Transitions Between Levels
Click a level pair — photon animates out with wavelength-matched color.
Key Notes
An atomic transition is the jump of an electron between two energy levels, with absorption or emission of a photon.
Energy conservation: hf = |E_i − E_f|. Frequency uniquely set by the level pair.
Emission (downward): electron drops from higher to lower level, EMITS a photon.
Absorption (upward): electron jumps from lower to higher level after ABSORBING a photon of matching energy.
Selection rules (full QM): Δl = ±1, Δm = 0, ±1. Not all transitions are allowed.
Lifetime of typical excited states: ~10⁻⁸ s (allowed) to ~10⁻³ s or longer (forbidden metastable).
Spontaneous emission: an isolated excited atom decays randomly; lifetime obeys exponential decay.
Stimulated emission: a photon of matching energy stimulates an excited atom to emit a coherent photon — basis of LASERS.
Formulas
Photon energy in a transition
Conservation of energy; sign chooses emission/absorption.
Wavelength of transition (Rydberg)
Direct formula for hydrogen-like atoms.
Number of possible lines from level n
All ordered pairs (i,f) with i > f.
Decay rate (mean lifetime)
Excited population decays exponentially with mean lifetime τ.
Important Points
A transition's WAVELENGTH is a 'fingerprint' — unique to a given level pair in a given atom.
Selection rules block some transitions even when energetically allowed — these are 'forbidden' lines.
Metastable states (forbidden transitions) can have very long lifetimes — used in atomic clocks and lasers.
Photon emitted has angular momentum ±ℏ — drives the Δl = ±1 selection rule.
Excitation by collision (e.g., gas discharge) populates many levels, then radiative cascade gives multi-line spectra.
STIMULATED emission needs a population INVERSION (more in excited state than ground) — engineered in lasers.
Transitions Between 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.