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 (in meters)
• \( R \) — Rydberg constant (typically 1.097×10⁷ m⁻¹ for hydrogen)
• \( n_1 \) — 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 Spectral Lines

Details: Spectral lines are fundamental to spectroscopy and are used to identify elements in stars and other celestial objects. Each element has a unique spectral fingerprint.

4. Using the Calculator

Tips: Enter the initial (n₁) and final (n₂) quantum numbers as integers (n₂ > n₁). The Rydberg constant defaults to the hydrogen value (1.097×10⁷ m⁻¹).

5. Frequently Asked Questions (FAQ)

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

Q2: Why does the Rydberg constant differ for elements?
A: The constant depends on nuclear charge and electron mass. For hydrogen-like atoms, it's R = R∞Z² where Z is atomic number.

Q3: What are typical values for n₁ and n₂?
A: For hydrogen, n₁ is usually 1-5, and n₂ is n₁+1 to n₁+10. The Balmer series (n₁=2) produces visible light.

Q4: How accurate is this formula?
A: Very accurate for hydrogen, but requires modifications for multi-electron atoms due to electron-electron interactions.

Q5: What's the physical meaning of the formula?
A: It represents the energy difference between electron orbits in Bohr's atomic model, with energy released as photons.