The figure below represents part of the emission spectrum...

The figure below represents part of the emission spectrum for a oneelectron ion in the gas phase. All the lines result from electronic transitions from excited states to the $n=3$ state. (See Exercise 126.) a. What electronic transitions correspond to lines $A$ and $B$ ? b. If the wavelength of line $B$ is $142.5 \mathrm{~nm}$, calculate the wavelength of line $A$.

The figure below represents part of the emission spectrum for a oneelectron ion in the gas phase. All the lines result from electronic transitions from excited states to the $n=3$ state. (See Exercise 126.)
a. What electronic transitions correspond to lines $A$ and $B$ ?
b. If the wavelength of line $B$ is $142.5 \mathrm{~nm}$, calculate the wavelength of line $A$.

Key Concepts

Emission Spectrum

An emission spectrum is a set of discrete wavelengths of light emitted by atoms or ions when they transition from higher energy levels to lower ones. The spectral lines seen in an emission spectrum correspond to the specific differences in energy between these quantized states, and each line is characteristic of the atom or ion’s structure and energy levels.

Electronic Transitions

Electronic transitions refer to the movement of an electron between energy levels within an atom. When an electron transitions from a higher to a lower energy level, a photon is emitted with a wavelength that matches the energy difference between the two states. This concept is fundamental to understanding the spectral lines observed in emission spectra.

Energy Levels

Energy levels are the discrete, quantized states that an electron can occupy in an atom. Each level is associated with a principal quantum number, and the energy differences between these levels determine the possible wavelengths of the emitted or absorbed light. In spectral analysis, understanding energy level transitions helps predict and explain the observed wavelengths.

One-Electron Ion

A one-electron ion is an ion that contains only a single electron, similar to the hydrogen atom. This simplification allows for the use of the Rydberg formula to accurately calculate the wavelengths of light emitted or absorbed during electronic transitions. The linearity of energy level spacing in such ions makes them ideal models for studying atomic spectra.

Rydberg Formula

The Rydberg formula is a mathematical relationship used to predict the wavelengths of the spectral lines of one-electron ions. It relates the inverse of the wavelength to the difference between the inverses of the squares of the principal quantum numbers of the two electronic energy levels involved in the transition. This formula is crucial in determining the wavelengths of emitted photons during electron transitions.

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