A one-electron atom with its Bohr orbits drawn to scale, an energy ladder beside them and a visible-spectrum strip underneath. Choose a start level and an end level, set the nuclear charge, and fire the transition: the photon’s energy, wavelength, frequency and spectral series all update as you drag, and the strip shows you exactly where — or whether — the line falls in visible light.
What Is the Bohr Model Simulator?
The Bohr model simulator is a free interactive physics lab that runs in your browser — nothing to install and no sign-up. Set the start and end levels, fire the jump, and read the photon energy and wavelength live from E = -13.6/n² eV. It reports start level Ei, end level Ef, photon energy ΔE, wavelength λ and frequency as you drag the sliders.
| Control | Range | Step |
|---|---|---|
| Starting principal quantum number | 1 – 8 | 1 |
| Final principal quantum number | 1 – 8 | 1 |
| Atomic number of the hydrogen-like ion | 1 – 3 (hydrogen) | 1 |
How to Use the Bohr Model Simulator
Two sliders pick the jump. The start level is where the electron begins and the end level is where it finishes, and their order is what decides the direction: put the start above the end and the atom sheds a photon, put it below and the atom has to swallow one. The button says which of the two it is before you press it, so you never have to work the sign out yourself. If you would rather do the arithmetic by hand, the Bohr model calculator runs the same three formulas with every step written out.
The readouts are what turn this into an argument rather than an animation. Hold the end level at 2 and walk the start level up one notch at a time: the photon energy rises 1.889, 2.550, 2.856, 3.022 eV while the wavelength falls 656.4, 486.2, 434.1, 410.2 nm, and the marker on the strip slides from red towards violet. Those two columns are the same fact stated twice, because energy and wavelength are inversely related — the relationship the photon energy formula sets out in full. Keep going and the gains shrink towards nothing: the energy never reaches 3.400 eV however high you start.
The Z slider strips the atom down to a heavier nucleus with one electron still attached, so Z = 2 is He+ and Z = 3 is Li2+. Every energy in the panel is multiplied by Z2 — the 10.2 eV Lyman jump becomes 40.80 eV and then 91.80 eV — while every radius is divided by Z, which you can watch happening as the drawn orbits contract. It is the cleanest demonstration in the lab that the whole spectrum of a one-electron atom is set by a single number on the nucleus.
The ladder on the right is there to break one specific habit. Textbook diagrams tend to draw energy levels as a neat evenly spaced staircase, and students carry that picture into their answers. This ladder puts every level at its true height, and the result is nothing like a staircase: the step from n = 1 to n = 2 swallows three quarters of the whole scale, and levels 4 through 8 are all squeezed into the top six per cent below zero. That crowding is the reason the far end of every series converges on a limit instead of marching on forever, and you can see it happen without being told.
Frequently asked questions
How do I use the simulator?
Set the start level with the first slider and the end level with the second, then press the button. The button itself tells you which way the energy is going: with the start level above the end level it reads Emit photon, and with the start level below it reads Absorb photon. Watch the electron cross the gap between the two orbits while the photon ring expands or closes in, then read the energy, wavelength and frequency in the panel. The Reset button puts you back at the 3 to 2 jump in hydrogen, which is the red line you can see with your own eyes in a discharge tube.
Why does the wavelength get shorter as I raise the start level?
Because the energy gap is getting wider, and wavelength is inversely proportional to that gap. Hold the end level at 2 and step the start level up from 3: the photon energy climbs from 1.889 eV through 2.550 eV to 2.856 eV, and the wavelength falls from 656.4 nm through 486.2 nm to 434.1 nm, red to blue-green to violet on the strip. The climb slows every step, because the levels themselves are crowding together near the top. Push the start level all the way to 8 and the energy still has not reached 3.400 eV, which is the Balmer series limit and the energy of the n = 2 level itself.
What does the Z slider do?
It changes the charge on the nucleus, turning hydrogen into a hydrogen-like ion: Z = 2 is a helium nucleus holding a single electron, written He+, and Z = 3 is Li2+. It is not neutral helium or lithium, because the Bohr model only works with one electron in play. Every energy in the panel scales by Z squared, so the same jump releases four times the energy at Z = 2 and nine times at Z = 3, while every orbit radius shrinks by a factor of Z. You can watch the atom itself contract in the drawing as you slide it.
Why does the sim show no photon when both levels are equal?
Because nothing has happened. If the start and end levels match, the energy difference is exactly zero, and there is no photon to emit or absorb. The wavelength formula divides a constant by that difference, so a zero gap would be a division by zero: rather than print an infinity, the simulator shows a dash for the wavelength and the frequency, greys out the spectrum strip, and disables the button, which changes its label to No transition. Move either slider and everything comes back.
Which colours should I expect to see?
Only the Balmer series lands in visible light, which is the family of jumps that end on level 2. Those are the four lines a school spectrometer shows: red at 656.4 nm, blue-green at 486.2 nm, violet at 434.1 nm and deep violet at 410.2 nm. Everything ending on level 1, the Lyman series, is ultraviolet and far off the left of the strip. Everything ending on level 3 or higher, starting with the Paschen series, is infrared and off the right. Raising Z shifts every line to shorter wavelengths, so at Z = 2 even the Balmer lines are dragged out of the visible band.
References & formula source
- Ling, Sanny & Moebs — University Physics Volume 3 (OpenStax), section on Bohr’s model of the hydrogen atom.
- Eisberg & Resnick — Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles, chapter on Bohr’s model of the atom.
- NIST Atomic Spectra Database — hydrogen energy levels and observed transition lines.
- Further reading: Bohr model — Wikipedia