Understanding Electromagnetic Energy and Spectra

Sep 10, 2024

Electromagnetic Energy and Line Spectra

Learning Objective

  • Distinguish between line and continuous emission spectra.

Continuous Emission Spectrum

  • Produced by solids, liquids, and condensed gases.
  • Example: Sun emits a wide range of light wavelengths, creating a continuous spectrum.
  • Can be separated into individual wavelengths using a prism.
  • Represents all wavelengths of visible light.

Line Spectrum

  • Produced when gas emits light under the influence of electrical energy.
  • Discrete wavelengths instead of continuous.
  • Examples: Sodium, Hydrogen, Calcium, and Mercury emit distinct line spectra.
  • Each line corresponds to a specific wavelength, not a range.

Hydrogen Line Spectrum

  • Hydrogen emits energy at very specific wavelengths.
  • Early 20th-century physicists studied why hydrogen emits at specific energy values.

Contributions by Physicists

  • Johann Balmer:
    • Modeled the first four visible wavelengths of hydrogen.
  • Johannes Rydberg:
    • Developed an equation to account for all of hydrogen's emissions.

Rydberg Equation

  • Formula: ( \frac{1}{\lambda} = R ( \frac{1}{n_1^2} - \frac{1}{n_2^2} ) )
    • ( R ) is the Rydberg constant: ( 1.097 \times 10^7 \text{ m}^{-1} )
    • ( n_1 ) and ( n_2 ) are integers, with ( n_2 > n_1 ).
  • The equation uses quantized integers to predict light emissions.
  • Important for the development of quantum mechanics and understanding electronic structures.