Question

What is the Rydberg constant? Write down its unit.

Hint:

The Rydberg constant is fundamental in spectroscopy and quantum mechanics for predicting spectral lines.

Answer 1

Step 1: The Rydberg constant \( R \) is a fundamental physical constant that represents the limiting value of the highest wavenumber (inverse wavelength) of any photon that can be emitted from the hydrogen atom. It corresponds to the inverse of the wavelength associated with the transition of an electron from the ionization limit (infinite energy level) to the ground state (lowest energy level). The Rydberg constant is crucial in the formulation of the Rydberg formula for predicting the wavelengths of spectral lines in hydrogen.
Step 2: The approximate value of the Rydberg constant is: \[ R = 1.097 \times 10^7 \, \text{m}^{-1}. \] This value is experimentally determined and is used extensively in atomic physics and spectroscopy for calculating the wavelengths of emitted or absorbed light in hydrogen and hydrogen-like atoms.