Hydrogen Spectrum Calculator

Calculate Atomic Transitions and Emission Lines

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Emission Line Calculator

Calculate wavelength and energy for specific electron transitions.

Emission Line: -

Complete Series Calculator

Calculate all emission lines in a spectral series.

Series Lines: -

Understanding the Hydrogen Spectrum

What is the Hydrogen Spectrum?

The hydrogen spectrum is the characteristic pattern of electromagnetic radiation emitted by hydrogen atoms when electrons transition between energy levels. It was crucial in developing our understanding of atomic structure and quantum mechanics.

Spectral Series

Major spectral series in hydrogen:

  • Lyman Series (UV): Transitions to n=1
  • Balmer Series (Visible): Transitions to n=2
  • Paschen Series (IR): Transitions to n=3
  • Brackett Series (IR): Transitions to n=4
  • Pfund Series (Far IR): Transitions to n=5

Historical Significance

Key developments in spectroscopy:

  • 1885: Balmer discovers his formula
  • 1888: Rydberg generalizes spectral lines
  • 1913: Bohr explains spectrum theoretically
  • 1916: Sommerfeld adds fine structure
  • 1926: Schrödinger provides quantum explanation

Applications

Hydrogen spectroscopy is used in:

  • Astronomical spectroscopy
  • Plasma diagnostics
  • Material analysis
  • Quantum optics
  • Chemical analysis

Essential Spectral Formulas

Energy Levels

En = -13.6 eV/n²

Transition Energy

ΔE = 13.6 eV(1/n₁² - 1/n₂²)

Wavelength

1/λ = R(1/n₁² - 1/n₂²)