Spectroscopy and the Electromagnetic Spectrum: Study Guide (Chemistry 3.11)

Light is a stream of energy packets

Light and other electromagnetic radiation travel as waves, but they deliver energy in separate packets called photons. Every photon of one wavelength carries the same amount of energy. Two simple rules link the wave and the packet:

• Shorter wavelength means higher frequency. All electromagnetic waves travel at the same speed in a vacuum, so if the waves are closer together, more of them pass a point each second.
• Higher frequency means more energy per photon. A photon of ultraviolet light carries far more energy than a photon of infrared light.

So you can rank photons by energy just by looking at their wavelengths: the shorter the wavelength, the more energetic the photon. In Topic 3.12 you will put numbers on this with c = λν and E = hν. In this topic, the ranking is enough.

The electromagnetic spectrum

The electromagnetic spectrum is the full range of wavelengths, from radio waves many metres long to gamma rays far smaller than an atom. Scientists split it into named regions. The boundaries are conventions, not sharp physical edges, so different books quote slightly different values.

Region	Approximate wavelength	What its photons do to a molecule
Radio	longer than about 1 m	too little energy for the changes in this topic
Microwave	about 1 mm to 1 m	change how fast the molecule rotates
Infrared (IR)	about 700 nm to 1 mm	change how strongly bonds vibrate (stretch and bend)
Visible	about 400 nm (violet) to 700 nm (red)	move electrons to higher energy levels
Ultraviolet (UV)	about 10 nm to 400 nm	move electrons to higher energy levels; can break bonds
X-ray and gamma	shorter than about 10 nm	remove electrons, even from inner shells (as in PES, Topic 1.6)

Two memory hooks help. Inside the visible region, red has the longest wavelength and violet the shortest. “Infra-red” is just beyond red (lower energy), and “ultra-violet” is just beyond violet (higher energy).

Three ways a molecule stores energy

A molecule is not a rigid, still object. It can hold energy in three separate ways:

1. Rotation. The whole molecule spins about its centre of mass.
2. Vibration. The atoms move back and forth relative to each other, so bonds stretch and compress and bond angles open and close.
3. Electronic energy. Electrons occupy particular energy levels; an electron can be moved to a higher level.

Each kind of energy is quantized: the molecule can only have certain allowed values, like the rungs of a ladder. To climb from one rung to the next, it must gain exactly the energy of the gap. The key fact for this topic is that the gaps are very different in size:

rotational gaps ≪ vibrational gaps ≪ electronic gaps

Spinning a whole molecule a little faster takes very little energy. Stretching a bond harder takes more. Moving an electron to a new energy level, against the pull of the nuclei, takes much more again.

Matching the region to the transition

Because a photon can only be absorbed if its energy matches a gap, the size of each gap decides which region of the spectrum can cause it. The table shows typical photon energies, given per mole of photons so you can compare them with bond energies from Unit 2.

Example wavelength	Region	Energy per mole of photons	Transition it matches
1.00 cm	microwave	about 0.012 kJ mol⁻¹	rotational
5.00 μm	infrared	about 23.9 kJ mol⁻¹	vibrational
500 nm	visible	about 239 kJ mol⁻¹	electronic
250 nm	ultraviolet	about 479 kJ mol⁻¹	electronic

The jumps are large: the infrared photon carries about 2000 times the energy of the microwave photon, and the ultraviolet photon about 20 times the energy of the infrared photon. Notice too that ultraviolet energies are similar to typical covalent bond energies (a few hundred kJ mol⁻¹). That is why ultraviolet light can break bonds and damage molecules, while infrared and microwaves only make molecules vibrate or rotate faster.

The rule to remember:

• Microwave → rotational transitions
• Infrared → vibrational transitions
• Ultraviolet / visible → electronic transitions

A higher-energy transition usually brings smaller changes with it. When a molecule absorbs a UV photon, its vibrational and rotational state can change at the same time, because those gaps are tiny by comparison. The reverse is not true: a microwave photon can never move an electron, because it carries far too little energy.

Absorption and emission

Spectroscopy studies the light that matter absorbs or emits.

• In an absorption spectrum, radiation passes through a sample. The sample removes only the photons whose energies match its gaps, so you see dips at those wavelengths. The molecule moves up a ladder.
• In an emission spectrum, the sample is first given extra energy (by heating or an electric discharge). It then drops down a ladder and gives out photons whose energies match the gaps.

For the same substance, the same gaps appear in both. A gap that absorbs at a certain wavelength also emits at that wavelength.

Colour is an electronic effect

When white light passes through a coloured solution, the solute absorbs some visible wavelengths through electronic transitions. Your eye sees the wavelengths that are left. The colour you see is roughly the complement of the colour absorbed: a substance that absorbs orange light looks blue, and one that absorbs violet light looks yellow. Copper(II) sulfate solution looks blue because it absorbs mainly in the orange-red part of the spectrum.

A colourless substance either has no electronic gaps in the visible region (its electronic transitions need UV photons) or absorbs too weakly to notice. Topic 3.13 turns this absorption into a measurement of concentration.

Worked example 1: identifying transitions from absorption data

Question. A fictional gas, Q, made of small polar molecules, absorbs radiation at three wavelengths: 2.40 mm, 6.10 μm and 185 nm. For each, name the region of the spectrum and the type of transition. Then rank the three transitions by energy gap.

1. Convert to one unit to compare. 2.40 mm = 2.40 × 10⁻³ m; 6.10 μm = 6.10 × 10⁻⁶ m; 185 nm = 1.85 × 10⁻⁷ m.
2. Place each wavelength.
   • 2.40 mm lies between 1 mm and 1 m: microwave, so a rotational transition.
   • 6.10 μm lies between 700 nm and 1 mm: infrared, so a vibrational transition.
   • 185 nm lies between 10 nm and 400 nm: ultraviolet, so an electronic transition.
3. Rank by energy. Shorter wavelength means more energy per photon, so the gaps rank: electronic (185 nm) > vibrational (6.10 μm) > rotational (2.40 mm).

Check. This ranking matches rotational ≪ vibrational ≪ electronic from Figure 2. In numbers, the 6.10 μm photon carries about 390 times the energy of the 2.40 mm photon, and the 185 nm photon about 33 times the energy of the 6.10 μm photon. You do not need these ratios here, but they confirm the large jumps between regions.

Common slip. Comparing “2.40” with “185” without converting units would rank the microwave line as the shortest wavelength. Always put wavelengths in the same unit first.

Worked example 2: what can an atom absorb compared with a molecule?

Question. A sample of argon gas and a sample of hydrogen chloride gas, HCl, are each tested with microwave, infrared and ultraviolet radiation. Predict which regions each gas can absorb in, and justify your answer in terms of transitions.

1. Hydrogen chloride is a molecule with a bond and a permanent dipole.
   • It can rotate, so it has rotational levels: it can absorb microwaves.
   • Its H–Cl bond can stretch, so it has vibrational levels: it can absorb infrared.
   • It has electrons in energy levels: it can absorb ultraviolet through electronic transitions.
2. Argon exists as single atoms.
   • A single atom has no bonds, so there is nothing to vibrate: no infrared absorption.
   • A single atom has no rotational energy levels of the kind a molecule has: no microwave absorption.
   • It does have electrons in quantized energy levels, so it can absorb only through electronic transitions. For argon these gaps are very large, so it absorbs only high-energy ultraviolet.

Answer. HCl can absorb in all three regions; argon absorbs only in the ultraviolet.

Why this matters. The example shows that a spectrum tells you about structure. Absorption in the infrared is direct evidence that the sample contains bonds that can vibrate.

Common misconceptions

• “Longer wavelength means more energy.” It is the reverse. Energy per photon falls as wavelength rises, so infrared photons carry less energy than visible photons.
• “Infrared radiation excites electrons.” In this course, infrared matches vibrational gaps. Electronic transitions need visible or ultraviolet photons.
• “Microwaves make molecules vibrate.” Microwave photons match rotational gaps. Vibrational gaps are much larger and need infrared.
• “A molecule absorbs any photon with enough energy, and keeps the extra.” A transition needs a photon whose energy matches a gap. Photons that do not match pass through.
• “The colour of a solution is the colour it absorbs.” You see the light that is not absorbed, roughly the complementary colour.
• “Brighter light can cause bigger transitions.” Brightness is the number of photons. The kind of transition depends on the energy of each photon, which depends on the wavelength.
• “Spectral regions have exact edges.” The boundaries are conventions. A wavelength near a boundary, such as 720 nm, could be called deep red or near infrared; the region tells you the type of transition only roughly at the edges.

Where this leads

This topic builds on the quantized electron energy levels from Topic 1.6, Photoelectron Spectroscopy, where high-energy photons remove electrons altogether. Next, Topic 3.12, Properties of Photons, gives you c = λν and E = hν so you can calculate the energy of each transition. Topic 3.13 then uses absorption of visible light to measure concentration. Try the practice questions now, then use the revision notes and the checklist to consolidate.