Quantised Energy Levels and Absorption

Introduction

A molecule stores energy in several ways at once: in the arrangement of its electrons, in the vibration of its bonds, in its rotation and, inside a magnetic field, in the orientation of certain nuclei. Each of these kinds of energy is quantised — only particular values are allowed. The spacing between the allowed values is very different for each kind, and that difference is the reason chemists need a whole family of spectroscopic techniques rather than just one.

Core explanation

Quantisation. In the everyday world, a ball can roll at any speed. At the molecular scale, energy is restricted to discrete levels, like the rungs of a ladder. A molecule can sit on one rung or another but never in between.

Absorption condition. A molecule absorbs a photon only when the photon's energy equals the gap between two levels:

ΔE = hf

If the photon energy is slightly too large or too small, it is not absorbed. This is why spectra show absorption at particular positions rather than across all energies.

Four types of energy level. The gaps differ enormously in size:

Type of energy Typical gap (kJ mol⁻¹) Radiation absorbed Technique --- --- --- --- Electronic about 150 – 600 UV and visible UV-visible Vibrational about 5 – 50 Infrared IR Rotational about 0.01 – 0.1 Microwave Microwave spectroscopy Nuclear spin (in a magnet) about 10⁻⁵ – 10⁻⁴ Radio NMR

Levels within levels. Each electronic level contains a set of vibrational levels, and each vibrational level contains a set of rotational levels. When a molecule in solution absorbs UV light, it often changes its vibrational and rotational state at the same time. Because solvent molecules also blur these fine levels, UV-visible spectra of solutions usually show broad bands rather than sharp lines.

Nuclear spin levels are special. Nuclei such as ¹H and ¹³C have a property called spin. Without an external magnetic field, the spin orientations have the same energy. In a strong magnetic field they split into two levels whose gap is tiny, which is why NMR uses low-energy radio waves.

Population of levels. At room temperature almost all molecules are in their electronic and vibrational ground states, because these gaps are large compared with thermal energy (about 2.5 kJ mol⁻¹ at 298 K). Rotational and nuclear spin levels, with much smaller gaps, are spread across many levels.

Step-by-step reasoning

To decide which kind of transition a photon can cause:

1. Calculate or look up the photon energy in kJ mol⁻¹. 2. Compare it with the typical gaps in the table. 3. Choose the type of transition whose gap is of similar size. 4. Name the technique that uses that region of the spectrum.

Visual explanation

Sketch two tall electronic "floors". On each floor, draw closely spaced vibrational lines, and between each pair of vibrational lines draw even finer rotational lines. A long vertical arrow from the lower floor to the upper one represents a UV-visible transition; a short arrow between vibrational lines represents an IR transition.

Real-world analogy

A building has floors (electronic levels), each floor has steps on its staircase (vibrational levels), and each step has a slightly uneven surface (rotational levels). A lift moves you between floors — a large energy change — while climbing a step is a much smaller change.

Real-world example

A microwave oven heats food because water molecules absorb microwave photons and gain rotational energy, which is passed to surrounding molecules as heat. The photons lack the energy to break bonds or excite electrons, so the food is heated rather than chemically altered by the radiation.

Why?

Why does IR radiation not change the electron arrangement in a molecule? Infrared photons carry at most about 50 kJ mol⁻¹, far less than the gap to the first excited electronic state in most molecules. They can only supply the smaller amounts needed to excite vibrations.

Common misconception

"A molecule absorbs any photon with at least the required energy." For transitions between bound energy levels, the photon energy must match the gap; it is not a minimum threshold. The threshold idea applies to ionisation, where the electron leaves completely.

Worked example

Question: A molecule absorbs IR radiation at 1700 cm⁻¹. Calculate the energy gap in kJ mol⁻¹.

Reasoning: λ = 1/1700 cm = 5.88 × 10⁻⁶ m. E per photon = hc/λ = (6.63 × 10⁻³⁴ × 3.00 × 10⁸) ÷ 5.88 × 10⁻⁶ = 3.38 × 10⁻²⁰ J. Per mole: 3.38 × 10⁻²⁰ × 6.02 × 10²³ = 2.04 × 10⁴ J mol⁻¹.

Answer: About 20 kJ mol⁻¹ — a typical vibrational gap.

Quick check

1. Which type of energy level has the largest gaps, and which radiation causes transitions between them? Answer: Electronic levels; they are excited by ultraviolet and visible radiation.

Exam focus

Learn the order of gap sizes: electronic > vibrational > rotational > nuclear spin, and match them to UV-visible, IR, microwave and radio. Use the phrase "photon energy equals the energy difference between two quantised levels" when explaining absorption.

Advanced insight

In the gas phase, a high-resolution IR spectrum of a small molecule such as HCl shows each vibrational band split into a series of closely spaced lines. Each line corresponds to a simultaneous vibrational and rotational change, and the line spacing can be used to calculate the bond length very precisely.

Summary

Molecular energy is quantised into electronic, vibrational, rotational and nuclear spin levels. A photon is absorbed only when its energy matches a gap between levels. Electronic gaps are largest (UV-visible), then vibrational (IR), rotational (microwave) and nuclear spin in a magnet (radio). Nested levels explain why UV-visible bands in solution are broad.

Practice questions

1. What is meant by saying that molecular energy is quantised? Answer: A molecule can only have certain fixed energy values, not any value in between. 2. Which region of the spectrum is used to excite nuclear spin transitions, and why? Answer: Radio waves, because the energy gap between nuclear spin states in a magnet is extremely small. 3. Explain why UV-visible spectra of solutions show broad bands. Answer: Electronic transitions are accompanied by many vibrational and rotational changes, and solvent interactions blur these levels, so many slightly different energies are absorbed. 4. A photon has an energy of 300 kJ mol⁻¹. What kind of transition is it likely to cause? Answer: An electronic transition, since 300 kJ mol⁻¹ falls in the UV-visible range of gap sizes.