StatGardenREF. DESK
Calculators/Physics/Rydberg Equation
Physics

Rydberg Equation calculator

Wavelength of light from an electron jumping between energy levels in a hydrogen-like atom.

What this calculator does

Rydberg Equation works out wavelength of light from an electron jumping between energy levels in a hydrogen-like atom. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.

The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.

The formula

Formula1/λ = R·Z²·(1/n1² − 1/n2²), R = 1.0973731568×10⁷ m⁻¹ (CODATA)

The inputs explained

FieldWhat to enter
Atomic number (Z, hydrogen = 1)A number. Starts at 1.
Lower energy level (n1)A number. Starts at 2.
Higher energy level (n2)A number. Starts at 3.

Worked examples

Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.

How the answer changes with atomic number (z, hydrogen = 1)

Every other input is held at the calculator’s starting values while atomic number (z, hydrogen = 1) varies. Select any row to load that scenario into the calculator.

How the answer changes with atomic number (z, hydrogen = 1)
Atomic number (Z, hydrogen = 1)Wavelength (λ)Wavelength (λ)Frequency
0.52,624.45 nm2.6244e-6 m1.1423e+14 Hz
0.751,166.42 nm1.1664e-6 m2.5702e+14 Hz
1656.11 nm6.5611e-7 m4.5692e+14 Hz
1.5291.61 nm2.9161e-7 m1.0281e+15 Hz
2164.03 nm1.6403e-7 m1.8277e+15 Hz
372.90 nm7.2901e-8 m4.1123e+15 Hz