A neon sign glows red-orange for one reason: its electrons can only fall between fixed energy rungs, and each fall spits out a photon of one exact color. The Bohr model pictures the hydrogen atom as a tiny solar system — one electron circling the nucleus in shells numbered 1, 2, 3, and so on — and it nails the two numbers that matter. The radius of shell n equals the Bohr radius times n squared (r = a₀n², with a₀ ≈ 5.29 × 10⁻¹¹ meters), and the energy of shell n equals negative 13.6 electron-volts divided by n squared.

Because radius grows with n², the shells spread out fast: shell 2 sits four times farther out than shell 1, shell 3 nine times farther. That spreading is why hydrogen's spectral lines crowd together toward the blue end — the famous Balmer series that makes nebulae glow pink in telescope photos.

This calculator handles the radius multiplication at the model's heart. Type the Bohr radius (0.0000000000529 meters, or 0.529 angstroms) in the Variable A box, and the shell number squared in the Variable B box — for example, 9 for the third shell. The Result box gives the orbit radius, the actual size of that electron shell in meters.

With the pre-filled defaults — Variable A 10, Variable B 5 — the Bohr Model Calculator returns Result 50.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.