Light, Spectra & the Bohr Model

Why a hydrogen lamp glows in a handful of exact colours — and how electrons jumping between energy levels make light.

High schoolIntro Gen ChemUni Year 1
⏱️ About 20 min

Run electricity through hydrogen gas and it glows. Split that glow with a prism and you don't get a smooth rainbow — you get a few razor-sharp coloured lines, always in the same places, for every hydrogen lamp on Earth and every star in the sky. Those lines are a barcode, and the Bohr model explains exactly how an atom prints it.

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The big idea: An atom's electrons can only sit at specific energy levels — like rungs on a ladder, never between them. When an electron drops from a higher rung to a lower one, the leftover energy leaves as a particle of light (a photon) whose energy equals the gap. Fixed gaps mean fixed colours: a line spectrum.
🎯 By the end, you'll be able to
  • Explain what it means for an atom's energy levels to be quantized
  • Describe how electrons absorb and emit photons when they change levels
  • Connect specific energy-level gaps to the specific colours in a line spectrum
  • Judge the Bohr model as a useful stepping stone toward the orbital picture
📎 Helpful to know first

A ladder, not a ramp

Earlier we pictured electrons somewhere in the space around the nucleus. Now we get specific about their energy. The key discovery behind the Bohr model is that an electron in an atom can't have just any energy — it can only sit at certain fixed values, called energy levels and labelled by a whole number n = 1, 2, 3, …

Think of a ladder rather than a ramp. You can stand on rung 1 or rung 2, but never halfway between. An electron is the same: it occupies a level or moves cleanly to another, but it is never found in between. We say the energy is quantized — it comes in discrete steps.

Level n = 1 is the lowest (the ground state) and sits closest to the nucleus. Higher levels are further out and higher in energy, and they bunch closer together as they climb.

🔑 Quantized means 'only certain values allowed'
For a hydrogen atom, the energy of level n is well approximated by En = −13.6 eV ÷ n². The minus sign means the electron is bound (it would take energy to pull it free); zero energy is a just-barely-free electron. Notice the levels get closer together as n grows — the ladder's rungs crowd near the top.
e⁻ n=1 (1 e⁻) 1 p⁺ 0 n Hydrogen · H · Z=1 · mass number 1
Hydrogen — the simplest atom and the star of this lesson: 1 proton, 0 neutrons, and 1 electron sitting on level n = 1. Add energy and that electron can jump to n = 2, 3, … then fall back and emit light. Generated from Z = 1, mass number 1.

Absorb to climb, emit to fall

An electron changes levels only by trading energy with light. Two moves:

  • Absorption: the electron soaks up a photon and jumps to a higher level — but only if the photon's energy matches the gap exactly. Wrong size, no jump.
  • Emission: an electron in a higher level falls to a lower one and releases the leftover energy as a photon. This is where the light from a glowing gas comes from.

Because the levels are fixed, the gaps between them are fixed, so the photons an atom can emit have fixed energies — and photon energy is what we see as colour. That is the whole secret of a line spectrum.

\[ E_{\text{photon}} = E_{\text{high}} - E_{\text{low}} = h\nu \]
The emitted photon carries exactly the energy gap between the two levels. Bigger gap → higher-energy photon → bluer light; smaller gap → redder light. (h is Planck's constant, ν the light's frequency.)
✨ Every element has its own barcode
Each element has its own unique set of energy levels, so it emits its own unique set of lines — a spectral fingerprint. This is literally how we know what distant stars are made of: we read the barcode in their light. Helium was spotted in the Sun's spectrum before it was ever found on Earth.

Hydrogen's visible lines (the Balmer set)

Hydrogen's most famous lines fall in the visible range and all share one thing: they are electrons landing on level n = 2. Drops from n = 3, 4, 5, … down to n = 2 make a red, a blue-green, and violet lines respectively. This family of visible lines is called the Balmer series.

Drops that land on n = 1 release much bigger gaps — those photons are ultraviolet, past what your eye can see. Landing on n = 3 gives small gaps in the infrared. Same rule every time: the gap sets the colour.

📝 Worked example: In a hydrogen atom, an electron drops from level n = 3 to level n = 2. How much energy does the emitted photon carry?
  1. Find each level with En = −13.6 eV ÷ n². E₃ = −13.6 ÷ 9 = −1.51 eV; E₂ = −13.6 ÷ 4 = −3.40 eV.
  2. The photon carries the gap: Ephoton = Ehigh − Elow = (−1.51) − (−3.40).
  3. = 1.89 eV. A gap this size corresponds to red light — this is hydrogen's familiar red line.
✓ About 1.89 eV, seen as a red line.
✏️ Practice: What is the energy of hydrogen's level n = 2? Use E = −13.6 eV ÷ n². (Give the value in eV, including the sign.)
eV
Solution
  1. En = −13.6 eV ÷ n², with n = 2.
  2. = −13.6 ÷ 4.
  3. = −3.4 eV. It's negative because the electron is bound to the atom.
✏️ Practice: An electron falls from n = 4 to n = 2 in hydrogen. What is the emitted photon's energy? (E₄ = −0.85 eV, E₂ = −3.40 eV. Answer in eV.)
eV
Solution
  1. The photon carries the gap: Ephoton = Ehigh − Elow.
  2. = (−0.85) − (−3.40).
  3. = 2.55 eV — a bigger gap than the n=3→2 drop, so this photon is bluer (hydrogen's blue-green line).
⚠️ Electrons are not tiny planets
The Bohr model draws electrons circling the nucleus on neat orbits, like planets round the Sun. That picture is a helpful model, not reality. Electrons don't follow fixed circular paths; the modern description replaces orbits with orbitals — fuzzy regions of probability where an electron is likely to be. What Bohr got gloriously right is the part that matters here: quantized energy levels, and light emitted when an electron changes level. Keep the energy-level idea; drop the planetary orbits.

Check your understanding

1. Why does a hydrogen lamp emit only a few specific colours instead of a smooth rainbow?
Fixed energy levels mean fixed gaps between them. An emitted photon must carry exactly one gap's worth of energy, so only certain photon energies — and therefore certain colours — appear.
2. Where does the light from a glowing gas actually come from?
Emission happens when an electron falls to a lower level and releases the energy difference as a photon. The photon's energy equals the gap between the two levels.
3. How should you treat the Bohr model's picture of electrons on circular orbits?
Bohr's quantized energy levels are a keeper and explain line spectra beautifully. The literal circular orbits are the part that's just a model — the modern picture uses probability orbitals instead.
🔎 Related lessons
Previous: Inside the Atom Electron Configuration The Periodic Table & Its Trends
✅ Key takeaways
  • Electron energies in an atom are quantized — allowed only at fixed levels (n = 1, 2, 3, …), like rungs on a ladder.
  • Absorbing a photon lifts an electron to a higher level; falling to a lower level emits a photon.
  • The emitted photon's energy equals the gap between levels, so fixed gaps give fixed colours — a line spectrum.
  • For hydrogen, E_n ≈ −13.6 eV ÷ n²; the visible (Balmer) lines are drops that land on n = 2.
  • Bohr nailed quantized energy levels, but electrons don't really orbit like planets — that idea gives way to orbitals next.
➡️ Bohr's fixed orbits can't quite capture where electrons really live. Replacing them with probability orbitals — and the rules for how electrons fill them — is exactly what electron configuration is about.
Want to test yourself on this? Try the Chemistry practice test →