Atomic Spectra and Hydrogen Spectrum

Because atomic energy levels are discrete, atoms emit and absorb only particular photon energies. For a transition: hf = |E_f−E_i| Therefore: λ = hc/|ΔE| An excited electron moves to a lower energy level and emits a photon. This produces discrete bright spectral lines.

An atom absorbs photons of particular energies that match allowed upward transitions. This produces dark absorption lines in a continuous background.

Hydrogen spectral wavelengths are described by the Rydberg relation: **1λ = R_H(1n_f² − 1n_i²)** for emission where: `n_i > n_f` and: `R<sub>H</sub> ≈ 1.097×10⁷m⁻¹`

Important hydrogen series include: **Lyman: final `n=1` Balmer: final `n=2` Paschen:** final `n=3`

**hf=|ΔE| λ=hc/|ΔE| Hydrogen: 1λ=R_H(1n_f²−1n_i²)**