Three emission lines involving three energy levels in an...

Three emission lines involving three energy levels in an atom occur at wavelengths $x, 1.5 x$, and $3.0 x$ nanometers. Which wavelength corresponds to the transition from the highest to the lowest of the three energy levels?

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Key Concepts

Spectroscopic Analysis

Spectroscopy involves studying the wavelengths of light emitted or absorbed by substances. By analyzing these emission lines, one can determine the energy levels within an atom and gain insight into its electronic structure.

Atomic Energy Levels

Atoms have discrete energy levels, and electrons occupy these specific levels. Transitions between these levels occur when electrons absorb or emit energy, with the magnitude of the energy change corresponding to the difference between the initial and final states.

Emission Lines

When an electron falls from a higher energy level to a lower level, it emits a photon. The energy of this photon is directly related to the energy difference between the two levels, resulting in an emission line at a specific wavelength that is characteristic of the element.

Energy-Wavelength Relationship

The energy of a photon is inversely proportional to its wavelength, according to the relation E = hc/?. This means that a larger energy gap between electron levels produces a photon with higher energy and therefore a shorter wavelength.

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