Rydberg Wavelength Calculator

Rydberg Formula:

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

Wavelength (λ):

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1. What is the Rydberg Formula?

The Rydberg formula calculates the wavelengths of spectral lines of many chemical elements. It's particularly accurate for hydrogen and hydrogen-like elements with a single electron.

2. How Does the Calculator Work?

The calculator uses the Rydberg formula:

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

Where:

\( \lambda \) — Wavelength (in 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: The formula predicts the wavelength of light resulting from an electron moving between energy levels in an atom.

3. Importance of Wavelength Calculation

Details: Calculating spectral lines is fundamental to understanding atomic structure, quantum mechanics, and has applications in astronomy, spectroscopy, and quantum physics.

4. Using the Calculator

Tips: Enter the Rydberg constant (1.097×10⁷ m⁻¹ for hydrogen), initial energy level (n₁), and final energy level (n₂). n₂ must be greater than n₁.

5. Frequently Asked Questions (FAQ)

Q1: What is the Rydberg constant for hydrogen?
A: The Rydberg constant for hydrogen is approximately 1.097×10⁷ m⁻¹.

Q2: What are typical values for n₁ and n₂?
A: For the Balmer series (visible light), n₁=2 and n₂=3,4,5... For Lyman series (UV), n₁=1.

Q3: Why does the formula only work for hydrogen-like atoms?
A: The formula assumes a single electron system. Multi-electron atoms have more complex interactions.

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

Q5: What are the units of the result?
A: The calculator outputs wavelength in nanometers (nm) for convenience.