Atom Spectrum

Atoms · light · sound

Every atom is a chord.

The emission lines of hydrogen to uranium, brought down forty octaves to the ear. A line is a frequency of light; divided by 2⁴⁰ it is a note, and the lines of an element sound together as the chord they are. Atom Spectrum plays that chord and takes it apart: which notes, which intervals, how rough, what pitch the ear settles on, and which levels each line fell between.

  • · 92 elements
  • · 203 100 lines
  • · 61 364 levels
  • · stages I to III
  • · nothing to install
Open it in your browser Hear sodium

· Sound starts with your first click or key: a browser waits for you to do something

Atom Spectrum on sodium in the dark theme: the periodic table on the left with Na chosen; on the right the audio spectrum, fifteen partials with the D line at 589.16 nm sounding at 462.8 Hz, and under it the Levels page, a Grotrian diagram of the 2S, 2P, 2D and 2F terms with the lines drawn between them in their own colours, the D line in orange.

Real screens. NIST's lines.

Every picture on this page is Atom Spectrum drawing its own window — headless, through its own test agent, at twice its size — or running in a browser tab. Every line in them is one the NIST Atomic Spectra Database lists, with its wavelength, its transition probability and the two levels it runs between. Nothing is drawn for effect.

Stages I to III of 92 elements, 203 100 lines and 61 364 levels, are packed into the program itself, so once it is open it needs no connection.

Hear it

Forty octaves down, every ratio kept.

Dividing every frequency by the same power of two keeps every interval between them. The visible octave, 384 to 789 THz, lands at 350 to 720 Hz; the ear's ten octaves take in 13.6 µm to 13.6 nm. A line that lands outside hearing is counted in the status line, not played, and never quietly folded back in.

A lamp of the element,
as loud as it shines.

  • Loudness from the gas. Each line is as loud as a unit volume of the gas radiates through it at 6000 K: abundance, stage fraction, g·A, the Boltzmann factor, and the partition function summed over every level NIST lists. Or NIST's own intensities, g·A, or every line alike.
  • Stages by Saha. The temperature and the electron density set how much of the element is neutral, singly or doubly ionised, and the gas sounds as that mixture: below about 5000 K iron is Fe I, above it Fe II. Or hear one stage alone.
  • Chords of elements. ⌘- or Ctrl-click, Shift+Enter or m adds an element, balanced by equal numbers of atoms or by the Sun's photospheric abundances.
  • The line's shape, heard. The Doppler width at that temperature, exaggerated as you like, played as slow frequency modulation. A flash empties every level at its lifetime, stretched from nanoseconds to seconds: strong lines vanish first and metastable ones linger.
  • Taken apart. Each partial's note and cents; the intervals between the loudest twelve and the just ratios they approach; Plomp–Levelt roughness; the dissonance curve of the atom against itself; the pitch the ear settles on; and the sound's live spectrum, spectrogram, scope and meter.
atomspectrum.dopecode.com/app/
Atom Spectrum in a browser, hydrogen sounding: seven partials of 535 lines, Lyman alpha at 121.57 nm loudest at 2.243 kHz, and the Sound page under it showing the live spectrum of what the loudspeaker plays, its tallest peak at 2.2 kHz.
Hydrogen, sounding: Lyman α at 2.243 kHz, and the live spectrum of what the loudspeaker plays
HydrogenLyman α at 2.243 kHz leads seven partials/app/?H Sodium's levelsThe D line at 589 nm, 462.8 Hz, and the levels it falls between/app/?Na+I&tab=levels Iron's harmony48 partials of 29 204 lines: intervals, roughness, the pitch the ear hears/app/?Fe&tab=harmony Iron as lightThe same lines on the whole electromagnetic spectrum/app/?Fe&tab=em Hydrogen's oscillators535 lines as the beats of 105 oscillators in 40 layers/app/?H&tab=oscillators The periodic tableRead back out of the tables: rows, blocks, Madelung's order/app/?tab=table

The page's query is the program's command line: an element by symbol, name or number, a stage, and tab= a page (settings, sound, lines, harmony, levels, atom, table, method) or a view of the spectrum (audio, em, oscillators).

See it

The same lines, as light.

The spectrum has three views. The audio spectrum is what you hear. The EM spectrum is the same lines on the whole electromagnetic spectrum, nineteen decades of frequency from radio to gamma, with the optical window under it from 10 nm to 1 mm in its ISO 21348 bands.

Atom Spectrum on iron in the dark theme: the EM spectrum view, radio to gamma above and the optical window from 1 mm to 10 nm below, iron's lines dense from the infrared to the extreme ultraviolet with the visible band in colour; under it the Lines page, a table of the sounding lines with wavelength, frequency, photon energy, note, level, weight, transition probability and transition.
Iron's 29 204 lines as light, and the ones that sound in the table under them

Every line,
read as light.

  • Hover a line and it reads as light: vacuum wavelength (and the air one, where NIST would quote it), frequency, photon energy, wavenumber, band, the transition with its probability A and NIST's accuracy grade of it — and then where it sounds.
  • In vacuum, everywhere. NIST quotes 200 to 2000 nm in air; the packer converts with Peck and Reeder's index, as NIST does, so c / λ is the line's frequency and the chord is exact.
  • In its own colour. Every line is drawn in the CIE 1931 standard observer's colour at its wavelength.
  • Zoom and pan the optical window with the wheel, = - and H L, or drag a span above.

The atom

The levels, against the laws found in them.

The Atom page is the other analysis: of the atom rather than the sound. Each line of its summary opens the table it was made from, sortable by any column and following the element.

Count the states.
Report every residual.

  • Hund's rules against the ground level, and every configuration's state count against the levels NIST has placed.
  • Ritz's combination principle over every observed line, and the Rydberg series of one running electron, with each member's quantum defect.
  • Landé's interval rule and g factors against LS coupling; hydrogen, He II and Li III against the Dirac equation with the reduced mass and recoil, whose residual is the Lamb shift.
  • Selection rules for every line by its multipole: intercombination and ΔL lines counted, not hidden.
  • Isoelectronic sequences: each level along its sequence, and its screening. Constants are CODATA 2022.
Atom Spectrum's Atom page for Fe II in the light theme: 1027 levels and 14471 lines, Hund's rules predicting the 6D 9/2 ground level NIST lists, iron's place on the chart and its ionisations, and a table of states per configuration with how many NIST has placed.
Fe II: Hund's rules agree with NIST's ground level; 8208 of 39 264 states placed

The periodic table,
counted from the tables.

  • Rows and blocks counted from the ground configurations alone: 2, 8, 8, 18, 18, 32, and s, p, d, f as 2, 6, 10, 14.
  • Madelung's n + l order against every ground configuration: seventeen atoms break it, chromium to uranium.
  • Which electron goes first. The d-block loses its s electron, not the d Madelung filled last.
  • Every dip of the first ionisation energy along a row, with its cause, and every rise down a column: the lanthanide contraction and relativity, silver to gold by 1.6 eV.
Atom Spectrum's Table page in the light theme: the chart counted from the tables, rows of 2, 8, 8, 18, 18, 32 and 6 elements from hydrogen to uranium, with their s, p, d and f blocks, against the 2n² the counting gives.

Oscillators

Which oscillators make the lines?

A level is an oscillator at E/h and a line is the beat of two, as a ring modulator makes it: hydrogen's 535 lines need 105 oscillators in 40 layers. The third view of the spectrum fits that bank without assuming the answer.

Atom Spectrum's Oscillators view for hydrogen in the dark theme: the ladder of NIST's levels against the bank's rungs by s, p, d and f; NIST's lines above the bank's beats from 1 GHz to 1 PHz; every line's residual, most within the dashed tolerance of one part in a million; and below, the ladder, momentum and wave-speed instruments with their switches and sliders.
Hydrogen: 390 of 535 lines within one part in a million of a bank of 105 oscillators

Five instruments,
tuned by the lines.

  • A ladder of layers: harmonic n, a box's n², a power law with its exponent free, or Coulomb's 1/n².
  • Momentum that moves a layer: quantum defects, spin–orbit by Dirac with α, the nucleus' recoil, the vacuum's Lamb shift, the electron's own moment.
  • Wave speed and c, gears (every line a master frequency times p/q) and sidebands (a hidden oscillator at F would put lines at ν ± F).
  • Tuned automatically by weighted least squares in hertz, the best ladder kept by the Bayesian information criterion; Blind does it without NIST's labels.
  • Hear NIST, the bank, or both at once: where they disagree, they beat.
on hydrogenthe bank finds
the power law's exponentp = 1.999 999, by itself
the median linewithin 5 × 10⁻⁸
the proton, from the recoil1836.0 electron masses
the 1s Lamb shift8.0 GHz
the electron's anomalous moment(1.151 ± 0.023) × 10⁻³

Two gases

A discharge lamp, or a nebula.

The default gas is a lamp of the element at 6000 K and 10²⁰ electrons per m³, in local thermodynamic equilibrium. Press t and it is an H II region or a planetary nebula instead: a thousand electrons per cm³, lit by a star, where nothing is in equilibrium.

Lit by a star,
level by level.

  • Photoionised by the star's blackbody through Verner's cross-sections, recombining at the tabulated rates: oxygen is O⁺ under a B star and O⁺⁺ under an O star.
  • Each level holds what feeds it over what drains it — collisions from the ground term, recombination with its cascade — and above its critical density its forbidden lines are quenched.
  • Hydrogen sings its Balmer decrement from recombination alone, Hα : Hβ : Hγ = 2.7 : 1 : 0.5 (2.86 : 1 : 0.47 in case B), and [O III] 5007 leads the chord at low density and vanishes at high.
Atom Spectrum on oxygen as a nebula in the dark theme: 80 % O III, the EM spectrum view of 3545 lines from the microwave to the extreme ultraviolet, and the Settings page with the regime set to Nebula (photoionised), the frequency mapping, the line strength and the line profile controls.
Oxygen as a nebula: 80 % of it O⁺⁺, its lines from the microwave to the extreme ultraviolet

Keys

Every control from the keyboard.

Vim's motions, dired's marks and readline in the element field. The control that has the keyboard hears a key first, so a plain letter is safe: the periodic table walks its cells, a slider keeps its arrows.

Space
Play and stop; Enter strikes
[]
The previous and the next element
/
An element by symbol, name or Z
hjkl
Walk the table, the rows, the lines
muU
Mark into the chord, unmark, unmark all
v
The next view: audio, EM, oscillators
t
An LTE gas or a nebula
1…8
Settings, Sound, Lines, Harmony, Levels, Atom, Table, Method
E
Export a WAV
?
Every key, as bound
  • Every key is a named action. ? lists what is active, and on the desktop a [keybindings] table in config.toml replaces the defaults per action.
  • Motion for the control that has the keyboard: g G to the ends, Ctrl+u Ctrl+d ten rows at a time, Enter to choose or to solo a line.
  • The element field takes readline: Ctrl+a Ctrl+e, Alt+b Alt+f, Ctrl+k Ctrl+u Ctrl+w.
  • Light or dark as your system is; F2 switches.
  • Accessible: every control has a name a screen reader says, and the accessibility audit is part of its tests.

Where the numbers come from

Every input named, with its source.

Nothing measured about an atom is exact. What can be exact is the bookkeeping: every number carries its source and its uncertainty, and every result is reported against the measurement it is compared with.

sourcewhatused for
NIST ASDKramida, Ralchenko, Reader and the ASD Teamevery line of stages I to III at any wavelength, in vacuum; their levels; the ionisation energiesthe chord, the light, the levels, the Atom and Table pages
Verner et al.1996photoionisation cross-sections and recombination ratesthe nebula's ionisation balance
Asplund et al.2009the Sun's photospheric abundancesbalancing a chord of elements
CODATA 2022R∞, α, the masses of the electron and the protonDirac, recoil, the oscillators
the 2019 SIc, h, e, kB, exactlyevery conversion

Lines with neither a strength nor two known levels are dropped. Atom Spectrum is not affiliated with NIST.

Privacy, itemised

Claims you can check.

The specific version, phrased so that you could go and verify it. The formal version is DopeCode's privacy policy.

what it sends
Nothing. No analytics, no crash reporter, no network of its own. The page downloads the program from this site, about 11 MB, and then talks to no one: the NIST tables are inside it.
what it hears
Nothing. It only plays. The page is not allowed the microphone, the camera or MIDI at all.
what it keeps
Nothing. No account and no cookies, and nothing in your browser's storage: every visit starts from the defaults.
what it makes
An exported WAV names Atom Spectrum <version> as its producer, and nothing about you or your machine.

The honest part

What it does not do.

Better read here than found out afterwards.

Not in Atom Spectrum

  • It measures no light. It reads NIST's tables; there is no spectrometer behind it.
  • Equilibrium is an assumption. The lamp is fair for a dense discharge or a photosphere and poor for anything thinner; the nebula is its own model, the coronal approximation, and an approximation too.
  • Stages I to III only. A highly ionised plasma — the Sun's corona — is not here.
  • The command-line analyses stay on the command line: the measured line lists behind NIST, blind level discovery, King plots and hydrogen's constants from its measurements are atom-analyse's, not the window's.

Where the browser gets in the way

Sound waits for you. A page may not make a sound before you have done something on it, so the sound starts with your first click or key.

The sound is made on the page's own thread, beside the drawing, so on a slow machine or in a busy tab a dense chord can stutter where the desktop window would not.

The keys are the defaults: the config.toml that rebinds them is the desktop's. Export WAV is a download.

Help

The questions people ask.

There is no sound.

Click anywhere on the page or press a key first: browsers wait for you to do something before a page may play. Then Play (Space); the status beside the element's name says sounding. If it does and you hear nothing, check that the tab is not muted.

Why does an element play so few notes?

By default a line is as loud as the gas radiates it, and in most atoms a handful of lines carry nearly all of it; others land outside hearing forty octaves down. The status line counts both. Under Settings, Stretched spreads the lines over the octaves you choose, and a line strength of Flat makes every line alike.

Can I link to an element?

Yes: the page's query is the command line. /app/?Fe+II&tab=lines opens iron's first ion on the table of lines; an element can be a symbol, a name or an atomic number, and tab= any page or view.

Is the browser version the whole program?

It is the same program as the desktop window, built for WebAssembly: every page, every view, every key. It needs WebAssembly and WebGPU or WebGL2, which current browsers have, and about 11 MB the first time.

Can I keep the sound?

Export WAV (E) renders four seconds of the chord — six with the flash — as a stereo WAV, which the browser downloads.

Still stuck? Write to hello@dopecode.com with your Atom Spectrum version (Help ▸ About) and what it said.

In your browser

Hear an atom.

Atom Spectrum opens on hydrogen. Press Play, then ] for the next element, and hear the periodic table one atom at a time.

Open it in your browser Hear neon

· Questions first? Help answers the common ones.