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Example data table
These sample rows show typical inputs and converted outputs.
| Scenario | Input | Output highlights |
|---|---|---|
| Photon energy | λ = 450 nm | E ≈ 2.755 eV, ṽ ≈ 22222 cm⁻¹ |
| Transition wavelength | ΔE = 3.10 eV | λ ≈ 400 nm, ν ≈ 749 THz |
| Boltzmann population | ΔE = 0.08 eV, T = 298 K, g₂/g₁ = 1 | N₂/N₁ ≈ 0.044, excited ≈ 4.2% |
| Stokes shift | λabs = 480 nm, λem = 520 nm | Δṽ ≈ 1603 cm⁻¹, ΔE ≈ 0.199 eV |
Values are rounded for readability; calculator outputs may differ slightly.
Formulas used
- E = hν, ν = c/λ, E = hc/λ
- ṽ = 1/λ (wavenumber), reported in cm⁻¹
- Per-mole conversion: E(mol) = E(photon)·NA
- Boltzmann ratio: N₂/N₁ = (g₂/g₁)·exp(−ΔE/kT)
- Stokes shift: ΔE = hc(1/λabs − 1/λem)
- Uncertainty limit: ΔE ≈ ħ/(2τ), with Δν = ΔE/h
How to use this calculator
- Select a calculation type that matches your experiment.
- Enter values and choose units from the dropdowns.
- Set precision and optional steps or history saving.
- Press Submit to show results above the form.
- Use CSV/PDF buttons to export the current run.
FAQs
1) What is an excited state?
An excited state is a higher-energy electronic configuration than the ground state. It forms after absorption of energy, often light, and relaxes by emission, heat, or chemical pathways.
2) Which unit should I use for ΔE?
Use eV for spectroscopy and electronic transitions, kJ/mol for chemistry thermodynamics, and cm⁻¹ for vibrational or optical spectroscopy. The calculator converts among them for comparison.
3) Why does refractive index affect wavelength?
In a medium, light slows down, so wavelength changes while frequency stays the same. If your wavelength is measured in a medium, the calculator estimates the vacuum wavelength using λvac = n·λ.
4) Are these results for absorption or emission?
Energy–wavelength conversions apply to both absorption and emission. Direction depends on your system: absorption uses the energy gap to climb, emission uses the gap released during relaxation.
5) How should I interpret the Boltzmann excited fraction?
It is the thermal population expected at equilibrium. For most electronic gaps at room temperature, the fraction is tiny. It becomes meaningful for small gaps, high temperatures, or large degeneracy ratios.
6) What does Stokes shift tell me?
Stokes shift measures how much emission is red-shifted from absorption. Larger shifts often indicate structural relaxation, solvent reorganization, or vibrational relaxation before fluorescence.
7) Is the lifetime linewidth exact?
It is a minimum broadening from the energy–time uncertainty principle. Real spectra also broaden from temperature, collisions, inhomogeneity, instrument resolution, and vibronic structure.
8) Can I use this for vibrational excited states?
Yes. Use wavenumber inputs for photon energy and Stokes shift, or use ΔE in cm⁻¹ in the Boltzmann model. For detailed vibrational structure, you may need a full spectral simulation.