Rydberg Equation Calculator Physics

Wavelength: --- nm
Series: ---
Wavelength: -- Frequency: -- Series: --

What is the Rydberg Equation Calculator?

Quick Answer: An interactive tool that uses the Rydberg formula to calculate the wavelength and frequency of spectral lines for hydrogen-like atoms. Enter the atomic number (Z) and the principal quantum numbers of the lower (n1) and upper (n2) levels to identify the spectral series and the exact wavelength of the emitted or absorbed photon.

Theory of the Rydberg Formula

The Rydberg equation predicts the wavelength of light resulting from an electron moving between energy levels in a hydrogen-like atom. The general formula is:
1/λ = R∞ Z2 (1/n12 - 1/n22)
where R∞ = 1.097373 × 107 m-1 (Rydberg constant), Z is the atomic number, n1 is the lower energy level, n2 is the higher energy level (n2 > n1). The tool computes wavelength in nanometres (nm) and frequency in terahertz (THz). The well‑known spectral series (Lyman, Balmer, Paschen, Brackett, Pfund) are determined by n1. The canvas draws an energy level diagram with an arrow for the transition.

Step-by-Step Examples

Example 1: Balmer H-alpha Line (Hydrogen)

  1. Set Z=1, n1=2, n2=3. Click Calculate. 1/λ = R (1/4 - 1/9) = 1.097e7 × 0.1389 = 1.523e6 m-1.
  2. λ = 656.3 nm (red light). Series: Balmer (visible).
  3. The diagram shows an arrow from n=3 down to n=2.

Example 2: Lyman Limit

  1. Press "Lyman (n1=1)", set n2=2. λ = 121.6 nm (UV). Series: Lyman.
  2. If n2 → ∞ (enter a large number like 30), λ = 91.2 nm (series limit).

Example 3: He+ ion

  1. Set Z=2, n1=2, n2=3. λ becomes 656.3 / 4 = 164.1 nm (extreme UV).

Frequently Asked Questions

What is the Rydberg constant?

R∞ = 1.097373 × 107 m-1. It is derived from fundamental constants and represents the limit of the highest wavenumber for hydrogen.

What do the spectral series represent?

Lyman (n1=1, UV), Balmer (n1=2, visible), Paschen (n1=3, IR), Brackett (n1=4, IR), Pfund (n1=5, IR). The series name depends on the lower energy level.

Can this be used for multi-electron atoms?

No, the Rydberg formula applies only to hydrogen-like species (single electron). For other atoms, screening effects modify the effective nuclear charge.

Why does the wavelength decrease as Z increases?

Because the Rydberg formula has a Z2 factor, so 1/λ increases with Z, making λ smaller (higher energy transitions).

What if n2 is very large?

When n2 → ∞, 1/n22 → 0, giving the series limit: 1/λ = R Z2 / n12.