Calculate the wavelength of light emitted when each of the...

Calculate the wavelength of light emitted when each of the following transitions occur in the hydrogen atom. What type of electromagnetic radiation is emitted in each transition?
a. $n=4 \rightarrow n=3$
b. $n=5 \rightarrow n=4$
c. $n=5 \rightarrow n=3$

Key Concepts

Hydrogen Atom Energy Levels

Hydrogen atoms have quantized energy levels that are determined by the principal quantum number n. When an electron transitions between these levels, it emits or absorbs a photon with energy equal to the difference between the levels. This quantum nature of energy levels is foundational to understanding atomic spectra.

Rydberg Formula

The Rydberg formula establishes a relationship between the wavelength of emitted or absorbed light and the initial and final energy levels of the electron in a hydrogen atom. It uses the Rydberg constant along with the difference in the reciprocals of the squares of the quantum numbers to determine the wavelength associated with the transition.

Spectral Series

Spectral series classify electronic transitions in a hydrogen atom based on the final energy level, such as the Lyman, Balmer, and Paschen series. Each series corresponds to a distinct range of wavelengths in the electromagnetic spectrum, with the Balmer series, for example, falling within the visible region.

Electromagnetic Spectrum

The electromagnetic spectrum comprises all types of electromagnetic radiation arranged according to wavelength or frequency. In the context of electron transitions, the energy of the emitted photon determines its position on the spectrum, identifying whether the radiation falls within the ultraviolet, visible, or infrared region.

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