Rydberg Equation
Calculate photon wavelengths for hydrogen-like atoms using the Rydberg formula 1/λ = RZ²(1/n₁² − 1/n₂²). Free online atomic physics calculator with spectral series, frequency, and energy results.
About This Calculator
The Rydberg Equation Calculator computes the wavelength, frequency, and energy of photons emitted during electron transitions in hydrogen and hydrogen-like (one-electron) atoms. Named after Swedish physicist Johannes Rydberg, this formula is one of the cornerstones of atomic physics and spectroscopy.
The Rydberg formula is expressed as 1/λ = R × Z² × (1/n₁² − 1/n₂²), where λ is the wavelength of emitted light, R is the Rydberg constant (1.097373 × 10⁷ m⁻¹), Z is the atomic number, and n₁ and n₂ are principal quantum numbers with n₂ > n₁. When an electron drops from a higher energy level (n₂) to a lower one (n₁), the energy difference is released as a photon. The formula can be extended to calculate frequency via f = c/λ and photon energy via E = hf = hc/λ.
This calculator identifies the spectral series automatically: Lyman series (n₁ = 1, ultraviolet), Balmer series (n₁ = 2, visible and ultraviolet), Paschen series (n₁ = 3, infrared), Brackett series (n₁ = 4, infrared), Pfund series (n₁ = 5, far infrared), and Humphreys series (n₁ = 6, far infrared). The Balmer series is particularly important because it includes the visible spectral lines of hydrogen, which are observed in astronomy to identify hydrogen in stars and nebulae.
Regional Notes
The Rydberg equation is based on universal physical constants and applies worldwide. The calculator uses standard SI units: wavelength in nanometers (nm), frequency in hertz (Hz), and energy in both joules (J) and electronvolts (eV). The Rydberg constant value (1.097373156816 × 10⁷ m⁻¹) follows the CODATA internationally recommended value used in physics education and research across all countries including India, the United States, and the United Kingdom.
Frequently Asked Questions
What is the Rydberg equation?
The Rydberg equation predicts the wavelengths of spectral lines emitted by hydrogen and hydrogen-like atoms. The formula is 1/λ = R × Z² × (1/n₁² − 1/n₂²), where R is the Rydberg constant (1.097 × 10⁷ m⁻¹), Z is the atomic number, and n₁ < n₂ are principal quantum numbers of the energy levels.
How do I use the Rydberg equation calculator?
Enter the atomic number Z (1 for hydrogen), the initial state n₂ (higher energy level, e.g. 3), and the final state n₁ (lower energy level, e.g. 2). Click Calculate to see the emitted photon's wavelength, frequency, energy, and the spectral series (Lyman, Balmer, Paschen, etc.).
What are the spectral series in hydrogen?
Hydrogen has six main spectral series: Lyman (n₁ = 1, ultraviolet), Balmer (n₁ = 2, visible/UV), Paschen (n₁ = 3, infrared), Brackett (n₁ = 4, infrared), Pfund (n₁ = 5, far infrared), and Humphreys (n₁ = 6, far infrared). Each series corresponds to electron transitions ending at a specific energy level.
What is the wavelength of the Balmer-alpha line?
The Balmer-alpha (Hα) line corresponds to the electron transition from n₂ = 3 to n₁ = 2 in hydrogen. Using the Rydberg formula, the wavelength is approximately 656.3 nm (red light), which is the most prominent line in the Balmer series.
Can the Rydberg equation be used for elements other than hydrogen?
Yes, the Rydberg equation works for hydrogen-like (one-electron) atoms such as He⁺, Li²⁺, and Be³⁺ by adjusting the atomic number Z. For multi-electron atoms, the simple Rydberg formula no longer applies due to electron-electron interactions and screening effects.
What is the Rydberg constant?
The Rydberg constant for hydrogen is approximately 1.097373 × 10⁷ m⁻¹. It is one of the most precisely determined physical constants, derived from quantum mechanics and the Bohr model of the atom. The constant is named after physicist Johannes Rydberg.
What is the difference between Lyman, Balmer, and Paschen series?
Lyman series transitions end at n₁ = 1 and produce ultraviolet light (91—122 nm). Balmer series transitions end at n₁ = 2 and include visible light (365—656 nm), making them historically important. Paschen series transitions end at n₁ = 3 and produce infrared light (820—1875 nm).
Is the Rydberg equation still used today?
Yes, the Rydberg equation remains fundamental in atomic physics and spectroscopy. It is used for identifying elements in stars and nebulae through their emission spectra, in quantum mechanics education, and for calibrating spectrometers. Modern quantum mechanics provides more precise calculations, but the Rydberg formula remains an excellent approximation for hydrogen-like atoms.