Bohr's Atomic Model & Atomic Spectra
Chapter 2 quantized light. This chapter quantizes the atom itself — solving a real, genuinely catastrophic problem with the atomic model physicists had settled on just two years earlier, and doing so by leaning directly on a formula nobody could yet explain.
A Real Crisis in the Rutherford Model
Ernest Rutherford's 1911 model pictured the atom as a tiny, dense, positively charged nucleus orbited by electrons — a miniature solar system. Real, classical electrodynamics created a genuine, serious problem for this picture directly: physicist Joseph Larmor had already shown, in 1897, that any accelerating electric charge radiates electromagnetic energy. An electron orbiting a nucleus is constantly accelerating (changing direction, even at constant speed), so classical theory demanded it continuously lose energy as radiation — spiralling inward and colliding with the nucleus almost instantly. Ordinary, stable matter, by this same classical reasoning, should not exist at all.
Bohr's Real 1913 Solution
Niels Bohr's real 1913 model resolved this by proposing that electrons could only occupy specific, quantized "stationary" orbits — ones where the electron's own angular momentum is restricted to whole-number multiples of ħ (h divided by 2π):
An electron in one of these permitted orbits genuinely does not radiate energy at all, regardless of what classical electrodynamics would otherwise demand — a real, deliberate departure from classical physics, justified purely by the fact that it correctly predicted observed reality.
A Real Echo of Kepler and Newton
Worked Example: A Real Hydrogen Spectral Line
Using the real Rydberg formula, calculate the wavelength of light emitted when a hydrogen electron falls from n = 3 to n = 2:
1/λ = (1.097×10&sup7;) × (0.25 − 0.1111)
1/λ ≈ 1.524×10&sup6; m&supminus;¹
λ ≈ 6.56×10&supminus;&sup7; m = 656 nm
This real, calculated value — 656 nm, a specific shade of red light — matches one of the real, observed lines in hydrogen's own visible spectrum exactly, confirming the model's own genuine predictive power.
Empirical Pattern vs. Theoretical Explanation
| Property | Balmer/Rydberg (1885/1888) | Bohr (1913) |
|---|---|---|
| Approach | Empirical — fitted to observed spectral lines | Theoretical — derived from quantized angular momentum |
| Answers | What wavelengths appear? | Why do those specific wavelengths appear? |
| Real parallel | The same Kepler/Newton relationship from Classical Mechanics & Thermodynamics Ch.6 | |
Hands-On Exercises
Quick Reference
- The Rutherford model had a real, fatal classical flaw: an orbiting electron should radiate energy and spiral into the nucleus almost instantly
- Bohr's 1913 fix: electrons occupy quantized orbits (L = nħ) that do not radiate energy
- Bohr's model directly explained the real, pre-existing empirical Balmer (1885) and Rydberg (1888) formulas for hydrogen's spectral lines
- Rydberg formula: 1/λ = RH(1/n1² − 1/n2²), RH ≈ 1.097×10&sup7; m&supminus;¹