The Lyman series of emission lines of the hydrogen atom are those for which nf = 1. (a) Determine the region of the electromagnetic spectrum in which the lines of the Lyman series are observed.

Verified step by step guidance

1. Identify the Lyman series in the context of the hydrogen atom's emission spectrum, where the final energy level (n_f) is 1.
2. Recall that the Lyman series involves electronic transitions from higher energy levels (n_i > 1) to the n_f = 1 level.
3. Use the Rydberg formula for hydrogen: \( \frac{1}{\lambda} = R_H \left( \frac{1}{1^2} - \frac{1}{n_i^2} \right) \), where \( R_H \) is the Rydberg constant and \( n_i \) is the initial energy level.
4. Recognize that the Lyman series transitions result in the release of photons with wavelengths in the ultraviolet (UV) region of the electromagnetic spectrum.
5. Conclude that the Lyman series lines are observed in the ultraviolet region, as these transitions involve high energy changes.

Key Concepts

Lyman Series

The Lyman series refers to a set of spectral lines corresponding to transitions of electrons in a hydrogen atom from higher energy levels (n ≥ 2) to the lowest energy level (n = 1). These transitions result in the emission of ultraviolet light, which is a key feature of hydrogen's emission spectrum.

Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, arranged by wavelength or frequency. It includes gamma rays, X-rays, ultraviolet light, visible light, infrared radiation, microwaves, and radio waves. The Lyman series specifically falls within the ultraviolet region of this spectrum.

Energy Level Transitions

Energy level transitions in an atom occur when an electron moves between different energy states. When an electron drops from a higher energy level to a lower one, it releases energy in the form of a photon. The energy of the emitted photon corresponds to the difference in energy between the two levels, determining the wavelength and thus the position in the electromagnetic spectrum.