Spectroscopy begins with a simple question: what happens when matter interacts with electromagnetic radiation? The answer depends on the energy carried by the radiation. Radio waves, microwaves, infrared radiation and ultraviolet or visible light do not all affect a molecule in the same way, because their photons carry very different amounts of energy.
The electromagnetic spectrum therefore acts like a set of differently sized probes. Low-energy radiation can distinguish very small energy gaps, while higher-energy radiation can promote much larger changes in a molecule. Once we understand wavelength, frequency, photons and quantised energy levels, the basis of NMR, rotational, infrared and UV-visible spectroscopy follows naturally.
Try these five questions before reading the chapter. They test the relationships between wavelength, frequency, photon energy and the molecular transitions used in spectroscopy.
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Photon 1: wavelength = 250 nm
Photon 2: wavelength = 500 nm
Electromagnetic radiation as a wave
Electromagnetic radiation consists of oscillating electric and magnetic fields travelling through space. Although different regions of the electromagnetic spectrum are given different names, they are all the same physical phenomenon. Radio waves, infrared radiation, visible light and X-rays differ mainly in their wavelength and frequency.
In a vacuum, all electromagnetic radiation travels at the same speed, c ≈ 3.00 × 10⁸ m s⁻¹. The wavelength λ is the distance between equivalent points on successive waves, while the frequency f is the number of wave cycles passing a point per second.
Wave relationship: c = fλ
Frequency and wavelength are inversely related
Because c is constant in a vacuum, increasing the frequency requires a corresponding decrease in wavelength. A short-wavelength electromagnetic wave therefore has a high frequency, whereas a long-wavelength wave has a low frequency.
Short wavelength: high frequency and, as we will shortly see, high photon energy.
Long wavelength: low frequency and low photon energy.
Useful units
Wavelength may be expressed in metres, micrometres or nanometres depending on the region of the spectrum. Frequency is measured in hertz, Hz, where 1 Hz means one cycle per second.
For light of wavelength 500 nm, first convert the wavelength to metres: λ = 500 × 10⁻⁹ m. Therefore f = c/λ = (3.00 × 10⁸)/(500 × 10⁻⁹) = 6.00 × 10¹⁴ Hz.
Electromagnetic radiation as photons
The wave description explains wavelength and frequency, but spectroscopy also requires a particle description of light. Electromagnetic radiation is exchanged with matter in discrete packets of energy called photons.
Here E is the energy of one photon, h is the Planck constant (6.63 × 10⁻³⁴ J s), and f is the frequency of the radiation. Combining E = hf with c = fλ gives E = hc/λ.
What determines photon energy?
Photon energy depends on frequency. A high-frequency photon carries more energy than a low-frequency photon. Since frequency and wavelength are inversely related, the same statement can be made using wavelength: shorter-wavelength photons carry more energy.
As wavelength decreases, frequency increases and photon energy increases.
In symbols: long λ → low f → low E, while short λ → high f → high E.
A worked photon-energy calculation
Consider light of wavelength 500 nm. From the previous calculation, f = 6.00 × 10¹⁴ Hz. The energy carried by one photon is therefore:
Notice that this is the energy of one photon, not one mole of photons. If an energy per mole were required, the photon energy would need to be multiplied by the Avogadro constant.
The electromagnetic spectrum
The electromagnetic spectrum arranges electromagnetic radiation according to wavelength or frequency. From radio waves to gamma rays, wavelength becomes shorter while frequency and photon energy increase.
Which regions matter in molecular spectroscopy?
Different regions of the spectrum contain photons of different energies. They can therefore probe energy gaps of very different sizes inside atoms and molecules. This is why different spectroscopic techniques reveal different aspects of molecular structure.
| Region | Typical spectroscopic transition | What changes? |
|---|---|---|
| Radiofrequency | Nuclear spin transitions in a magnetic field | Nuclear spin state |
| Microwave | Rotational transitions | Molecular rotational state |
| Infrared | Vibrational transitions | Bond vibrations |
| Visible / ultraviolet | Electronic transitions | Electronic state |
Different spectroscopic techniques probe different-sized energy gaps. Radiofrequency radiation corresponds to very small gaps, while UV-visible radiation can correspond to much larger electronic energy gaps.
Where do X-rays and gamma rays fit?
X-rays and gamma rays have still shorter wavelengths and much higher photon energies. They are part of the electromagnetic spectrum, but they are not the main regions used for the molecular spectroscopic techniques being introduced here. The central sequence for this chapter is therefore radiofrequency → microwave → infrared → visible/ultraviolet.
Quantisation of molecular energy
The photon picture becomes especially important because the internal energies of atoms and molecules are also quantised. A molecule cannot possess every conceivable value of electronic, vibrational or rotational energy. Instead, only particular energy states are allowed.
Think of energy levels as rungs on a ladder
A useful first model is a ladder. A person can stand on one rung or another rung, but not remain stationary halfway between them. Similarly, a molecule may occupy one allowed energy level or another, but it does not possess a stable energy corresponding to an arbitrary point between the levels.
Different kinds of energy level
Molecular energy can be described in terms of electronic, vibrational and rotational contributions. In spectroscopy, these energy scales are not equal.
Electronic energy gaps: relatively large, so transitions commonly require visible or ultraviolet photons.
Vibrational energy gaps: smaller than typical electronic gaps, so infrared radiation is commonly appropriate.
Rotational energy gaps: smaller again and commonly associated with microwave radiation.
Nuclear spin energy gaps: extremely small and, in NMR, arise when suitable nuclei are placed in an external magnetic field. Radiofrequency radiation can induce transitions between these levels.
A useful energy-gap order is: electronic > vibrational > rotational, while nuclear spin separations used in NMR are smaller still.
Absorption and energy-level transitions
Suppose a molecule initially occupies a lower energy level E₁ and another allowed level exists at E₂. To move from E₁ to E₂, the molecule must gain an amount of energy equal to the gap between the two levels.
If electromagnetic radiation supplies a photon with the appropriate energy, that photon may be absorbed and the molecule undergoes a transition to the higher energy state.
Why does a molecule absorb only particular frequencies?
If the energy levels are discrete, the gaps between them also have particular values. Radiation of an appropriate frequency can therefore be absorbed, whereas radiation that does not correspond to a suitable allowed transition is not absorbed for that transition.
This is the heart of spectroscopy. Instead of absorbing every possible wavelength equally, a substance absorbs characteristic frequencies. Measuring those absorptions reveals information about its energy-level structure and ultimately about the molecule itself.
If an allowed transition has ΔE = 4.00 × 10⁻¹⁹ J, then f = ΔE/h = (4.00 × 10⁻¹⁹)/(6.63 × 10⁻³⁴) = 6.03 × 10¹⁴ Hz. Radiation close to this frequency has the photon energy required for that transition.
Matching the energy gap is necessary, but quantum rules also matter
At an introductory level, we often say that absorption occurs when hf = ΔE. This is the essential energy requirement. More precisely, however, not every mathematically possible pair of levels necessarily gives a strong spectroscopic transition. Quantum-mechanical selection rules determine which transitions are allowed or intense enough to be observed.
For this chapter, the important foundation is that the photon must have the correct energy and the transition must be allowed.
Emission from excited states
Absorption raises a system from a lower energy level to a higher one. The reverse energy change is possible when an excited system returns to a lower energy state.
If that de-excitation occurs by emitting a photon, conservation of energy requires the emitted photon to carry the energy difference between the two states.
Absorption and emission are opposite directions
| Process | Energy-level change | Photon |
|---|---|---|
| Absorption | Lower level → higher level | Photon is absorbed |
| Emission | Higher level → lower level | Photon may be emitted |
An upward energy-level transition represents absorption; a downward radiative transition represents emission.
How the spectrum connects to spectroscopy
We can now put the entire argument together. Electromagnetic radiation has a frequency, and each photon therefore carries an energy hf. Atoms and molecules possess discrete energy levels. A spectroscopic transition can occur when the energy carried by the radiation corresponds to an allowed energy-level separation.
Different kinds of molecular motion or electronic behaviour have differently sized energy gaps. Consequently, different regions of the electromagnetic spectrum become useful for different spectroscopic techniques.
The central spectroscopy map
| Radiation | Relative photon energy | Main transition introduced here |
|---|---|---|
| Radiofrequency | Very low | Nuclear spin |
| Microwave | Low | Rotational |
| Infrared | Intermediate | Vibrational |
| Visible / ultraviolet | Higher | Electronic |
This map is the bridge to the individual spectroscopic methods. The techniques may look different experimentally, but the same underlying idea keeps returning: measure which electromagnetic frequencies interact with matter, then use those frequencies to infer the allowed energy gaps.
Common Mistakes
| Common mistake | Why it is wrong | Better approach |
|---|---|---|
| Thinking longer wavelength means greater photon energy | E = hc/λ, so photon energy decreases as wavelength increases. | Remember: short λ → high f → high E. |
| Writing c = f/λ | This gives the wrong relationship between wavelength and frequency. | Start from c = fλ. |
| Confusing intensity with the energy of one photon | The energy of an individual photon is determined by f through E = hf. | Separate photon energy from the total amount of radiation reaching the sample. |
| Saying IR radiation causes electronic transitions | The photon energies normally used in IR spectroscopy correspond mainly to vibrational transitions. | Associate IR with vibration and UV-visible with electronic transitions. |
| Thinking quantised means all molecules have the same energy | A molecule may occupy different discrete allowed levels. | Think of separate rungs on a ladder rather than one fixed energy. |
| Drawing absorption as a downward energy arrow | Absorption increases the energy of the system. | Draw absorption upward and emission downward. |
What you should be able to do
Use c = fλ
Calculate wavelength or frequency and convert wavelength units correctly.
Calculate photon energy
Apply E = hf and E = hc/λ to electromagnetic radiation.
Order the electromagnetic spectrum
Relate radio, microwave, infrared, visible, ultraviolet, X-ray and gamma radiation to wavelength, frequency and energy.
Explain quantisation
Describe molecular energy levels as discrete allowed states rather than a continuous range.
Connect radiation to spectroscopy
Associate radiofrequency, microwave, infrared and UV-visible radiation with the corresponding types of transition.
Explain absorption and emission
Use ΔE = hf to relate energy-level transitions to photon absorption or photon emission.
These ten questions test whether you can apply the relationships between wavelength, frequency, photon energy and quantised spectroscopic transitions.
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Frequently asked questions
Questions students often ask about electromagnetic radiation and spectroscopy
The equations themselves are quite short, but several ideas are easy to mix up when wavelength, frequency, photon energy and molecular energy levels are first introduced.
What is the relationship between wavelength and frequency?
They are inversely related because c = fλ and c is constant for electromagnetic radiation in vacuum. A shorter wavelength therefore corresponds to a higher frequency, while a longer wavelength corresponds to a lower frequency.
Is photon energy determined by wavelength or frequency?
Either can be used because the two are connected. From E = hf, energy is directly proportional to frequency. Combining this with c = fλ gives E = hc/λ, showing that photon energy is inversely proportional to wavelength.
Does greater light intensity mean that each photon has more energy?
Not necessarily. The energy of an individual photon depends on frequency through E = hf. Increasing the intensity at the same frequency generally means that more radiant energy is delivered, not that the energy of each individual photon has changed.
Why do different spectroscopic techniques use different regions of the electromagnetic spectrum?
Different molecular transitions involve different-sized energy gaps. Electronic gaps are generally much larger than vibrational gaps, which are larger than rotational gaps. Nuclear spin separations in NMR are smaller still. Different photon frequencies are therefore needed to match these different energy scales.
What exactly does quantised energy mean?
It means that only particular energy states are allowed. The molecule cannot possess every value of energy between two allowed levels. The ladder analogy is useful: the allowed energies are like individual rungs rather than a continuous ramp.
Must the photon energy equal the energy gap exactly for absorption?
The central energy requirement is ΔE = hf for the particular transition. In a more complete treatment, quantum-mechanical selection rules also determine whether a transition is allowed, and real spectra can show broadened absorption features rather than infinitely sharp mathematical lines.
Is visible light always involved in electronic transitions?
Visible and ultraviolet photons commonly promote electronic transitions when suitable electronic energy gaps exist. A molecule does not automatically absorb every wavelength of visible light; absorption occurs only where appropriate allowed transitions are available.
Why is infrared radiation associated with bond vibration?
Molecular vibrations have quantised energy levels whose separations commonly correspond to infrared photon energies. Absorption of suitable IR frequencies can therefore promote vibrational transitions. This is the foundation of infrared spectroscopy.
Why are microwaves associated with molecular rotation?
Rotational energy levels are separated by relatively small energy gaps. Microwave photons have suitably low energies to produce transitions between many of these rotational states.
Why are radio waves used in NMR if they have such low energy?
That low photon energy is exactly what is needed. In an external magnetic field, appropriate nuclei can occupy nuclear spin states separated by very small energy differences. Radiofrequency radiation can match these small separations and induce NMR transitions.
What is the difference between absorption and emission on an energy-level diagram?
Absorption moves the system from a lower energy state to a higher one, so it is shown by an upward arrow. Radiative emission occurs when the system moves to a lower energy state while releasing a photon, so it is shown by a downward arrow.
The electromagnetic spectrum is more than a list of different kinds of radiation. It provides the energy scale that makes spectroscopy work. Once c = fλ, E = hf and ΔE = hf are connected to quantised molecular energy levels, the logic behind UV-visible, infrared, rotational and NMR spectroscopy becomes much easier to see.