Rydberg Equation Calculator

Rydberg Equation:

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

Initial Energy Level (n₁):

(integer)

Final Energy Level (n₂):

(integer)

Rydberg Constant (R):

m⁻¹

Wavelength (λ):

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1. What is the Rydberg Equation?

The Rydberg equation predicts the wavelength of light resulting from an electron moving between energy levels in a hydrogen atom. It was formulated by the Swedish physicist Johannes Rydberg in 1888.

2. How Does the Calculator Work?

The calculator uses the Rydberg equation:

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

Where:

\( \lambda \) — Wavelength of emitted/absorbed light (meters)
\( R \) — Rydberg constant (1.097373×10⁷ m⁻¹ for hydrogen)
\( n_1 \) — Principal quantum number of lower energy level
\( n_2 \) — Principal quantum number of higher energy level

Explanation: The equation calculates the inverse wavelength of the photon emitted when an electron transitions from a higher energy level (n₂) to a lower one (n₁).

3. Importance of the Rydberg Equation

Details: The Rydberg equation accurately predicts the wavelengths of the hydrogen spectral lines (Lyman, Balmer, Paschen series) and was crucial in the development of quantum mechanics.

4. Using the Calculator

Tips: Enter the initial (n₁) and final (n₂) energy levels as positive integers with n₂ > n₁. The Rydberg constant is pre-filled but can be adjusted for different hydrogen-like atoms.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for n₁ and n₂?
A: For visible spectrum (Balmer series), n₁=2 and n₂=3,4,5... For UV (Lyman series), n₁=1. For IR (Paschen series), n₁=3.

Q2: Why does the equation use 1/λ instead of λ?
A: The equation was originally formulated in terms of wavenumber (1/λ), which is proportional to energy.

Q3: Can this be used for other elements?
A: The equation works best for hydrogen and hydrogen-like ions (He⁺, Li²⁺). For other elements, modified versions are needed.

Q4: What are the limitations of the Rydberg equation?
A: It doesn't account for fine structure, hyperfine structure, or other quantum effects that cause small shifts in spectral lines.

Q5: How accurate is the Rydberg constant?
A: The current accepted value is 1.0973731568160(21)×10⁷ m⁻¹, one of the most precisely determined physical constants.