Energielevels

Energielevels are discrete values of energy that a quantum system bound by a potential can possess. They reflect the wave-like nature of particles and the boundary conditions that restrict a system to stationary states. In atoms and molecules, electrons occupy specific Energielevels, while in solids these levels merge into bands separated by gaps.

In atoms, Energielevels arise from solutions to the Schrödinger equation. For a hydrogen-like atom, the energy depends mainly on the principal quantum number n and follows E_n = -13.6 eV / n^2. In multi-electron atoms, shielding, electron repulsion, and relativistic effects modify the levels, which are labeled by quantum numbers n, l, m_l, and j. Each level has a degeneracy reflecting the number of distinct states with the same energy.

Transitions between Energielevels involve exchange of energy with electromagnetic radiation. The energy difference ΔE between levels equals the photon energy hν. Absorption promotes an electron to a higher Energielevel; emission releases a photon. Selection rules determine which transitions are allowed, influencing the observed spectral lines.

In solids, the discrete Energielevels of individual atoms broaden into energy bands because of interactions among many atoms in a periodic lattice. Electrons fill bands according to the Pauli principle, creating valence and conduction bands with a band gap in insulators and semiconductors. The structure of these bands governs electrical conductivity and optical properties.

Energielevels are central to spectroscopy, lasers, atomic clocks, and quantum technologies. Precise knowledge of level energies enables measurements of fundamental constants and the manipulation of quantum states.

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