Rydberg Equation Calculator
Calculate hydrogen emission spectrum wavelengths and frequencies using the Rydberg formula for atomic spectroscopy
Calculate Hydrogen Spectral Lines
Hydrogen-like atoms only
Must be greater than final state
Lower energy level (ground state = 1)
Spectral Line Results
Visible spectrum region
Transition Details
Atom: Hydrogen (H)
Transition: n=3 → n=2
Energy Change: ΔE = 1.890 eV
Physical Properties
Wavelength (m): 6.561e-7
Frequency (Hz): 4.569e+14
Energy (J): 3.028e-19
Rydberg Equation: 1/λ = R·Z²·(1/n₁² - 1/n₂²) = 1.524 × 10⁶ m⁻¹
Rydberg Constant: R = 1.0974e+7 m⁻¹
Example Calculation
Balmer Series: n=4 → n=2 (Hydrogen)
Transition: Fourth to second energy level
Calculation: 1/λ = R·1²·(1/2² - 1/4²) = 1.097×10⁷·(1/4 - 1/16)
Result: 1/λ = 1.097×10⁷·(0.25 - 0.0625) = 2.056×10⁶ m⁻¹
Wavelength: λ = 486 nm (Blue-green light)
Series: Balmer series (visible spectrum)
Lyman Series: n=2 → n=1 (Hydrogen)
Transition: Second to ground state
Calculation: 1/λ = R·1²·(1/1² - 1/2²) = 1.097×10⁷·(3/4)
Wavelength: λ = 122 nm (Ultraviolet)
Energy: 10.2 eV (Lyman alpha line)
Hydrogen Spectral Series
n → 1
n → 2
n → 3
n → 4
n → 5
n → 6
Physics Constants
Famous Spectral Lines
Understanding the Rydberg Equation
What is the Rydberg Equation?
The Rydberg equation is a mathematical formula used to predict the wavelengths of spectral lines in hydrogen and hydrogen-like atoms. It was developed by Johannes Rydberg in 1888 and provides a precise way to calculate the electromagnetic radiation emitted during electron transitions.
Key Principles
- •Electrons exist only in specific energy levels
- •Energy is emitted when electrons drop to lower levels
- •Each transition produces a specific wavelength
- •Different series correspond to different final states
Rydberg Formula
1/λ = R·Z²·(1/n₁² - 1/n₂²)
- λ: Wavelength of emitted light
- R: Rydberg constant (1.097 × 10⁷ m⁻¹)
- Z: Atomic number (1 for hydrogen)
- n₁: Lower energy level (final state)
- n₂: Higher energy level (initial state)
Note: The equation is most accurate for hydrogen and hydrogen-like ions with only one electron.
Applications in Science
Atomic Spectroscopy
Identify elements in stars, gases, and laboratory samples by analyzing their characteristic spectral lines and emission patterns.
Quantum Mechanics
Fundamental evidence for quantized energy levels in atoms, supporting Bohr's model and modern quantum mechanical theory.
Astronomy
Determine composition, temperature, and motion of celestial objects through analysis of hydrogen absorption and emission lines.