Rydberg Equation Calculator

Rydberg Equation for Hydrogen

The Rydberg formula predicts the wavelengths of spectral lines emitted when an electron in a hydrogen atom transitions between principal quantum levels. It is one of the foundational results of early quantum theory.

Rydberg Formula

$$\frac{1}{\lambda} = R\left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)$$

$R = 1.097 \times 10^7\ \text{m}^{-1}$ is the Rydberg constant, $n_1$ is the lower energy level, and $n_2$ is the upper level with $n_2 > n_1$. Wavelength $\lambda$ is in meters.

Example: the Balmer $H_\alpha$ line (2 → 3) gives $\lambda \approx 656.3$ nm (red light).

Spectral Series

When $n_1 = 1$, lines fall in the Lyman series (UV). $n_1 = 2$ gives the Balmer series (visible). $n_1 = 3$ produces the Paschen series (infrared). Each series corresponds to transitions down to a fixed lower level.

Frequently Asked Questions

Why must n₂ be greater than n₁?

Emission occurs when the electron drops from a higher level ($n_2$) to a lower one ($n_1$). The formula requires $n_2 > n_1$ so the term in parentheses is positive.

Does this work for atoms other than hydrogen?

The basic Rydberg form applies to hydrogen-like ions with an adjusted effective nuclear charge. Multi-electron atoms need more complex models.

How is photon energy related to wavelength?

Photon energy $E = hc/\lambda$. A handy approximation is $E\,(\text{eV}) \approx 1240 / \lambda\,(\text{nm})$.

What is the Rydberg constant?

$R \approx 1.097 \times 10^7\ \text{m}^{-1}$ for hydrogen. It sets the scale of atomic emission and absorption wavenumbers.

Report

Rydberg Equation for Hydrogen

Rydberg Formula

Spectral Series

Frequently Asked Questions

Related Tools

Recent Visits