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).