Bohr's Model (Qualitative)

In 1913, Danish physicist Niels Bohr proposed a revolutionary model of the hydrogen atom that resolved a fundamental crisis in classical physics: why don't electrons spiral into the nucleus? Classical electromagnetism predicted that an electron orbiting a nucleus should continuously radiate energy and collapse inward within a fraction of a second. Bohr solved this by introducing the radical idea that electrons can only occupy certain fixed, discrete orbits — called shells — without radiating energy. These allowed orbits are labelled K (n=1), L (n=2), M (n=3), N (n=4), and so on, where n is the principal quantum number. The central insight of Bohr's model is that energy is quantised. An electron in a given shell possesses a specific, fixed amount of energy. It cannot exist between shells. When an electron absorbs exactly the right amount of energy — from heat, electricity, or light — it jumps to a higher shell (excitation). When it falls back to a lower shell (relaxation), it releases that same precise packet of energy as a photon of light. The energy of the photon corresponds exactly to the difference in energy between the two shells. This directly explained why hydrogen gas, when electrically excited, emits only specific colours of light — its atomic emission spectrum. Although Bohr's model was later superseded by quantum mechanics (which replaced neat circular orbits with probability clouds called orbitals), it remains an essential foundation for understanding atomic structure, electron energy levels, and spectroscopy. It successfully predicted the wavelengths of lines in the hydrogen emission spectrum with remarkable accuracy and introduced the concept of quantised energy levels that underpins all of modern chemistry and physics.

Key takeaways
  • Discrete Electron Shells (K, L, M, ...)
  • Stationary States — No Radiation While in Orbit
  • Excitation — Absorbing a Photon to Jump Up
  • Relaxation — Emitting a Photon When Falling Down
  • Hydrogen Energy Levels

Discrete Electron Shells (K, L, M, ...)

Electrons orbit the nucleus only in allowed shells labelled by principal quantum number n = 1, 2, 3, ... The innermost shell K (n=1) is closest to the nucleus and has the lowest energy. Shells L (n=2) and M (n=3) are progressively farther out and higher in energy. Each shell has a maximum electron capacity: K holds 2 electrons, L holds 8, M holds 18 (given by 2n²).

Stationary States — No Radiation While in Orbit

Bohr postulated that while an electron remains in a given shell, it does NOT radiate energy, contradicting classical electromagnetic theory. These stable orbits are called stationary states. The electron's total energy (kinetic + potential) stays constant in each stationary state, giving atoms their stability.

Excitation — Absorbing a Photon to Jump Up

If an electron absorbs a photon whose energy equals exactly the energy difference between its current shell and a higher shell (ΔE = E_upper − E_lower), it jumps upward to that higher shell. The atom is now in an excited state. This is why certain wavelengths of light are absorbed by atoms — producing dark lines in an absorption spectrum. The electron can only absorb photons of the exact right energy; photons of other energies pass straight through.

Relaxation — Emitting a Photon When Falling Down

An excited electron is unstable and very quickly (within ~10⁻⁸ seconds) falls back to a lower shell. As it does, it emits a photon whose energy equals the energy difference between the two shells: E_photon = hf = ΔE. Because the energy levels are fixed, only photons of specific frequencies (colours) are emitted — explaining the bright lines of atomic emission spectra. For hydrogen, visible light emissions are called the Balmer series (transitions falling to n=2).

Hydrogen Energy Levels

For hydrogen, Bohr derived the energy of each shell: E_n = −13.6 / n² eV. The ground state (n=1) has energy −13.6 eV. The negative sign means the electron is bound to the nucleus. As n increases, energy becomes less negative (increases toward zero). When n → ∞, the electron is completely free (ionised), so the ionisation energy of hydrogen from its ground state is 13.6 eV. The energy difference between shells n_i (initial) and n_f (final) is ΔE = 13.6(1/n_f² − 1/n_i²) eV for emission (n_i > n_f).

The Key Equation

En=−13.6n2 eVE_n = -\frac{13.6}{n^2} \text{ eV}
  • E_n — Energy of shell n (electron-volt (eV)): The total energy of the electron when occupying the nth Bohr orbit. Negative values indicate a bound (stable) electron; the more negative, the more tightly bound.
  • 13.6 — Rydberg energy for hydrogen (eV): A constant equal to the ionisation energy of hydrogen from its ground state (n=1). Derived from fundamental constants: me⁴/(8ε₀²h²).
  • n — Principal quantum number (dimensionless (integer)): Labels the shell: n=1 is K (ground state), n=2 is L, n=3 is M, etc. Must be a positive integer (1, 2, 3, ...).
  • \Delta E — Photon energy / energy difference (eV or Joules): When an electron transitions between shells n_i and n_f, it absorbs or emits a photon of energy ΔE = E_f − E_i = hf, where h is Planck's constant and f is the photon frequency.

Worked Example

Problem. An electron in a hydrogen atom falls from the n=3 shell (M shell) to the n=2 shell (L shell). Calculate the energy of the photon emitted, and determine whether this photon is in the visible light range. (1 eV = 1.6 × 10⁻¹⁹ J; h = 6.63 × 10⁻³⁴ J·s; c = 3.00 × 10⁸ m/s)

ΔE=1.89 eV,λ=658 nm (red light)\Delta E = 1.89 \text{ eV},\quad \lambda = 658 \text{ nm (red light)}

Answer. The emitted photon has energy 1.89 eV (3.02 × 10⁻¹⁹ J), wavelength 658 nm — red visible light (H-alpha line of the Balmer series).

Figure
Diagram
Bohr Model — Hydrogen Atom: Electron Shells and Transitionsp⁺K (n=1)L (n=2)M (n=3)e⁻e⁻e⁻EMISSIONphoton released(n=3 → n=1)ABSORPTIONphoton absorbed(n=1 → n=3)Energy Levels (H atom)n=1: −13.6 eVn=2: −3.4 eVn=3: −1.5 eVn=4: −0.85 eVn=∞: 0 eV (ionised)658 nm(red, Hα)
Origins · 1 minNiels Bohr and how this was discovered
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Niels Bohr
1885–1962 · Danish

Bohr proposed his quantised model of the hydrogen atom in 1913 while working in Ernest Rutherford's laboratory in Manchester. By combining Rutherford's nuclear atom with Planck's quantum hypothesis and Einstein's photon concept, he derived an equation that predicted the wavelengths of hydrogen's spectral lines with extraordinary precision. He was awarded the Nobel Prize in Physics in 1922 for this work, and his Institute for Theoretical Physics in Copenhagen became the world centre of quantum physics in the 1920s. Bohr was also a passionate football (soccer) player and played goalkeeper for the Akademisk Boldklub in Copenhagen. His brother Harald Bohr was an Olympic silver medallist in football for Denmark in 1908!

  • Rutherford's Nuclear Model — Bohr built directly on Rutherford's 1911 discovery that atoms have a tiny, dense, positively charged nucleus — Bohr kept the nuclear model but added quantised orbits to prevent electron collapse.
  • Atomic Emission Spectra — Bohr's model was specifically designed to explain why hydrogen emits only specific colours of light. Understanding emission spectra is the direct experimental evidence for quantised energy levels.
  • Quantum Mechanical Model and Orbitals — The modern model of the atom replaces Bohr's neat circular orbits with probability distributions called orbitals (s, p, d, f). Bohr's shells become the principal quantum number n in quantum mechanics.
  • Photons and the Photoelectric Effect — Bohr's model relies on photons carrying discrete packets of energy E = hf (Planck-Einstein relation). Understanding photons explains why only specific photon energies cause electron transitions.
  • Electron Configuration — The shell labels K, L, M from Bohr's model directly map onto electron configurations (1s, 2s2p, 3s3p3d). Filling rules for electrons in shells are the practical application of Bohr's energy level concept.