UV-Vis Converter: Wavelength, Energy, Frequency & Wavenumber

Photon energy and wavelength are reciprocals, scaled by hc. The Planck-Einstein relation E = hν = hc/λ says a 400 nm violet photon carries about 3.10 eV (or 299 kJ/mol when scaled by Avogadro's number), while a 700 nm red photon carries 1.77 eV. The factor hc = 1240 eV·nm is the only conversion to memorize for UV-Vis work. Frequency follows from the same equation as ν = c/λ, and wavenumber (cm⁻¹) is 10⁷/λ(nm). Every UV-Vis spectrum maps directly onto a ladder of electronic-transition energies.

The core relationship is E = hc/λ, where h = 6.626 × 10⁻³⁴ J·s and c = 2.998 × 10⁸ m/s. Plug in λ in meters and you get energy in joules per photon. For a single photon that's a tiny number, so chemists prefer eV (1 eV = 1.602 × 10⁻¹⁹ J) or kJ/mol (multiply single-photon energy by Avogadro's number, 6.022 × 10²³). A quick shortcut: E(eV) ≈ 1240 / λ(nm). Memorize that and you can estimate photon energies in your head during a lecture.

Common mistake: forgetting to convert nm to meters before plugging into E = hc/λ. If you leave λ in nanometers, your energy is off by a factor of 10⁹. The calculator handles unit conversion automatically, but on an exam you need to remember: 1 nm = 10⁻⁹ m. Also, energy and wavelength are inversely proportional—shorter wavelength means higher energy. UV photons carry more energy than visible light, which is why UV causes sunburn and visible light doesn't.

Frequency (ν) and wavenumber (ν̃) are two ways to express the same information. Frequency in Hz tells you oscillations per second: ν = c / λ. Wavenumber in cm⁻¹ tells you waves per centimeter: ν̃ = 1 / λ(cm) = 10⁷ / λ(nm). IR spectroscopists live in wavenumber space, but UV-Vis people usually stick with nm or eV. Still, converting between them is routine when comparing data across techniques.

The relationship between frequency and wavenumber is straightforward: ν = c × ν̃, where c is in cm/s (2.998 × 10¹⁰ cm/s). Wavenumber is directly proportional to energy: E = hcν̃. This is why IR spectroscopists like wavenumber—it scales linearly with energy, unlike wavelength (which is inversely proportional). A peak at 1700 cm⁻¹ has exactly twice the energy of a peak at 850 cm⁻¹. That linear relationship makes comparing peak energies intuitive.

For UV-Vis work, visible light spans roughly 14,300–25,000 cm⁻¹ (700–400 nm). UV extends to about 100,000 cm⁻¹ (100 nm). If a paper reports an absorption at 22,200 cm⁻¹ and you need nm: λ = 10⁷ / 22,200 = 450 nm. That's blue light absorption, so the compound appears orange (complementary color).

Knowing which spectral region a wavelength falls in tells you what kind of transition you're looking at. UV photons (100–400 nm) have enough energy to promote electrons between molecular orbitals—π→π* and n→π* transitions in organic molecules, d→d transitions in metal complexes. Visible photons (400–700 nm) do the same but for smaller energy gaps, often in conjugated systems or transition metal compounds.

Near-IR (700–2500 nm) involves overtones and combination bands of molecular vibrations. Far-UV or vacuum UV (below 200 nm) is absorbed by atmospheric O₂ and N₂, so measurements require a vacuum or nitrogen purge—hence the name. Most teaching-lab UV-Vis spectrophotometers cover 190–1100 nm, with a deuterium lamp for UV and a tungsten-halogen lamp for visible/near-IR, switching around 340–380 nm.

The UV spectrum is subdivided by biological effect. UV-C (100–280 nm) is the most energetic and is used for germicidal sterilization—DNA absorbs strongly near 260 nm, and UV-C photons cause thymine dimers that kill microorganisms. Earth's ozone layer blocks solar UV-C completely. UV-B (280–315 nm) causes sunburn and is partially blocked by ozone. UV-A (315–400 nm) penetrates deeper into skin, causes tanning and aging, and passes through window glass.

In the visible range: violet (380–450 nm), blue (450–495 nm), green (495–570 nm), yellow (570–590 nm), orange (590–620 nm), red (620–750 nm). The color you see is the complement of the absorbed color. A solution absorbing at 450 nm (blue) appears orange. Absorbing at 580 nm (yellow) appears violet. This complementary relationship is critical for interpreting UV-Vis spectra of dyes, indicators, and metal complexes.

Exam pitfall: students confuse absorbed color with observed color. If a problem says "the solution is blue," it absorbs orange light (around 600 nm), not blue. The color wheel helps: draw the visible spectrum as a circle, and the complement is directly across.

Every conversion in this calculator traces back to three fundamental constants. Planck's constant: h = 6.626 × 10⁻³⁴ J·s. Speed of light: c = 2.998 × 10⁸ m/s. Avogadro's number: Nₐ = 6.022 × 10²³ mol⁻¹. From these you derive the conversion factor hc = 1.986 × 10⁻²⁵ J·m, or equivalently 1240 eV·nm.

Other useful derived values: 1 eV = 1.602 × 10⁻¹⁹ J = 96.485 kJ/mol = 8065.5 cm⁻¹. The Boltzmann constant k_B = 1.381 × 10⁻²³ J/K gives thermal energy at room temperature: k_BT ≈ 0.026 eV at 298 K. Comparing photon energy to k_BT tells you whether a transition is thermally accessible. A 400 nm photon (3.1 eV) is 120× thermal energy—not thermally accessible, which is why electronic transitions require light, not heat.

Why do conjugated molecules absorb at longer wavelengths? More conjugation means a smaller HOMO-LUMO gap. Electrons delocalized over a larger π system need less energy to jump, so the absorption shifts to longer wavelengths (lower energy). This is why β-carotene (11 conjugated double bonds) absorbs blue-violet and appears orange, while ethylene (one double bond) absorbs in the far UV around 165 nm.

What's the difference between a nm and an Å in spectroscopy? 1 nm = 10 Å. Older literature and crystallography use Ångströms; modern UV-Vis spectroscopy uses nanometers. If a paper from the 1960s reports λ_max = 4500 Å, that's 450 nm.

Can I convert wavelength to bond dissociation energy? Only roughly. The photon energy E = hc/λ gives the minimum energy to break a bond if the molecule dissociates upon absorption. But most absorptions lead to excited states, not dissociation. The actual bond energy depends on the potential energy surface, not just the absorption wavelength.

Why does my spectrophotometer cut off below 190 nm? Atmospheric oxygen absorbs strongly below 200 nm. Standard instruments use air paths, so they can't measure in the vacuum UV. Nitrogen-purged instruments extend to about 175 nm. Below that, you need a vacuum spectrometer or synchrotron radiation.

Problem: A compound has λ_max = 450 nm. Convert this to energy in eV, kJ/mol, frequency in Hz, and wavenumber in cm⁻¹. Identify the absorbed color and predict the observed color.

Cross-check: 2.756 eV × 96.485 kJ/(mol·eV) = 265.9 kJ/mol ✓. The slight rounding difference (265.8 vs. 265.9) comes from intermediate rounding—both are correct to 4 significant figures. At 265.8 kJ/mol, this photon energy is comparable to a C–Cl bond strength (~339 kJ/mol) but well below a C–H bond (~413 kJ/mol), which is why visible light doesn't break most organic bonds.