Physics:Quantum Spectral lines and series

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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.[1]

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:

E=hν=Ei−Ef

where:

  • h is Planck’s constant
  • ν is the frequency of the radiation
  • Ei, Ef are the initial and final energy levels

This leads to sharply defined spectral lines rather than a continuous spectrum.[2]

Hydrogen spectral series

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

En=−13.6 eVn2

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

1λ=R(1nf2−1ni2)

where:

  • R is the Rydberg constant
  • ni>nf

This relation accurately predicts observed hydrogen spectral lines.[3]

Major series

  • Lyman series (nf=1) – ultraviolet region
  • Balmer series (nf=2) – visible region
  • Paschen series (nf=3) – infrared region
  • Brackett series (nf=4) – infrared
  • Pfund series (nf=5) – far infrared

Each series corresponds to transitions ending at a fixed lower energy level.[4]

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.[5][6]

Selection rules

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

  • Δl=±1
  • Δm=0,±1

These arise from conservation of angular momentum and symmetry properties of atomic wavefunctions.[7]

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.”[8]

See also

Table of contents (185 articles)

Index

Full contents

9. Quantum optics and experiments (5) ↑ Back to index
14. Plasma and fusion physics (8) ↑ Back to index
Conceptual illustration of plasma physics in a fusion context, showing magnetically confined ionized gas in a tokamak and the collective behavior governed by electromagnetic fields and transport processes.
Conceptual illustration of plasma physics in a fusion context, showing magnetically confined ionized gas in a tokamak and the collective behavior governed by electromagnetic fields and transport processes.

References

  1. ↑ Spectral line – Britannica
  2. ↑ Spectroscopy in Astronomy – OpenStax
  3. ↑ Strong Lines of Hydrogen – NIST
  4. ↑ Bohr’s Theory of the Hydrogen Atom – OpenStax
  5. ↑ Zeeman effect – Britannica
  6. ↑ Stark effect – Britannica
  7. ↑ Atomic Spectra and X-rays – OpenStax
  8. ↑ Spectroscopy: Applications – Britannica
Author: Harold Foppele

Source attribution: Quantum Spectral lines and series

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