The Bohr Model – Arc Labs

⚛ What Is the Bohr Model?

In 1913, Danish physicist Niels Bohr proposed a new picture of the atom: a tiny, dense, positively charged nucleus at the center, with electrons orbiting it in fixed circular paths — like planets around the sun.

What made Bohr's model revolutionary wasn't the orbits themselves — it was the idea that electrons can only exist at specific, fixed energy levels. They can't be anywhere in between. This single idea explained why atoms are stable and why they glow in specific colors when heated.

🔑 Core Idea

Electrons occupy fixed "shells" (energy levels), numbered n = 1, 2, 3... To move between shells, an electron must absorb or emit a photon with exactly the right amount of energy.

🕰 From Plum Pudding to Quantized Orbits

Bohr's model didn't appear out of nowhere — it solved a problem left behind by two earlier models.

Thomson Model

~1904

"Plum pudding" — electrons sit embedded in a sphere of positive charge, like fruit in a pudding.

Rutherford Model

1911

A tiny, dense nucleus with electrons orbiting freely — but physics said they should spiral in and collapse!

Bohr Model

1913

Electrons orbit only at fixed, quantized energy levels — solving the collapse problem.

📐 Bohr's Three Postulates

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1. Quantized Orbits

Electrons can only travel in specific circular orbits, each with a fixed energy. These are labeled by a whole number n = 1, 2, 3... called the principal quantum number.

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2. Stable Orbits

While in one of these allowed orbits, an electron does not radiate energy and does not spiral into the nucleus — it stays at that energy indefinitely.

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3. Quantum Jumps

An electron can jump to a higher orbit by absorbing a photon, or drop to a lower orbit by emitting one — with energy exactly equal to the gap between levels: ΔE = E_high − E_low.

🔢 Shell Capacity — The 2n² Rule

Each energy level (shell) can hold a maximum number of electrons, given by the formula 2n², where n is the shell number. For most atoms encountered in introductory chemistry, shells fill in order: 2, 8, 8, 18...

Shell 1 (n=1)

2 × 1² = 2 electrons max. Closest to the nucleus, lowest energy.

Shell 2 (n=2)

2 × 2² = 8 electrons max.

Shell 3 (n=3)

2 × 3² = 18 electrons max (often shown filling to 8 first in simple models).

Shell 4 (n=4)

2 × 4² = 32 electrons max. Farthest shown here, highest energy.

⚠️ Limitations of the Bohr Model

The Bohr model was a huge leap forward — but it isn't the full picture. Modern quantum mechanics replaced it with a more accurate (and more complex) model.

Only works well for Hydrogen

The model's energy formula is exact for hydrogen (1 electron) but breaks down for atoms with many electrons that repel each other.

Electrons aren't tiny planets

Quantum mechanics shows electrons exist as probability "clouds" (orbitals), not as points on a fixed circular path.

Can't explain fine spectral detail

It misses subtle splitting of spectral lines caused by electron spin and magnetic effects.

Why we still use it

Despite its flaws, the Bohr model is the easiest way to understand energy levels, electron shells, and why atoms emit light at specific colors — the foundation for everything that comes after it.

🔢 Drawing a Bohr Diagram — Step by Step

We'll build the Bohr diagram for sodium (Na, atomic number 11) — a great example because it shows shell-filling across three energy levels.

Step 1

⚡ Quantized Energy Levels

For hydrogen, Bohr's model gives an exact formula for the energy of each shell: E_n = −13.6 eV / n². The energy is negative because the electron is bound to the nucleus — n = 1 is the most tightly bound (the ground state), and energy increases (becomes less negative) as n increases. At n = ∞, the electron is completely free (E = 0): the atom is ionized.

Notice how the gaps between levels shrink as n increases — this matches the diagram below, where the lines bunch together near the top.

🔬 Try It: Absorption & Emission

Pick a lower energy level and an upper energy level for a hydrogen atom, then fire a photon. Watch the electron absorb the photon and jump up — then fall back down, emitting a photon of light with a very specific color.

Lower Level (start)

Upper Level (excited)

🌈 Spectral Series

Transitions that land on the same lower level form a "series" of spectral lines, named after the scientists who discovered them.

Lyman Series

Any transition ending at n = 1. These photons are high-energy ultraviolet light — invisible to our eyes.

Balmer Series

Any transition ending at n = 2. Several of these fall in the visible range — this is the hydrogen spectrum you can see with a prism.

Paschen Series

Any transition ending at n = 3. These photons are lower-energy infrared light — felt as heat, not seen.

⚛ Select an Element

⚛ Bohr Diagram

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The Bohr Model of the Atom