1. What is the Rydberg Formula?

The Rydberg formula calculates the wavelengths of spectral lines of many chemical elements. It was formulated by the Swedish physicist Johannes Rydberg and is used to describe the wavelengths of spectral lines of hydrogen and hydrogen-like elements.

2. How Does the Calculator Work?

The calculator uses the Rydberg formula:

Where:

• \( \lambda \) — Wavelength of the emitted light
• \( R \) — 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 formula calculates the inverse wavelength of light emitted when an electron transitions between energy levels in a hydrogen atom.

3. Importance of the Rydberg Formula

Details: The Rydberg formula is fundamental in atomic physics and spectroscopy. It accurately predicts the wavelengths of the hydrogen spectral series (Lyman, Balmer, Paschen, etc.) and was key in the development of quantum mechanics.

4. Using the Calculator

Tips: Enter integer values for n₁ and n₂, where n₂ > n₁. The calculator will return the wavelength in nanometers (nm) of the emitted photon during the electron transition.

5. Frequently Asked Questions (FAQ)

Q1: What are the valid values for n₁ and n₂?
A: Both must be positive integers with n₂ > n₁. Typically n₁ ≥ 1 and n₂ ≥ 2.

Q2: What is the Rydberg constant?
A: The Rydberg constant (R) is 1.097 × 10⁷ m⁻¹ for hydrogen. It represents the limiting value of the highest wavenumber of any photon that can be emitted by hydrogen.

Q3: What spectral series does this correspond to?
A: n₁=1 (Lyman series, UV), n₁=2 (Balmer series, visible), n₁=3 (Paschen series, IR), etc.

Q4: Can this be used for elements other than hydrogen?
A: The formula works best for hydrogen or hydrogen-like ions (single electron systems). For multi-electron atoms, modifications are needed.

Q5: Why is the result in nanometers?
A: Nanometers are a convenient unit for atomic spectra as most wavelengths fall between 100-1000 nm.