Spectroscopy begins with a surprisingly simple idea: molecules do not absorb arbitrary amounts of energy. Their internal energies are restricted to particular allowed values. When electromagnetic radiation interacts with a molecule, energy can therefore be transferred only in particular amounts.
This is the idea of quantisation of energy. Once you can connect photon energy to the gap between two molecular energy levels, the different regions of the electromagnetic spectrum begin to make sense. Ultraviolet and visible radiation, infrared radiation, microwaves and radio waves do not merely have different wavelengths — their photons carry different energies and therefore probe different kinds of molecular energy changes.
Try these five questions before reading the chapter. They test the relationships between wavelength, frequency, photon energy and molecular energy levels.
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Electromagnetic radiation carries energy
Before considering the energy levels inside a molecule, we need a way to describe the radiation interacting with it. Electromagnetic radiation can be viewed in two complementary ways.
In the wave description, radiation is characterised by its wavelength, λ, and frequency, ν. In the particle description, the radiation consists of packets of energy called photons. These two descriptions are connected mathematically.
The same electromagnetic radiation can be described using wave quantities such as ν and λ, or using photons whose individual energies are E = hν.
Frequency and wavelength
The frequency of a wave tells us how many oscillations pass a point per second, while its wavelength is the distance between corresponding points on successive waves. For electromagnetic radiation in vacuum:
where c is the speed of light, ν is the frequency and λ is the wavelength.
Because c is constant, frequency and wavelength are inversely related. Radiation of high frequency has a short wavelength, while radiation of low frequency has a long wavelength.
Energy of a photon
The energy carried by a single photon is proportional to the frequency of the radiation:
where h is Planck's constant.
Combining this with c = νλ gives another very useful form:
High-frequency radiation: high photon energy and short wavelength.
Low-frequency radiation: low photon energy and long wavelength.
If the wavelength of electromagnetic radiation is halved, the frequency doubles because c = νλ. The photon energy therefore also doubles because E = hν. Equivalently, E = hc/λ shows the inverse relationship directly.
What does quantisation of energy mean?
In everyday mechanics, we often imagine energy changing smoothly. A moving object can gradually speed up and possess a continuous range of kinetic energies. Molecular energy behaves differently.
A molecule can occupy only particular allowed energy states. Values between these states are not permitted. We therefore say that the molecular energy is quantised.
Quantisation means that a molecule can possess only certain discrete energies rather than every possible energy value.
Thinking in terms of energy levels
An energy-level diagram represents each allowed energy by a horizontal line. Higher lines correspond to higher energies. The empty space between two lines does not represent additional allowed states; it represents an energy interval that the molecule cannot occupy continuously.
The levels do not have to be equally spaced. What matters in spectroscopy is the energy difference between a pair of allowed states.
Different kinds of molecular energy are quantised
A molecule can store energy in several ways. The important forms for this discussion are electronic, vibrational, rotational and nuclear-spin energy. Each form has its own pattern of allowed states and its own characteristic size of energy separation.
Electronic energy levels
Electronic energy levels arise from the possible electronic states of a molecule. Moving the molecule from a lower electronic state to a higher electronic state usually requires a relatively large amount of energy. Consequently, electronic transitions are associated principally with ultraviolet and visible radiation.
Vibrational energy levels
Atoms bonded together are not completely stationary. Bonds may undergo stretching and bending motions. The vibrational energy associated with these motions is also quantised.
The energy differences between vibrational levels are generally smaller than those between electronic levels. Vibrational transitions are therefore commonly associated with infrared radiation.
Rotational energy levels
A molecule may also possess rotational energy as it rotates in space. Rotational energy levels are more closely spaced than vibrational levels, so transitions between rotational states involve still smaller energy differences. They are associated particularly with microwave or far-infrared radiation.
Nuclear-spin energy levels
Certain nuclei possess nuclear spin. In the context of NMR spectroscopy, placing suitable nuclei in an external magnetic field produces different nuclear-spin energy states. The separations between these states are extremely small compared with electronic, vibrational and rotational energy separations.
Transitions between these nuclear-spin states are induced using radiofrequency radiation.
| Type of energy transition | Relative energy gap | Typical electromagnetic radiation | Molecular change being probed |
|---|---|---|---|
| Electronic | Largest of these molecular transitions | Ultraviolet / visible | Change in electronic state |
| Vibrational | Smaller | Infrared | Bond stretching and bending |
| Rotational | Smaller still | Microwave / far-infrared | Change in molecular rotational state |
| Nuclear spin | Very small | Radiofrequency | Change between nuclear-spin states in a magnetic field |
Larger energy gap: requires a higher-frequency, shorter-wavelength photon.
Smaller energy gap: can be matched by a lower-frequency, longer-wavelength photon.
Transitions occur between allowed energy levels
Suppose a molecule initially occupies a lower energy state with energy E₁ and can move to a higher allowed state with energy E₂. The required energy is not E₂ itself. It is the difference between the two levels:
If electromagnetic radiation is to cause this transition, an absorbed photon must provide this energy difference:
Combining the photon-energy expression with the wave relationship also gives:
Spectroscopy is fundamentally sensitive to differences between energy levels. The observed photon energy corresponds to ΔE, not simply to the absolute energy of either level.
Why the photon energy matters
Imagine that the molecule requires an energy ΔE to reach a particular higher state. A photon with the corresponding frequency can supply exactly that energy because its energy is hν. This is why the frequencies absorbed by a sample contain information about its molecular energy-level structure.
If two molecular states are separated by ΔE, the corresponding spectroscopic frequency satisfies ν = ΔE/h. A larger separation therefore produces a higher-frequency absorption, while a smaller separation produces a lower-frequency absorption.
Absorption and emission
Quantised energy levels allow energy to be exchanged in two directions. A molecule may move from a lower state to a higher state by absorption, or from a higher state to a lower state by emission.
Absorption
During absorption, the molecule gains energy. A photon is absorbed and the molecule undergoes a transition from a lower energy state to a higher one:
For the two levels involved:
Emission
During emission, a molecule in a higher energy state moves to a lower state and releases the energy difference as electromagnetic radiation:
The energy of the emitted photon again corresponds to the difference between the two states.
Absorption: lower energy state → higher energy state; the molecule gains energy from electromagnetic radiation.
Emission: higher energy state → lower energy state; the molecule releases energy as electromagnetic radiation.
Why different spectroscopic methods use different radiation
The connection between quantisation and the electromagnetic spectrum can now be seen directly. Different types of molecular motion or molecular state have different characteristic energy separations.
Since the energy of a photon is E = hν, radiation of different frequency supplies different photon energies. A spectroscopic method therefore uses a region of the electromagnetic spectrum appropriate to the size of the energy gap being studied.
| Radiation | Relative photon energy | Main energy transition considered here |
|---|---|---|
| Ultraviolet / visible | High | Electronic |
| Infrared | Intermediate | Vibrational |
| Microwave / far-infrared | Lower | Rotational |
| Radiofrequency | Very low | Nuclear spin in an external magnetic field |
Different regions of the electromagnetic spectrum probe different molecular energy separations because photon energy depends on frequency.
Common Mistakes
| Common mistake | Why it is wrong | Better approach |
|---|---|---|
| Thinking that a longer wavelength means a higher photon energy. | E = hc/λ, so energy decreases as wavelength increases. | Remember the chain: short λ → high ν → high E. |
| Thinking that quantised energy means the molecule has only one possible energy. | A molecule may occupy many allowed states; the restriction is that energies between the allowed levels are not permitted. | Think of quantisation as a set of discrete levels rather than one fixed value. |
| Using the energy of the upper level instead of the energy difference. | The photon causes a transition between two states, so the relevant quantity is ΔE = Eupper − Elower. | Always calculate the gap between the two levels first. |
| Confusing absorption with emission. | Absorption moves the molecule upward in energy; emission moves it downward. | Associate absorption with gaining photon energy and emission with releasing photon energy. |
| Assuming all molecular energy gaps are similar in size. | Electronic, vibrational, rotational and nuclear-spin separations occur on very different energy scales. | Link each type of transition to its characteristic region of the electromagnetic spectrum. |
| Forgetting the role of an external magnetic field in NMR. | The spectroscopically useful separation of nuclear-spin states arises in the applied magnetic field. | Connect NMR with nuclear spins, an external magnetic field and radiofrequency radiation. |
What you should be able to do
Use c = νλ
Relate the wavelength and frequency of electromagnetic radiation.
Use E = hν and E = hc/λ
Relate photon energy to frequency and wavelength.
Explain quantisation
State clearly that molecules occupy discrete allowed energy states.
Compare molecular energy gaps
Distinguish electronic, vibrational, rotational and nuclear-spin energy levels.
Apply ΔE = hν
Connect a spectroscopic transition to the energy of the absorbed or emitted photon.
Distinguish absorption and emission
Interpret upward and downward transitions on an energy-level diagram.
These ten questions test whether you can connect electromagnetic radiation, photon energy and quantised molecular energy levels.
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Frequently asked questions
Questions students often ask about quantisation of energy
The equations in this topic are short, but several important ideas are hidden inside them. These questions connect the mathematics with the physical meaning of molecular energy levels.
What exactly does “quantised” mean?
It means that only particular energy values are allowed. A molecule can move from one allowed energy state to another, but it does not continuously occupy every energy value between those two states.
Is a quantum the same thing as a photon?
A quantum is a discrete amount of a physical quantity. A photon is the quantum of electromagnetic radiation. Each photon has an energy E = hν.
Why does shorter-wavelength radiation have greater photon energy?
Since c = νλ, decreasing λ increases ν. Since E = hν, the photon energy therefore increases. Combining the equations gives E = hc/λ directly.
Does spectroscopy measure the energy of an individual molecular level?
Spectroscopic transitions reveal the energy difference between two states. If an absorbed photon has energy hν, the associated states are separated by ΔE = hν.
Why are UV and visible photons associated with electronic transitions?
Electronic states are typically separated by relatively large energies. UV and visible radiation has sufficiently high photon energies to match energy separations of this scale.
Why is infrared radiation associated with molecular vibrations?
Vibrational levels have characteristic separations smaller than typical electronic energy gaps. Infrared photon energies correspond to this lower energy scale and can therefore probe changes in molecular vibrational states.
Why are rotational transitions associated with microwaves?
Rotational energy levels are generally separated by smaller energy differences than vibrational levels. Lower-frequency microwave or far-infrared photons therefore correspond to the appropriate energy scale.
What does the magnetic field do in NMR spectroscopy?
For suitable nuclei, an external magnetic field produces nuclear-spin states with different energies. Radiofrequency radiation can then cause transitions between these very closely spaced states.
What is the difference between absorption and emission?
Absorption occurs when a molecule gains photon energy and moves to a higher energy state. Emission occurs when a molecule moves to a lower energy state and releases the energy difference as electromagnetic radiation.
Which equation should I start with in a spectroscopy calculation?
First identify what information is given. Use c = νλ to convert between frequency and wavelength, E = hν or E = hc/λ for photon energy, and ΔE = hν when the question concerns the separation between two molecular energy levels.
Do the allowed energy levels have to be equally spaced?
No. Quantisation means that only particular energy states are allowed; it does not mean that the difference between every pair of neighbouring levels must be identical.
Quantisation provides the bridge between molecular structure and spectroscopy. Molecules possess discrete energy states, electromagnetic radiation arrives in photons of energy hν, and a spectroscopic transition connects the two through ΔE = hν. The next step is to examine the electromagnetic spectrum in greater detail and see how different regions are used to probe different molecular energy changes.