1. What is the Rydberg Formula?

The Rydberg formula calculates 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 formula:

Where:

• \( \lambda \) — Wavelength of the emitted light (meters)
• \( R \) — Rydberg constant (1.097 × 10⁷ m^-1)
• \( n_1 \) — Principal quantum number of the lower energy level
• \( n_2 \) — Principal quantum number of the higher energy level

Explanation: The formula predicts the wavelength of light resulting from an electron moving 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 provides evidence for quantized energy levels in atoms and is used in astronomical spectroscopy to identify hydrogen in stars and galaxies.

4. Using the Calculator

Tips: Enter integer values for n1 and n2 where n2 > n1. The calculator will return the wavelength in nanometers (nm) corresponding to the spectral line.

5. Frequently Asked Questions (FAQ)

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

Q2: Why is the Rydberg constant important?
A: It's a fundamental physical constant that appears in the solution of the Schrödinger equation for the hydrogen atom.

Q3: What is the shortest possible wavelength?
A: The series limit when n2 approaches infinity gives the shortest wavelength for each series.

Q4: Can this formula be used for other elements?
A: With modifications, it can approximate spectra for single-electron ions (He+, Li2+, etc.), but not multi-electron atoms.

Q5: How accurate is this calculation?
A: It's very accurate for hydrogen, though real-world measurements may show small deviations due to relativistic effects and nuclear motion.