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Repair Quantum Collection B backlink template

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{{Quantum book backlink|Atomic and spectroscopy}}
'''Spectral lines''' are discrete wavelengths of light emitted or absorbed by atoms and molecules, arising from transitions between quantized energy levels, and they provided some of the earliest direct evidence for quantum theory.<ref>[https://www.britannica.com/science/spectral-line Spectral line – Britannica]</ref>

[[File:Quantum_spectral_lines_and_series.svg|thumb|400px|Spectral lines arise from discrete electronic transitions in atoms, forming characteristic series such as Lyman, Balmer, and Paschen.]]

== Origin of spectral lines ==

In quantum mechanics, electrons in atoms occupy discrete energy eigenstates. When an electron transitions between two states, a photon is emitted or absorbed with energy given by:

<math>E = h \nu = E_i - E_f</math>

where:
* <math>h</math> is Planck’s constant
* <math>\nu</math> is the frequency of the radiation
* <math>E_i</math>, <math>E_f</math> are the initial and final energy levels

This leads to sharply defined spectral lines rather than a continuous spectrum.<ref>[https://openstax.org/books/astronomy-2e/pages/5-3-spectroscopy-in-astronomy Spectroscopy in Astronomy – OpenStax]</ref>

== Hydrogen spectral series ==

The hydrogen atom provides the simplest and most important example of spectral line structure. Its energy levels are given by:

<math>E_n = - \frac{13.6 \text{ eV}}{n^2}</math>

Transitions between these levels produce series of spectral lines described by the Rydberg formula:

<math>\frac{1}{\lambda} = R \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right)</math>

where:
* <math>R</math> is the Rydberg constant
* <math>n_i > n_f</math>

This relation accurately predicts observed hydrogen spectral lines.<ref>[https://physics.nist.gov/PhysRefData/Handbook/Tables/hydrogentable2.htm Strong Lines of Hydrogen – NIST]</ref>

=== Major series ===

* '''Lyman series''' (<math>n_f = 1</math>) – ultraviolet region
* '''Balmer series''' (<math>n_f = 2</math>) – visible region
* '''Paschen series''' (<math>n_f = 3</math>) – infrared region
* '''Brackett series''' (<math>n_f = 4</math>) – infrared
* '''Pfund series''' (<math>n_f = 5</math>) – far infrared

Each series corresponds to transitions ending at a fixed lower energy level.<ref>[https://openstax.org/books/college-physics-2e/pages/30-3-bohrs-theory-of-the-hydrogen-atom Bohr’s Theory of the Hydrogen Atom – OpenStax]</ref>

== Fine structure and splitting ==

Real spectral lines are not perfectly sharp. They exhibit splitting due to additional physical effects:

* '''Fine structure''' — relativistic corrections and spin–orbit coupling
* '''Zeeman effect''' — splitting in an external magnetic field
* '''Stark effect''' — splitting in an electric field

These effects reveal deeper structure in atomic energy levels.<ref>[https://www.britannica.com/science/Zeeman-effect Zeeman effect – Britannica]</ref><ref>[https://www.britannica.com/science/Stark-effect Stark effect – Britannica]</ref>

== Selection rules ==

Not all transitions are allowed. Selection rules determine which spectral lines appear:

* <math>\Delta l = \pm 1</math>
* <math>\Delta m = 0, \pm 1</math>

These arise from conservation of angular momentum and symmetry properties of atomic wavefunctions.<ref>[https://openstax.org/books/university-physics-volume-3/pages/8-5-atomic-spectra-and-x-rays Atomic Spectra and X-rays – OpenStax]</ref>

== Spectroscopy and applications ==

Spectral lines are fundamental in many areas of physics and astronomy:

* Identifying chemical elements in stars and galaxies
* Measuring Doppler shifts and cosmic expansion
* Determining temperatures and densities of plasmas
* Laser technology and atomic clocks

Each element has a unique spectral “fingerprint.”<ref>[https://www.britannica.com/science/spectroscopy/Applications Spectroscopy: Applications – Britannica]</ref>

=See also=
{{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also}}

==References==
{{reflist|3}}
{{Author|Harold Foppele}}

{{Sourceattribution|Quantum Spectral lines and series|1}}

Physics:Quantum Spectral lines and series - Revision history

imported>WikiHarold: Repair Quantum Collection B backlink template

imported>WikiHarold: Repair Quantum Collection B backlink template