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Quantum Bohr Model

Rydberg Transitions & Spectroscopy

Principles & Guide

Quantized Energy Levels: In a hydrogen-like atom with atomic number $Z$, electron energies are quantized: $E_n = -13.606 \frac{Z^2}{n^2}\text{ eV}$ for principal quantum number $n \in \{1, 2, \dots, 7\}$.

Rydberg Formula: Transition between shells $n_1$ and $n_2$ emits or absorbs a photon with wavelength: $$\frac{1}{\lambda} = R_\infty Z^2 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)$$ where $R_\infty = 1.097373 \times 10^7\text{ m}^{-1}$ and $\Delta E = \frac{hc}{\lambda} = 1239.84\text{ eV}\cdot\text{nm}/\lambda$.

Dan Bruton Color Mapping: Emitted photons in the 380–780 nm range produce vivid visible spectrum lines; $<380\text{ nm}$ is Ultraviolet (Lyman series), $>780\text{ nm}$ is Infrared (Paschen, Brackett, Pfund).

Quantum Transition ($n_i \to n_f$) Emission
E₃ = -1.51 eV
E₂ = -3.40 eV
Emitted / Absorbed Photon Metrics
656.28 nm Visible (Red)
Balmer H-alpha ($3 \to 2$)
Photon Energy (ΔE)
1.889 eV
Frequency (ν)
4.568 × 10¹⁴ Hz
Auto-Loop Transitions
¹H
Hydrogen Bohr Atom
Ground State: -13.606 eV
n: 3 → 2
Balmer
Emission Spectrum & Line Spectrograph (Click spectral line to jump)
<380nm UV 380–780nm Visible >780nm IR
90 nm (UV) 380 nm 434 nm (Hγ) 486 nm (Hβ) 656 nm (Hα) 780 nm 2000 nm (IR)