ONE FORMULA, ONE ANSWER
Hydrogen Transition Wavelength Calculator
Estimate a hydrogen emission wavelength between two principal quantum numbers using a Rydberg model. Choose input units and calculate one value within the stated conditions.
Inputs
Calculations run in this browser. Scientific notation such as 1.2e-3 is supported. Do not group thousands.
Result
Vacuum emission wavelength λ
Enter values and select Calculate.
1/λ = R_H(1/n𝒻² − 1/nᵢ²)
Assumptions
Required: integer nᵢ>n𝒻≥1 and R_H>0. Supply a hydrogen coefficient that accounts for finite nuclear mass. The default 1.096776×10⁷ m⁻¹ is an educational approximation. The result is a vacuum wavelength. Excluded: fine and hyperfine structure, Lamb shifts, precision isotope corrections and external fields. Principal quantum numbers alone do not determine selection rules or line intensity.
Displayed values are floating-point approximations. Design safety factors and unprovided error contributions are not calculated.
Formula references and credits
NaNa Lab created the code, descriptions, icons and preview images. Text, figures and code from the linked references have not been reproduced.
Physical constants: NIST / CODATA 2022. The values of μ₀ and ε₀ are measured recommendations, not exact defining constants. Values and precision notes are in the source record.
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