Rutherford, Planck, and Bohr (The Atomic Model)
High-Yield Summary
- Planck (1900): energy is quantized, emitted/absorbed only in discrete packets (quanta). E = hf.
- Rutherford (1911): gold foil experiment overturned the plum pudding model — revealed a small, dense, positively charged nucleus surrounded by mostly empty space.
- Bohr (1913): hydrogen's electron occupies quantized circular orbits (stationary states) with angular momentum L = nh/2π; orbit energy E = −Rh/n².
- Ground state = lowest-energy, most stable configuration. Excited state = higher energy, reached by absorbing a photon or thermal energy.
- Absorption (ground → excited, dark line) and emission (excited → lower level, bright line) together form an element's atomic spectrum — a unique fingerprint.
- Hydrogen's spectral lines group into Lyman (→n=1, UV), Balmer (→n=2, visible), Paschen (→n=3, infrared) series. Wavelength of any transition: Rydberg formula.
Key Terms
- Quantized
- Restricted to discrete values rather than a continuous range (energy, angular momentum).
- Plum pudding model
- Pre-1911 model: electrons scattered through a diffuse positive 'pudding'. Disproven by Rutherford.
- Stationary states
- Bohr's allowed, stable electron orbits — no energy radiated while in one.
- Ground state / excited state
- Lowest-energy, most stable configuration vs. a higher-energy configuration reached by absorbing energy.
- Photon
- A particle of light whose energy exactly matches the gap between two energy levels during a transition.
Planck, Bohr, and the Rydberg Formula
E = hf | L = nh/2π | E = −Rh/n² | 1/λ = Rh(1/n₁² − 1/n₂²)
- h = Planck's constant
- n = Principal quantum number (positive integer)
- Rh = Rydberg constant for hydrogen (≈2.18×10⁻¹⁸ J energy form; ≈1.097×10⁷ m⁻¹ wavenumber form)
- n₁, n₂ = Lower (final) and higher (initial) principal quantum numbers of the transition
- Negative sign in E = −Rh/n² reflects a bound state; energy = 0 when electron and nucleus are infinitely far apart.
- The energy and wavenumber forms of Rh are related by Rh(energy) = Rh(wavenumber) × hc — don't mix them up mid-calculation.
Hydrogen Spectral Series
| Series | Transition → Region |
|---|---|
| Lyman | n > 1 down to n = 1 → Ultraviolet |
| Balmer | n > 2 down to n = 2 → Visible |
| Paschen | n > 3 down to n = 3 → Infrared |
Common MCAT Trap
- Absorption produces a dark line (electron jumps up, ground → excited); emission produces a bright line (electron falls down, excited → lower) — easy to swap under pressure.
- The Bohr model only works for hydrogen (one-electron systems) — it fails for any multi-electron atom.
- Balmer series lines are visible (historically the first observed); Lyman is UV, Paschen is IR — don't mix up which series falls in which region.
Quick Recall
What did Rutherford's gold foil experiment reveal about atomic structure?
What is quantized in Bohr's model of the hydrogen atom?
A hydrogen electron falls from n = 4 to n = 2 — which spectral series is this, and what region of light results?
Does absorption or emission produce a bright line in a spectrum?