Energy Levels
Eₙ = −13.6 Z²/n² eV — horizontal levels with continuum above the ionization limit.
Key Notes
Atomic energy levels are the discrete energies an electron can have in an atom: E_n = −13.6 Z²/n² eV for hydrogen-like.
Levels are NEGATIVE for bound states (relative to a free electron at rest, E = 0).
Larger n: shallower (less negative) — closer to ionisation. Smaller n: deeper (more negative).
Ground state: n = 1 (lowest energy, most stable). Excited states: n = 2, 3, …
Differences between levels give photon energies in transitions: hf = E_i − E_f.
Energy-level diagram: horizontal lines labelled with n; arrows showing transitions.
Hydrogen's first excited state (n=2) is −3.4 eV; spacing E₁ − E₂ = 10.2 eV (Lyman-α).
Multi-electron atoms have more complex level structure (different sub-shells s, p, d, f within same n).
Formulas
Hydrogen-like energy
Negative — bound. Z = 1 for H.
Transition energy
Emission if i > f; absorption if i < f.
Wavelength (Rydberg form)
R = 1.097 × 10⁷ m⁻¹ (Rydberg constant).
Ionisation energy from level n
Energy required to remove the electron from level n to infinity.
Important Points
Energy levels are DISCRETE — only specific values allowed (consequence of quantization).
E_n is NEGATIVE for bound states. E = 0 is a free electron at rest. Positive E means continuum (unbound).
Spacing between adjacent levels DECREASES rapidly with n: gaps converge to the continuum as n → ∞.
Multi-electron atoms split levels into sub-shells: spdf — but Bohr's basic n picture is a useful starting point.
Ionization from ground state = E_ion = +13.6 eV (H). From n = 2 it's only +3.4 eV.
Allowed transitions are governed by selection rules (Δl = ±1) — Bohr's model ignores them, full QM doesn't.
Energy Levels notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.