The atom that comes in steps. In the Bohr model of hydrogen an electron can only sit in fixed orbits, each with a definite energy En = −13.6/n² — never in between. Move it up to an excited level, then let it fall: it releases the energy as a single photon of wavelength λ = 1240/ΔE, and that light lands as a coloured line on the emission spectrum below. Drop electrons to level 2 and the famous red, cyan and violet Balmer lines of hydrogen appear one by one. It all runs on your device.
Orbit radius ∝ n² — set two levels, then emit or absorb
Balmer visible lines:
Transitionn=3 → n=2 (emission)
E(nᵢ)−1.51 eV
E(n_f)−3.40 eV
Photon ΔE1.89 eV
Wavelength λ656.5 nm
Frequency4.57×10¹⁴ Hz
SeriesBalmer
ColourVisible · red
Fixed levels in, one colour out. Hydrogen's electron is only allowed energies En = −13.6/n², so the gaps between levels come in fixed sizes. When the electron drops from a higher level to a lower one it emits a photon carrying exactly that gap, ΔE = 13.6(1/nlow² − 1/nhigh²), which fixes its wavelength through λ = 1240/ΔE. That is why each element shines with its own set of sharp spectral lines — and why the jumps to level 2 paint hydrogen's visible Balmer series in red, cyan and violet.
Reading the simulation
What the orbits, the travelling photon and the two diagrams are telling you.
1
The orbits grow as n²
On the left, each ring is an allowed Bohr orbit and its radius follows the real relation rn = n²·a₀ — so level 2 sits four times farther out than level 1, level 3 nine times, and so on. The orange ring is your initial level ni, the indigo ring your final level nf, and the blue dot is the electron. Move the two sliders and watch which rings light up.
2
A jump moves a photon
Press the action button and the electron slides from ni to nf. If it drops (nf below ni) it emits a photon that flies outward; if it climbs it absorbs one that flies inward. The photon is drawn as a travelling wave whose colour is set by the energy gap ΔE — true spectral colours in the visible range, and a muted tint labelled UV or IR when the line falls outside it.
3
The diagram and spectrum place the line
On the right, the energy-level diagram stacks the levels at En = −13.6/n² — crowding toward 0 eV at the top — and draws the jump as an arrow (down for emission, up for absorption). Under it, a 380–740 nm strip shows where a visible line lands, or flags it as UV/IR. The lower spectrum keeps every line you make, so pressing Balmer series paints hydrogen's red, cyan and violet fingerprint at once.
How It Works
Quantised orbits, a jump between them, and a photon whose colour is set by the gap.
1
Only certain orbits are allowed
Bohr's rule is that the electron can occupy only special orbits, numbered n = 1, 2, 3…, each with a fixed energy En = −13.6/n² electron-volts. Level 1 is the tightest and lowest; higher levels crowd together near zero. The electron can never sit between them, so the atom's energy is quantised — the energy-level diagram labels each level with its energy.
2
A jump exchanges a photon
As the electron moves between nhigh and nlow it exchanges the energy difference ΔE = 13.6(1/nlow² − 1/nhigh²) as a single photon — emitting it on the way down, absorbing it on the way up. Because that energy is fixed, so are the colour and pitch: the wavelength is λ = 1240/ΔE nanometres and the frequency f = ΔE·e/h, the same relation as the Rydberg formula.
3
The lines build a spectrum
Every photon lands as a coloured line on the spectrum at its wavelength. Jumps to level 1 (the Lyman series) sit in the ultraviolet; jumps to level 2 (Balmer) fall in the visible as the red 656 nm, cyan 486 nm and violet lines; jumps to level 3 (Paschen) are infrared. Press Lyman, Balmer or Paschen series to emit a whole series at once and watch that fingerprint appear.
What is the Bohr model of the atom?
The Bohr model, proposed by Niels Bohr in 1913, pictures the electron in a hydrogen atom as orbiting the nucleus only in certain allowed orbits, each with a fixed energy En = −13.6/n² electron-volts. The electron cannot exist between these levels. It can jump to a higher level by absorbing exactly the right amount of energy, and it falls back down by emitting a photon whose energy equals the gap between the levels. This quantisation explains why atoms emit and absorb only specific colours of light.
Why do atoms emit only certain colours of light?
Because the energy levels are quantised, the gaps between them come in fixed sizes, and each gap corresponds to one photon energy — and therefore one wavelength, from λ = 1240/ΔE with ΔE in electron-volts. An electron dropping from level 3 to level 2 in hydrogen always releases 1.89 eV, giving the red 656 nm line, no matter which atom it is. The full set of allowed jumps produces the atom's line spectrum, a barcode of colours unique to each element.
What is the Balmer series?
The Balmer series is the set of hydrogen transitions that end on level n = 2. These are special because they fall in the visible range: the 3→2 jump gives the red Hα line at 656 nm, 4→2 the blue-green Hβ at 486 nm, and 5→2 and 6→2 the violet lines at 434 and 410 nm. Jumps that end on level 1 (the Lyman series) are ultraviolet, and those ending on level 3 (Paschen) are infrared. Press "Balmer series" in this tool to emit all four visible lines at once.
How do you calculate the wavelength of a spectral line?
First find the photon energy, ΔE = 13.6 (1/nlow² − 1/nhigh²) electron-volts, the gap between the two Bohr levels. Convert it to a wavelength with λ = 1240/ΔE (nanometres), or to a frequency with f = ΔE·e/h. This is equivalent to the Rydberg formula 1/λ = R(1/nlow² − 1/nhigh²). This simulator does every step for you: it draws the jump as an arrow on the energy-level diagram — down for emission, up for absorption — and marks the resulting line on a 380–740 nm spectrum.
A ready-to-assign lab using the simulation above. Free to use — nothing to install or sign up for, and no student data leaves the browser.
High school, College10–20 minInteractive simulation
Learning objectives
Explain quantized energy levels in the hydrogen atom.
Relate electron transitions to emitted or absorbed photons.
Connect transitions to spectral lines.
Variables to change
Initial energy level
Final energy level
Procedure
Excite the electron to a higher level and watch it drop back.
Record the photon (color/wavelength) emitted for different transitions.
Compare transitions ending on n=2 (visible series) with others.
Observations
Record which transitions emit visible light and how photon energy relates to the size of the energy jump.
Questions
Why are only certain energies allowed?
What determines the energy of an emitted photon?
Which transitions produce visible light in hydrogen?
What happens when the electron absorbs a photon?
Why is the ground state (n=1) the most stable?
Explanation
In the Bohr model the hydrogen electron occupies quantized levels E_n = −13.6/n² eV. Dropping between levels emits a photon of energy equal to the gap (E = hf); the specific gaps produce the discrete spectral lines, with n→2 transitions giving hydrogen’s visible Balmer series.
Answer key (for instructors)
1. The Bohr model quantizes the electron’s orbits, so only discrete energy levels E_n = −13.6/n² eV exist.
2. The difference between the two levels: E_photon = E_high − E_low = hf.
3. The Balmer series — transitions ending at n = 2.
4. It jumps to a higher level, but only if the photon’s energy matches a level difference.
5. It is the lowest energy level; the electron cannot drop any lower, so it stays there unless excited.
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