A hydrogen atom in the ground state absorbs a photon whose...

A hydrogen atom in the ground state absorbs a photon whose wavelength is $95.0 \mathrm{nm}$. The resulting excited atom then emits a photon of $1282 \mathrm{nm}$. What are the regions of the electromagnetic spectrum for the radiations involved in these transitions? What is the principal quantum number of the final state resulting from the emission from the excited atom?

Key Concepts

Electromagnetic Spectrum Regions

The electromagnetic spectrum is divided into regions based on photon wavelength or frequency. In contexts such as hydrogen transitions, absorbed radiation in the ultraviolet (UV) range and emitted radiation in the infrared (IR) range can indicate the energy scale of the transitions. Identifying the regions helps in understanding both the energetic nature of the photons and their interaction with matter.

Rydberg Formula

The Rydberg formula relates the wavelengths of the photons absorbed or emitted by the hydrogen atom to the difference between the inverse squares of the principal quantum numbers of the initial and final states. It is a key tool in predicting the energy transitions in hydrogen and is used to determine which energy levels are involved in a particular spectral line.

Electronic Transitions

Electronic transitions refer to the process by which an electron moves between these quantized energy levels. When a hydrogen atom absorbs energy–for example, from a photon–an electron jumps from a lower to a higher energy level; conversely, when the electron falls to a lower level, it emits a photon with energy equal to the difference between the two levels.

Hydrogen Atomic Energy Levels

In hydrogen, the electron is confined to discrete energy levels characterized by a principal quantum number. These quantized states, as described by the Bohr model, determine the energy an electron has when it is in a particular orbit and set the stage for understanding how electrons transition between levels by absorbing or emitting energy.

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