1. What is the Rydberg Equation for Hydrogen Ion?

The Rydberg equation predicts the wavelength of light resulting from an electron moving between energy levels in a hydrogen atom or hydrogen-like ion (like H⁺). It's fundamental to atomic physics and spectroscopy.

2. How Does the Calculator Work?

The calculator uses the Rydberg equation:

Where:

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

Explanation: When an electron transitions between energy levels, the energy difference corresponds to a photon with specific wavelength calculated by this equation.

3. Importance of the Rydberg Equation

Details: The equation accurately predicts the spectral lines of hydrogen observed in astronomy, quantum mechanics, and spectroscopy. It was key in developing Bohr's atomic model.

4. Using the Calculator

Tips: Enter integer values for n₁ (initial level) and n₂ (final level). For emission spectra, n₂ > n₁; for absorption, n₂ < n₁. Typical values range from 1 to 7.

5. Frequently Asked Questions (FAQ)

Q1: Why is this called the "hydrogen ion" calculator?
A: While primarily for hydrogen atoms, the same equation applies to hydrogen-like ions (single electron systems) with appropriate Rydberg constant adjustment.

Q2: What are typical values for n₁ and n₂?
A: For visible spectrum (Balmer series), n₁=2 and n₂=3-7. For UV (Lyman series), n₁=1 and n₂≥2.

Q3: How accurate is this equation?
A: Extremely accurate for hydrogen, with small corrections needed only for very precise measurements.

Q4: Can this calculate energy as well as wavelength?
A: Yes, energy can be calculated using E = hc/λ where h is Planck's constant and c is light speed.

Q5: What about other elements?
A: The equation works best for single-electron systems. Multi-electron atoms require more complex quantum mechanical calculations.