the speed of light (3.00 × 10⁸ m s⁻¹) and λ is the wavelength. A large gap requires high-energy, short-wavelength radiation; a small gap is bridged by lower-energy, longer-wavelength radiation. After absorption the molecule is in an excited state with one electron in a higher orbital.

The energy ranges involved. Visible light (400–700 nm) corresponds to photon energies of about 170–300 kJ mol⁻¹, and near-ultraviolet light (200–400 nm) to about 300–600 kJ mol⁻¹. These values are comparable with gaps between molecular orbitals, which is why electrons respond to this part of the spectrum. Wavelengths below about 190 nm are absorbed by the oxygen in air and by most solvents, so ordinary UV-visible instruments work between about 190 and 800 nm.

What the spectrum shows. A UV-visible spectrum plots absorbance against wavelength. Instead of the sharp lines seen in atomic spectra, molecules give broad bands . The wavelength at the top of a band is called λmax , and its height tells us how strongly the transition absorbs.

Why bands are broad. Each electronic state has many vibrational and rotational levels. An electronic transition can start and finish on many of these sub-levels, so a whole spread of slightly different energies is absorbed. In solution, collisions with solvent molecules blur these further into a smooth, wide band.

What happens to the energy? Excited states are short-lived. Most molecules lose the energy as heat through collisions within nanoseconds; some re-emit light (fluorescence); a few undergo chemical change, which is why ultraviolet light can damage materials and living tissue.

Formulae

ΔE = hf = hc/λ for one photon. Per mole of photons: E = N A hc/λ, where N A = 6.02 × 10²³ mol⁻¹. A useful shortcut: E (kJ mol⁻¹) ≈ 1.196 × 10⁵ ÷ λ (nm).

Step-by-step reasoning

To link an absorption band to an orbital gap:

1. Read λmax from the spectrum and convert it to metres (1 nm = 10⁻⁹ m). 2. Calculate the photon energy with E = hc/λ. 3. Multiply by the Avogadro constant to obtain the energy per mole. 4. Interpret: a longer λmax means a smaller HOMO–LUMO gap, a shorter λmax means a larger gap.

Visual explanation

Draw an energy-level ladder with σ at the bottom, then π, then n, then π , and σ at the top. Mark electrons as paired arrows in σ, π and n. A vertical arrow from an occupied rung to an empty rung represents one electronic transition; the longer the arrow, the shorter the wavelength of light absorbed.

Real-world analogy

Think of a building where people can only stand on floors, never between them. To move someone from the third floor to the fifth, you must supply exactly the energy for that climb. Offering half the energy achieves nothing; the photon must match a whole floor-to-floor gap.

Real-world example

Sunscreens contain organic molecules such as avobenzone whose HOMO–LUMO gaps match ultraviolet photons in the 300–380 nm range. They absorb this radiation and convert the energy harmlessly to heat, preventing the photons from reaching and damaging DNA in skin cells.

Why?

Why do saturated alkanes such as hexane not absorb in the normal UV-visible range? Their only electrons are in strong σ bonds, and the σ → σ gap is very large. The matching wavelengths are below about 150 nm, outside the instrument's range, so hexane is a useful transparent solvent.

Common misconception

"Absorbing UV light breaks the molecule's bonds." Usually it does not. The electron is promoted to a higher orbital, and in most cases the energy is quickly released as heat and the molecule returns unchanged to its ground state.

Worked example

Question: A compound has λmax = 250 nm. Calculate the energy gap per mole.

Reasoning: E = hc/λ = (6.63 × 10⁻³⁴ × 3.00 × 10⁸) ÷ (250 × 10⁻⁹) = 7.96 × 10⁻¹⁹ J per photon. Per mole: 7.96 × 10⁻¹⁹ × 6.02 × 10²³ = 4.79 × 10⁵ J mol⁻¹.

Answer: About 479 kJ mol⁻¹.

Quick check

1. If one compound absorbs at 220 nm and another at 320 nm, which has the smaller HOMO–LUMO gap? Answer: The compound absorbing at 320 nm, because longer wavelength means lower photon energy and therefore a smaller gap.

Exam focus

Be ready to state that UV-visible absorption promotes electrons to higher-energy orbitals, and to use E = hc/λ with correct unit conversions. Examiners often penalise forgetting to convert nm to m or forgetting the Avogadro constant when a molar energy is asked for.

Advanced insight

Not every transition that is energetically possible is observed strongly. Selection rules based on orbital symmetry and electron spin decide how probable a transition is. Spin-forbidden transitions, where the electron would have to change its spin, are extremely weak; symmetry-forbidden ones are weak but visible. These rules underlie the large differences in band intensity met in later topics.

Summary

UV-visible spectroscopy detects electronic transitions, in which a photon promotes an electron from an occupied orbital (often the HOMO) to an empty one (often the LUMO). The energy gap and wavelength are linked by ΔE = hc/λ: bigger gaps absorb shorter wavelengths. Bands are broad because vibrational and rotational sub-levels and solvent effects spread the absorbed energies. λmax marks the wavelength of strongest absorption.

Practice questions

1. What happens to an electron when a molecule absorbs a UV photon of suitable energy? Answer: It is promoted from an occupied molecular orbital to a higher-energy unoccupied orbital, producing an excited state. 2. Explain why UV-visible spectra show broad bands rather than sharp lines. Answer: Each electronic level has many vibrational and rotational sub-levels, so a range of transition energies is possible, and solvent interactions blur them into a continuous band. 3. Calculate the wavelength, in nm, of light needed for an energy gap of 3.00 × 10⁻¹⁹ J per molecule. Answer: λ = hc/E = (6.63 × 10⁻³⁴ × 3.00 × 10⁸) ÷ 3.00 × 10⁻¹⁹ = 6.63 × 10⁻⁷ m, which is 663 nm (red light). 4. Why is hexane a suitable solvent for UV-visible spectroscopy? Answer: It contains only σ bonds, whose σ → σ transitions need wavelengths below the instrument's range, so it does not absorb in the region being measured.