Rydberg Equation Calculator Hydrogen Atom

Rydberg Equation for Hydrogen:

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

Wavelength:

Energy:

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1. What is the Rydberg Equation?

The Rydberg equation predicts the wavelengths of spectral lines of many chemical elements, particularly hydrogen. It was formulated by the Swedish physicist Johannes Rydberg and presented in 1888.

2. How Does the Calculator Work?

The calculator uses the Rydberg equation for hydrogen:

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

Where:

\( \lambda \) — Wavelength of emitted/absorbed light (in meters)
\( R \) — Rydberg constant (1.097 × 10⁷ m⁻¹)
\( n_1 \) — Principal quantum number of lower energy level
\( n_2 \) — Principal quantum number of higher energy level

Explanation: The equation calculates the inverse wavelength of light emitted when an electron transitions between energy levels in a hydrogen atom.

3. Importance of Hydrogen Spectrum

Details: The hydrogen emission spectrum is fundamental to quantum mechanics and spectroscopy. It provided key evidence for the Bohr model of the atom and helps astronomers determine the composition of stars.

4. Using the Calculator

Tips: Enter integer values for n₁ (≥1) and n₂ (>n₁). The calculator will output the wavelength in nanometers (nm) and corresponding energy in electron volts (eV).

5. Frequently Asked Questions (FAQ)

Q1: What are the Lyman, Balmer, and Paschen series?
A: These are spectral series for hydrogen corresponding to n₁=1 (Lyman, UV), n₁=2 (Balmer, visible), and n₁=3 (Paschen, IR).

Q2: Why does the equation only work perfectly for hydrogen?
A: Hydrogen has one electron, making its energy levels simple. Multi-electron atoms have more complex interactions.

Q3: What is the Rydberg constant?
A: A physical constant relating to atomic spectra, equal to 1.097×10⁷ m⁻¹ for hydrogen.

Q4: Can this calculate absorption wavelengths?
A: Yes, the same equation applies for absorption (electron moving to higher n) or emission (moving to lower n).

Q5: What is the shortest possible wavelength?
A: As n₂ approaches infinity, the series limit gives the shortest wavelength for each series (n₁=1: 91.2 nm, n₁=2: 364.7 nm, etc.)