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.