To what series does the spectral line of atomic hydrogen...

To what series does the spectral line of atomic hydrogen belong if its wave number is equal to the difference between the wave numbers of the following two lines of the Balmer series: $486.1$ and $410.2 \mathrm{~nm} ?$ (a) Lyman series (b) Balmer series (c) Paschen series (d) Brackett series

To what series does the spectral line of atomic hydrogen belong if its wave number is equal to the difference between the wave numbers of the following two lines of the Balmer series: $486.1$ and $410.2 \mathrm{~nm} ?$
(a) Lyman series
(b) Balmer series
(c) Paschen series
(d) Brackett series

Key Concepts

Atomic Spectral Series

In the hydrogen atom, electrons transition between discrete energy levels, and the emitted or absorbed light corresponds to specific wavelengths grouped into series such as the Lyman, Balmer, Paschen, etc. Each series is characterized by transitions ending on the same lower energy level; for example, the Balmer series involves transitions ending at the n=2 level, while the Lyman series involves transitions terminating at n=1. This categorization helps in understanding and predicting the spectral lines observed in hydrogen spectra.

Wave Number

The wave number is defined as the inverse of the wavelength (typically measured in cm?¹) and is directly proportional to the energy of a photon. In spectroscopy, wave numbers are used because they provide a linear measure of energy differences between the quantum states. Since energy differences between levels can be stated as differences in wave numbers, calculating these differences is crucial to understanding the transitions associated with specific spectral series.

Rydberg Formula

The Rydberg formula quantitatively describes the wavelengths of the spectral lines of hydrogen based on transitions between energy levels. It expresses the wave number of a photon emitted or absorbed during an electron transition as the difference in reciprocals of the squares of the quantum numbers (n). This formula provides a direct connection between the observed spectral lines and the underlying quantum transitions, allowing one to identify the series (e.g., Lyman, Balmer) involved by matching the calculated wave numbers with those observed.

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