Calculate Wavelength Of Light Emitted From Hydrogen Atom

Rydberg Formula:

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

Wavelength:

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1. What is the Rydberg Formula?

The Rydberg formula predicts the wavelengths of spectral lines of many chemical elements, particularly hydrogen. It describes the light emitted when electrons transition between energy levels in a hydrogen atom.

2. How Does the Calculator Work?

The calculator uses the Rydberg formula:

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

Where:

\( \lambda \) — Wavelength of emitted light (meters)
\( R \) — 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 drops from energy level n₂ to n₁ in a hydrogen atom.

3. Importance of Hydrogen Spectrum Calculation

Details: The hydrogen spectrum is fundamental to quantum mechanics and spectroscopy. It helped establish quantum theory and is used in astronomy to identify hydrogen in stars and galaxies.

4. Using the Calculator

Tips: Enter integer values for quantum numbers. n₁ must be ≥ 1, n₂ must be > n₁. The calculator provides results in both meters and nanometers.

5. Frequently Asked Questions (FAQ)

Q1: What are the typical values for n₁ and n₂?
A: For visible light (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 formula use 1/λ instead of λ?
A: The formula calculates wavenumber (1/λ), which is proportional to energy. This makes the equation linear with respect to energy differences.

Q3: Can this formula be used for other elements?
A: The basic form works best for hydrogen-like atoms (single electron). For multi-electron atoms, modified versions are used.

Q4: What is the significance of the Rydberg constant?
A: It represents the limiting value of the highest wavenumber of any photon that can be emitted from hydrogen atom.

Q5: How accurate is this formula?
A: Extremely accurate for hydrogen. The predicted wavelengths match experimental measurements to within 0.001%.