Excited State
An excited state is any quantum state of an atom, molecule, or nucleus in which one or more particles occupy energy levels higher than the ground state, having absorbed energy from a photon, collision, or thermal source. Excited states are inherently unstable — atoms typically remain in an excited state for about 10⁻⁸ seconds (nanosecond timescale) before spontaneously returning to a lower energy state by emitting a photon. The controlled management of excited states is fundamental to lasers (population inversion), fluorescence microscopy, and phosphorescence.
Key Formula
Eₙ = −13.6 eV / n², for n = 2, 3, 4, … (excited states of hydrogen)
LaTeX: E_n = -\frac{13.6\,\text{eV}}{n^2}, \quad n = 2, 3, 4, \ldots
| Symbol | Meaning | Unit |
|---|---|---|
| Eₙ | Energy of the nth excited state | eV |
| n | Principal quantum number (n ≥ 2 for excited states) | dimensionless |
| 13.6 eV | Ground state ionization energy of hydrogen | eV |
Worked Example
Problem
A hydrogen atom in the n = 4 excited state spontaneously decays to n = 2. Calculate the wavelength and color of the emitted photon.
Solution
Step 1: Calculate energies. E₄ = −13.6 / 16 = −0.850 eV E₂ = −13.6 / 4 = −3.400 eV Step 2: Calculate photon energy. ΔE = E₄ − E₂ = −0.850 − (−3.400) = 2.550 eV Step 3: Convert to wavelength. λ = hc / ΔE = (4.136×10⁻¹⁵ eV·s × 3×10⁸ m/s) / 2.550 eV λ = 1.241×10⁻⁶ / 2.550 = 4.87×10⁻⁷ m
Answer
λ ≈ 487 nm — blue-green light (the H-beta line of the Balmer series).
Typical Lifetimes and Properties of Atomic Excited States
| State Type | Typical Lifetime | Transition Type | Example Application |
|---|---|---|---|
| Singlet excited state | ~1–10 ns | Spontaneous emission (fluorescence) | Fluorescent dyes, LEDs |
| Triplet excited state | ~µs to ms | Phosphorescence (spin-forbidden) | Glow-in-the-dark materials |
| Metastable state | ~ms to s | Forbidden transition (long lifetime) | Laser gain medium (population inversion) |
| Rydberg state (large n) | µs range | Spontaneous emission to lower n | Quantum computing experiments |
| Nuclear excited state | ps to years | Gamma-ray emission | Medical isotopes (Tc-99m) |
Interactive Tools
PhET Models of the Hydrogen Atom
Visualize electron transitions between excited and ground states.
Open ToolKhan Academy — Electron Transitions and Spectral Lines
Video lessons on excited states, emission, and the Bohr model.
Open ToolNIST Atomic Spectra Database
Lookup excited state energies and transition probabilities for elements.
Open Tool
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Related Terms
Ground State
The ground state is the lowest possible energy state of a quantum mechanical system, such as an atom, molecule, or nucleus, in which all quantum numbers take their minimum allowed values consistent with the Pauli Exclusion Principle. A system in the ground state is thermodynamically stable and does not spontaneously emit radiation. The ground state energy of hydrogen is −13.6 eV, and the ground state represents the reference level from which excitation energies of higher states are measured.
Energy Level
An energy level is one of the discrete, quantized values of energy that a bound quantum system (such as an electron in an atom or a molecule) is permitted to have. Unlike classical systems where energy can take any continuous value, quantum mechanics constrains bound particles to specific allowed states, each characterized by a set of quantum numbers. Transitions between energy levels result in the absorption or emission of photons with energies exactly equal to the difference between the two levels, producing the characteristic spectral lines used in atomic spectroscopy.
Emission Spectrum
An emission spectrum is the set of discrete wavelengths (spectral lines) of electromagnetic radiation emitted by an atom or molecule when its electrons transition from higher to lower energy levels, releasing photons. Each element produces a unique pattern of spectral lines that serves as its "fingerprint," allowing identification of elements in distant stars, gas clouds, and laboratory samples. The energy of each emitted photon equals exactly the energy difference between the two levels involved in the transition: E = hf = hc/λ.
"Excited" comes from the Latin excitare (to rouse, to stir up), from ex- (out) + citare (to put in motion). In physics, "excitation" has been used since the late 19th century to describe a system in a higher-energy, active state. The quantum mechanical formalization of excited states developed in the 1920s alongside Bohr's model and wave mechanics.