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.
Key Formula
1/λ = R_H × (1/n₁² − 1/n₂²)
LaTeX: \frac{1}{\lambda} = R_H \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)
| Symbol | Meaning | Unit |
|---|---|---|
| λ | Wavelength of emitted photon | m |
| R_H | Rydberg constant = 1.097 × 10⁷ m⁻¹ | m⁻¹ |
| n₁ | Lower energy level (final state) | dimensionless |
| n₂ | Higher energy level (initial state, n₂ > n₁) | dimensionless |
Worked Example
Problem
Using the Rydberg formula, calculate the wavelength of the second line of the Balmer series in hydrogen (transition from n = 4 to n = 2).
Solution
Step 1: Identify values. n₁ = 2 (Balmer series: final state), n₂ = 4 R_H = 1.097 × 10⁷ m⁻¹ Step 2: Apply the Rydberg formula. 1/λ = 1.097×10⁷ × (1/4 − 1/16) 1/λ = 1.097×10⁷ × (4/16 − 1/16) 1/λ = 1.097×10⁷ × (3/16) 1/λ = 1.097×10⁷ × 0.1875 1/λ = 2.057 × 10⁶ m⁻¹ Step 3: Solve for λ. λ = 1 / 2.057×10⁶ = 4.86 × 10⁻⁷ m
Answer
λ ≈ 486 nm (blue-green light — the H-beta line of the Balmer series).
Hydrogen Emission Spectral Series
| Series | Final Level (n₁) | Wavelength Range | Region of Spectrum |
|---|---|---|---|
| Lyman | 1 | 91 – 122 nm | Ultraviolet |
| Balmer | 2 | 365 – 656 nm | Visible (and UV) |
| Paschen | 3 | 820 nm – 1.875 µm | Near infrared |
| Brackett | 4 | 1.46 – 4.05 µm | Mid infrared |
| Pfund | 5 | 2.28 – 7.46 µm | Mid infrared |
Interactive Tools
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Related Terms
Absorption Spectrum
An absorption spectrum is produced when a continuous (white-light) source passes through a cool gas or solid, and atoms absorb photons at specific wavelengths that correspond exactly to allowed upward transitions between energy levels. The result is a continuous spectrum crossed by dark lines — each dark line marking a wavelength absorbed by a particular element. Absorption spectra are complementary to emission spectra and are used in stellar spectroscopy (Fraunhofer lines in sunlight), remote chemical analysis, and atmospheric science.
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.
Bohr Model
The Bohr model, proposed by Niels Bohr in 1913, describes the hydrogen atom as having electrons orbiting the nucleus in discrete, quantized circular orbits with specific allowed energies. Electrons can jump between orbits by absorbing or emitting photons whose energy equals the difference between the two energy levels, explaining the discrete spectral lines of hydrogen. While superseded by quantum mechanics, the Bohr model correctly predicts hydrogen's spectral series and introduced the revolutionary idea of quantized atomic energy levels.
"Emission" derives from the Latin emittere (to send out), from e- (out) + mittere (to send). "Spectrum" comes from the Latin spectrum (appearance, image), used by Newton (1671) to describe the rainbow band produced by a prism. The Rydberg formula was empirically derived by Johan Rydberg in 1888.