Wave Number of Line Spectrum of Hydrogen Calculator

Wave Number Formula:

\[ \nu'_{HA} = R_{\infty} \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \]

Wave Number (m^-1):

Definition: The wave number represents the spatial frequency of a wave in hydrogen's line spectrum, measured in reciprocal meters (m^-1).

Purpose: This calculator determines the wave number of spectral lines in hydrogen's emission spectrum using the Rydberg formula.

The calculator uses the Rydberg formula:

\[ \nu'_{HA} = R_{\infty} \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \]

Where:

Explanation: The formula calculates the difference in energy between two quantum states of a hydrogen atom.

Details: Wave numbers are fundamental in spectroscopy for identifying elements and studying atomic structure.

Tips: Enter the principal quantum numbers (n₁ must be less than n₂). Common series:

Q1: What is the Rydberg constant?
A: The Rydberg constant (10973731.6 m^-1) is a physical constant relating to atomic spectra.

Q2: Why must n₂ be greater than n₁?
A: This ensures the electron transitions to a higher energy level, emitting a photon.

Q3: How does this relate to wavelength?
A: Wavelength (λ) = 1/wave number (ν'). The calculator gives ν' directly.

Q4: What are typical values for n₁ and n₂?
A: For visible spectrum (Balmer series), n₁=2, n₂=3-7.

Q5: Can this be used for other elements?
A: The formula is specific to hydrogen-like atoms. Other elements require modifications.