Atomic energy level diagrams

Radon energy level diagram

Energy levels and transitions of neutral radon (Rn I): the 10 strongest classified lines below 2 µm from the NIST Atomic Spectra Database and the 11 levels they connect, each line with its vacuum wavelength, frequency and, for 0 of them, the reduced dipole matrix element derived from the NIST transition rate. Measured lifetimes, transition rates, hyperfine constants and isotope shifts from the literature are included, each with its citation.

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Radon energy level diagram with transition wavelengths and dipole matrix elements

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Key transitions of radon

Transitionλ vac (nm)λ air (nm)ν (THz)|⟨J‖er‖J′⟩| (ea₀)A (s⁻¹)Γ/2π up. (MHz)branch (%)Use
2[3/2]°2 – 2[5/2]3745.2048744.9996402.2954––––the line of the only laser-spectroscopy study of radon: c…

λ, ν from NIST level energies unless a measured frequency for this isotope is available. A: measured value or NIST. Γ/2π: natural linewidth of the upper level, 1/(2πτ).

221Rn hyperfine structure (I = 7/2)

LevelA (MHz)B (MHz)Shift of each F level from the centre of gravity (MHz)
2[3/2]°2-18.4(6)2184(4)F=3/2: +1335.81 F=5/2: +314.64 F=7/2: -568.91 F=9/2: -768.74 F=11/2: +417.30
2[5/2]3-3.8(4)2082(6)F=1/2: +1166.25 F=3/2: +788.75 F=5/2: +258.75 F=7/2: -275.00 F=9/2: -604.25 F=11/2: -461.25 F=13/2: +481.25

Measured A, B constants; sources in the data file.

Closed and nearly closed transitions of radon

Transitionλ vacuum (nm)Lower levelA (s⁻¹)Leak per scattered photonPhotons before a leakWhere the leak goes
1S0 → 2[3/2]°1178.6064ground–closed–no other level can be reached by electric-dipole decay
2[3/2]°2 → 2[5/2]3745.2048metastable–closed–no other level can be reached by electric-dipole decay

A transition is closed when its upper level can decay only to the level it was excited from, so the atom keeps scattering photons. “closed”: among the levels NIST lists, no other level below the upper level has the opposite parity and |ΔJ| ≤ 1, so no other electric-dipole decay exists. Otherwise the leak is the sum of the branching ratios of the other decay lines of the upper level (or 1 − branching ratio where that of the line itself has been measured), and the number of photons is 1 / leak. “≥” and “≤”: at least one possible decay path has no listed rate, so the leak is a lower limit. These numbers are derived from the branching ratios, lifetimes and rates of this page, not measured as such; the tag names the weakest of the inputs, * marks theory and ≈ a model or semi-empirical calculation. Listed: lines that start on the ground level or on a metastable level and leak at most 10 %, unless more than three possible decay paths have no listed rate. Fine-structure levels only: hyperfine and Zeeman dark states and forbidden decays without a listed rate are not considered. Select a line in the diagram for the full list of its leak channels.

Listed Rn transitions below 2 µm

Lower levelUpper levelλ vacuum (nm)λ air (nm)ν (THz)Type|⟨J‖er‖J′⟩| (ea₀)A (s⁻¹)Branching (%)Source of matrix element / A
1S02[1/2]°1145.1561–2065.3104E1––––
1S02[3/2]°1178.6064–1678.5089E1––––
2[3/2]°22[5/2]3435.0819434.9596689.0484E1––––
2[3/2]°22[3/2]2705.7372705.5427424.7933E1––––
2[3/2]°12[1/2]0727.0110726.8107412.3630E1––––
2[3/2]°22[5/2]3745.2048744.9996402.2954E1––––
2[3/2]°12[3/2]2781.1951780.9802383.7613E1––––
2[3/2]°12[3/2]1810.1712809.9485370.0359E1––––
2[3/2]°22[5/2]2827.3228827.0955362.3645E1––––
2[3/2]°22[1/2]1860.2432860.0069348.4973E1––––

Reduced dipole matrix elements follow the convention A = ω³|d|²/(3πε₀ħc³(2J′+1)), with J′ the upper level. Tags show where a number comes from: measured, NIST compilation, high-accuracy theory, or a model calculation.

Rn energy levels

LevelEnergy (cm⁻¹)JParityLifetimegJHyperfine A (MHz)Hyperfine B (MHz)Lifetime sourceHyperfine source
1S00.0000evenstable–––––
2[3/2]°254620.3502odd––-18.42184.4–Borchers, Neugart, Otten, Duong, Ulm, Wendt and the ISOLDE Collaboration, Hyperfine Inter…
2[3/2]°155989.0301odd––––––
2[1/2]166244.9701even––––––
2[5/2]266707.5302even––––––
2[5/2]368039.4803even––-3.752082.5–Borchers, Neugart, Otten, Duong, Ulm, Wendt and the ISOLDE Collaboration, Hyperfine Inter…
2[3/2]168332.1001even––––––
2[3/2]268789.9302even––––––
2[1/2]°168891.3401odd––––––
2[1/2]069743.9800even––––––
2[5/2]377604.5303even––––––

Rn⁺ ionisation limit 86692.50 cm⁻¹ = 10.74850 eV (115.350 nm)

Sources

Radon is the least-studied of these atoms: apart from the classical emission spectra there is a single collinear-laser-spectroscopy study (ISOLDE, published 1987) on the 745 nm line, whose hyperfine constants were read in the third pass (2026-10-02) from the CERN preprint scan of the conference paper (data/literature/pdf/Rn_Borchers_1987.pdf); its isotope shifts exist only as a graph. Nuclear spins, half-lives and moments are taken from the IAEA table; moments printed there for even-even isotopes belong to isomers and were left out. The site's default isotope (222Rn) has I = 0, so no hyperfine structure applies to it.

Atoms with measured data

All elements: periodic table