To calculate the wavelength (\(W\)):
\[ W = \frac{1}{R \cdot Z^2 \cdot \left( \frac{1}{nf^2} - \frac{1}{ni^2} \right)} \]
Where:
The Rydberg equation is a fundamental mathematical formula that describes the wavelengths of light emitted or absorbed by atoms. It was developed by the Swedish physicist Johannes Rydberg in the late 19th century and revolutionized our understanding of atomic structure.
The significance of the Rydberg equation lies in its ability to provide a quantitative explanation for the spectral lines observed in the emission and absorption spectra of atoms. When an atom absorbs energy, its electrons jump to higher energy levels. Subsequently, when these electrons return to lower levels, they release energy in the form of light. The Rydberg equation allows us to predict the exact wavelengths of light emitted during these transitions.
By understanding the precise wavelengths of light emitted or absorbed by atoms, scientists can unravel the complex structure of atoms and their energy levels. This knowledge is crucial in various fields of science, such as astrophysics, chemistry, and quantum mechanics.
Let's assume the following values:
Using the formula:
\[ W = \frac{1}{1.097 \times 10^7 \cdot 1^2 \cdot \left( \frac{1}{2^2} - \frac{1}{3^2} \right)} \approx 6.56 \times 10^{-7} \text{ meters} \]
The wavelength is approximately \(6.56 \times 10^{-7}\) meters.
