Overview
This lecture explains the difference between continuous and line emission spectra, emphasizing their formation and the mathematical description of hydrogen's line spectrum.
Continuous Emission Spectrum
- Continuous emission spectra are produced by solids, liquids, and condensed gases.
- The sun's emission is an example of a continuous spectrum, covering all visible wavelengths.
- When separated (e.g., by a prism), a continuous spectrum shows a range of colors without gaps.
Line Emission Spectrum
- Passing electricity through a gas in a tube produces a line spectrum, not a continuous one.
- A line spectrum consists of discrete lines, each corresponding to a specific wavelength.
- Gases emit light at very specific, quantized energy values, not over a range.
- Each element (e.g., sodium, hydrogen, calcium, mercury) has a unique line spectrum.
Hydrogen Line Spectrum & Its Significance
- Hydrogen emits light at only certain specific wavelengths, puzzling early physicists.
- Johann Balmer mathematically modeled the first four visible lines of hydrogen's spectrum.
- Johannes Rydberg created an equation to account for all hydrogen emissions.
The Rydberg Equation
- The Rydberg equation: 1/λ = R∞ (1/n₁² − 1/n₂²)
- R∞ (Rydberg constant) = 1.097 × 10⁷ m⁻¹.
- n₁ and n₂ are integers, with n₂ > n₁.
- The equation predicts the wavelength of any hydrogen spectral line using quantized integer values.
- This quantization supported the development of quantum mechanics for electronic structure.
Key Terms & Definitions
- Continuous spectrum — light spectrum with all wavelengths present, no gaps.
- Line spectrum — spectrum showing only specific wavelengths as discrete lines.
- Rydberg constant (R∞) — constant used in the Rydberg equation, 1.097 × 10⁷ m⁻¹.
- Quantum/Quantized — occurring in discrete values rather than a continuous range.
Action Items / Next Steps
- Review the Rydberg equation and practice applying it to hydrogen spectral lines.
- Familiarize yourself with the appearance of both continuous and line spectra.