Excited H atoms have many emission lines. One series of...

Excited H atoms have many emission lines. One series of lines, called the Pfund series, occurs in the infrared region. It results when an electron changes from higher energy levels to a level with $n=5 .$ Calculate the wavelength and frequency of the lowest energy line of this series.

Key Concepts

Hydrogen Atom Energy Levels

In the hydrogen atom, electrons reside in specific quantized energy states characterized by a principal quantum number. The energy associated with each level is given by a formula that shows an inverse square dependence on the quantum number, meaning energy differences between successive levels decrease as the quantum number increases.

Electron Transitions

When an electron moves between these quantized energy levels, it either absorbs or emits a photon corresponding to the energy difference between the levels. Emission occurs when the electron falls from a higher to a lower energy level, producing a photon with an energy equal to that difference.

Rydberg Formula

The Rydberg formula is a key relation in atomic physics that predicts the wavelengths of photons emitted or absorbed during electron transitions in hydrogen and hydrogen-like atoms. It expresses the reciprocal of the wavelength in terms of the difference between the reciprocals of the squares of the initial and final energy level quantum numbers.

Photon Energy, Wavelength, and Frequency Relationships

A photon's energy is directly proportional to its frequency and inversely proportional to its wavelength, as expressed by the equations E = h? and c = ??. These relationships allow the calculation of one property (wavelength or frequency) when the other and the energy are known.

Electromagnetic Spectrum - Infrared Region

The electromagnetic spectrum is divided into regions based on wavelength, and the infrared region is characterized by wavelengths longer than visible light. Transitions that result in the emission of infrared light indicate smaller energy differences between the electron energy levels involved.

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