A photon’s energy has to fit
Lesson 2.2.3 showed that an atom absorbs only photons whose energy exactly matches the gap between two electron energy levels. Molecules work the same way, but they have more than one kind of energy: besides the energy of their electrons, molecules are always vibrating and rotating, and those motions are quantized too, with only certain allowed energies.
For a molecule to absorb a photon, the photon’s energy, E = hν = hc/λ, must equal the gap between two of the molecule’s energy levels. Different kinds of levels have different spacings, so different regions of the spectrum do different things to a molecule.
Three kinds of levels, three regions
- Rotational energy levels转动能级 are the most closely spaced and match the lowest-energy photons, microwaves. Absorbing a microwave photon makes a molecule rotate faster.
- Vibrational energy levels振动能级 are farther apart and match infrared photons. Absorbing infrared light makes the bonds stretch and bend more vigorously.
- Electronic energy levels电子能级 are the farthest apart and match visible and ultraviolet photons. Absorbing one promotes a valence electron to a higher energy level: an electronic transition电子跃迁.
The approximate wavelength ranges below come from Wikipedia, “Electromagnetic spectrum”, and the energies per mole of photons are calculated from E = hcN_A/λ. The regions have no sharp edges; visible light, for example, is often given as 380–750 nm.
| Region | Approximate wavelength | Energy per mole of photons | Effect on a molecule | Example |
|---|---|---|---|---|
| Microwave | 1 mm – 1 m | about 0.0001 – 0.12 kJ/mol | Rotation | A microwave oven heating the water in food |
| Infrared | 700 nm – 1 mm | about 0.12 – 171 kJ/mol | Vibration | CO₂ absorbing infrared radiation from the ground |
| Visible | 400 – 700 nm | about 171 – 299 kJ/mol | Electronic transitions | The violet color of iodine vapor |
| Ultraviolet | 10 – 400 nm | about 299 – 1.2 × 10⁴ kJ/mol | Electronic transitions (the most energetic can also break bonds or ionize) | The ozone layer absorbing the Sun’s ultraviolet light |
Typical covalent bond energies are a few hundred kJ/mol (the average H–Cl bond energy is 431 kJ/mol). Microwave and infrared photons come nowhere near breaking a bond or promoting an electron. Higher-energy ultraviolet light and X-rays can even knock electrons out of molecules and atoms, which is how photoelectron spectroscopy works (U1.6).
Drag the wavelength to see the photon energy and what it does to an HCl molecule, then switch to the second mode to compare with :
Region boundaries from Wikipedia, “Electromagnetic spectrum”; the regions have no sharp edges. The molecule shown is HCl.
Why some substances are colored
White light contains every visible wavelength. If a substance absorbs some of them, the rest is transmitted or reflected, and that mixture is the color we see. So the color we see is the light that is not absorbed, roughly the complement of the absorbed color.
- The electronic energy levels of are fairly close together, so some visible photons have just the right energy and are absorbed to promote an electron. The remaining light together looks violet.
- The electrons in are held very tightly by the triple bond, so its electronic levels are far apart. No visible photon has enough energy; only ultraviolet light is absorbed. All visible light passes through, and is colorless.
Most colorless substances (, , ) have electronic transitions only in the ultraviolet.
Spectra: which wavelengths are absorbed
An absorption spectrum吸收光谱 shows how much light a substance absorbs at each wavelength. Absorption peaks appear where the photon energy matches an energy gap:
- Infrared spectra have peaks from bond vibrations. Bonds such as O–H and C=O absorb in characteristic wavelength ranges, so an infrared spectrum shows which bonds a molecule contains.
- Ultraviolet–visible spectra have peaks from electronic transitions. The wavelength of strongest absorption is called λmax; in U3.13, solution concentrations are measured at λmax.
Example 1: Can an infrared photon break a bond?
A molecule absorbs radiation of wavelength 5.0 μm. Find the energy of one photon and of a mole of photons, decide what change it causes in the molecule, and decide whether it can break an H–Cl bond (431 kJ/mol).
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Convert units and identify the region. λ = 5.0 μm = 5.0 × 10⁻⁶ m, between 700 nm and 1 mm, so it is infrared.
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Energy of one photon.
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Energy of a mole of photons. Multiply by Avogadro’s number and convert to kJ:
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Compare with the bond energy. 24 kJ/mol is only about 1/18 of the H–Cl bond energy (431 kJ/mol), so it can’t break the bond or excite an electron.
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Conclusion. This energy matches the spacing of molecular vibrational levels, so absorbing it makes the bonds vibrate more strongly, which is the basis of infrared spectroscopy.
Example 2: The colors of I₂ and N₂
vapor is violet, while is colorless. Explain in terms of electronic energy levels.
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Where color comes from. A substance absorbs part of the visible light, and the light left over gives the color we see. Absorbing visible light requires an electronic transition, and only when the energy gap matches the photon energy.
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The energy range of visible photons. Wavelengths of 400–700 nm correspond to about 171–299 kJ per mole of photons.
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Compare the two molecules.
- : its electronic energy gap is smaller and falls within the energy range of visible photons, so it absorbs some visible light (mainly yellow-green) and the rest looks violet.
- : its gap is larger than the energy of any visible photon, so it absorbs only ultraviolet light, lets all visible light through, and is colorless.
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Note. The reason is whether the energy gap matches the photon energy, not molecular size or physical state.
- 12 cm microwaves in a microwave oven
Microwaves match rotational levels.
- Radiation with a wavelength of 10 μm
Infrared, which matches vibrational levels.
- Radiation with a wavelength of 250 nm
Ultraviolet, which can promote valence electrons.
- A solution absorbing 600 nm orange light
Absorbing visible light means an electronic transition.
- CO₂ absorbing infrared radiation from the ground
Infrared light makes bonds vibrate more vigorously.
- Radiation with a frequency of 2.4 × 10¹⁰ Hz
λ = c/ν = 1.25 cm: a microwave.
- Iodine vapor absorbing green light
Visible light causes electronic transitions.
- Radiation with a frequency of 3.0 × 10¹³ Hz
λ = c/ν = 10 μm: infrared.
- A sunscreen molecule absorbing 300 nm light
Ultraviolet light causes electronic transitions.
- Radiation with a wavelength of 3.0 mm
A microwave.
- Using an infrared spectrum to check for O–H bonds
Each kind of bond absorbs at its own infrared wavelengths as it vibrates.
Common mistakes
Mistake 1: “Infrared light breaks chemical bonds.” A mole of infrared photons carries at most a little over a hundred kJ, and usually only a few to a few tens of kJ, far less than typical bond energies of several hundred kJ/mol. Infrared light makes bonds vibrate more vigorously; it doesn’t break them.
Mistake 2: “Absorbing infrared light promotes an electron to a higher level.” Electronic levels are far apart and need ultraviolet or visible photons. Infrared light matches vibrational levels.
Mistake 3: “A substance’s color is the color of the light it absorbs.” We see the light that is not absorbed but transmitted or reflected. Iodine vapor absorbs green light and looks violet, not green.
Quick check
Which set of matches is completely correct?
Level spacing increases from rotational to vibrational to electronic, matching photon energy that increases from microwave to infrared to visible and ultraviolet.
Iodine vapor is violet, but is colorless. Which explanation is best?
Absorbing visible light takes an electronic transition, so what matters is whether the energy gap matches the photon energy. A and B are not the reason (iodine vapor is violet too); D is wrong because vibrations match infrared light.
A gas-phase molecule absorbs radiation with a wavelength of 4.3 μm. What most likely happens?
4.3 μm is infrared, which matches vibrational levels. B: infrared photons carry far less energy than a bond; C: electronic transitions need ultraviolet or visible light; D: rotation matches microwaves.
Which list is in order of increasing photon energy?
E = hc/λ: the shorter the wavelength, the higher the energy. From longest to shortest wavelength: microwave, infrared, visible, ultraviolet.
What is the energy of a mole of photons of 300 nm ultraviolet light?
E = hc/λ = (6.626 × 10⁻³⁴)(3.00 × 10⁸) ÷ (3.00 × 10⁻⁷) = 6.63 × 10⁻¹⁹ J per photon; multiplying by 6.022 × 10²³ gives 3.99 × 10⁵ J/mol = 399 kJ/mol. A is one photon, in the wrong unit; B and D convert between J and kJ incorrectly.
A solution looks blue. Which visible light is it most likely absorbing?
The color we see is the light not absorbed, roughly the complement of the absorbed color, and the complement of blue is orange. A is Mistake 3; C and D aren't visible light, so they don't affect the color we see.
AP-style free response
A colorless gas-phase molecule X is exposed to three kinds of radiation in turn: (1) λ = 1.0 cm; (2) λ = 10. μm; (3) λ = 250 nm.
(a) Identify the region of the electromagnetic spectrum for each kind of radiation, and the main change each causes in X.
(b) Calculate the energy of one photon of radiation (3).
(c) A student claims, “The sample got warmer under radiation (2), so radiation (2) broke bonds in X.” The weakest bond in X has a bond energy of about 350 kJ/mol. Use a calculation to evaluate the claim.
(d) Explain why X is colorless, in terms of electronic energy levels.
Model answer and scoring
(a) (1) Microwave: the molecule rotates faster. (2) Infrared: the bonds vibrate more vigorously. (3) Ultraviolet: a valence electron is promoted to a higher energy level.
(b)
(c) Energy per mole of photons = hcN_A/λ = (6.626 × 10⁻³⁴)(3.00 × 10⁸)(6.022 × 10²³) ÷ (1.0 × 10⁻⁵) J/mol = 1.2 × 10⁴ J/mol = 12 kJ/mol, far less than 350 kJ/mol, so no bonds can break. The claim is wrong: the infrared light makes the bonds vibrate more vigorously, raising the energy of the molecules so the sample warms, but the bonds stay intact.
(d) The gaps between the electronic energy levels of X are larger than the energy of any visible photon, so no visible light is absorbed; it all passes through, and X looks colorless (it absorbs only ultraviolet light).
Scoring: (a) all three regions and changes correctly matched; (b) 7.95 × 10⁻¹⁹ J; (c) about 12 kJ/mol compared with the bond energy, and the warming explained by increased vibration; (d) the energy gap is larger than the energy of visible photons.
Summary
- Molecular energy is quantized: rotational levels are the closest together, vibrational levels farther apart, and electronic levels farthest apart. A photon is absorbed only if its energy matches a gap.
- Microwave: rotation; infrared: vibration; visible and ultraviolet: electronic transitions. The most energetic ultraviolet light can also break bonds or ionize molecules.
- Infrared photons carry far less energy than a bond; they neither break bonds nor promote electrons.
- A substance is colored when its electronic transitions absorb part of the visible light; we see the light that is not absorbed. Iodine vapor is violet; is colorless.
AP tip: When asked what a kind of radiation does to a molecule, first find the region from the wavelength or frequency, then state the matching change: microwave, rotation; infrared, vibration; ultraviolet or visible, electronic transitions. “Infrared light breaks bonds” and “infrared light causes electronic transitions” are favorite wrong answers.