1. What is the Balmer Series Formula?

The Balmer series formula calculates the wavelength of spectral lines emitted when electrons transition between energy levels in hydrogen atoms. It specifically describes transitions to the n=2 energy level.

2. How Does the Calculator Work?

The calculator uses the Balmer series formula:

Where:

• \( \lambda \) — Wavelength (m)
• \( R \) — Rydberg constant (1.097×10⁷ 1/m)
• \( n \) — Principal quantum number (≥3)

Explanation: The formula calculates the inverse wavelength of light emitted when an electron drops from energy level n to level 2 in a hydrogen atom.

3. Importance of Wavelength Calculation

Details: Calculating spectral wavelengths is fundamental to atomic physics, spectroscopy, and understanding quantum transitions in hydrogen atoms.

4. Using the Calculator

Tips: Enter the principal quantum number n (must be an integer ≥3). The calculator will compute the corresponding wavelength in meters.

5. Frequently Asked Questions (FAQ)

Q1: What is the Rydberg constant?
A: The Rydberg constant (R = 1.097×10⁷ m⁻¹) is a physical constant relating to atomic spectra and represents the limiting value of the highest wavenumber of any photon that can be emitted from hydrogen.

Q2: Why must n be ≥3?
A: The Balmer series specifically describes transitions to the n=2 level from higher energy levels (n=3,4,5,...).

Q3: What are some typical wavelength values?
A: For n=3: λ≈656 nm (red), n=4: λ≈486 nm (blue-green), n=5: λ≈434 nm (violet), n=6: λ≈410 nm (violet).

Q4: Can this formula be used for other elements?
A: The formula is specifically derived for hydrogen atoms. Other elements have more complex spectral patterns due to multiple electrons.

Q5: What are the practical applications?
A: This formula is used in spectroscopy, astronomy (analyzing stellar spectra), and quantum mechanics education to verify theoretical predictions.