Five lines in the H atom spectrum have these wavelengths ( in Ȧ):(a) 1212.7 ;(b) 4340.5 ;(c) 486

step 1 So for this problem, five lines in the hydrogen atom spectrum have the given wavelengths in anst

Five lines in the H atom spectrum have these wavelengths (...

Five lines in the $\mathrm{H}$ atom spectrum have these wavelengths $($ in $\dot{A}):(a) 1212.7 ;(b) 4340.5 ;(c) 4861.3 ;(d) 6562.8 ;(e) 10,938$ Three lines result from transitions to $n_{\text {finul }}=2$ (visible series). The other two result from transitions in different series, one with $n_{\text {final }}=1$ and the other with $n_{\text {final }}=3$. Identify $n_{\text {initial }}$ for each line.

Five lines in the $\mathrm{H}$ atom spectrum have these wavelengths $($ in $\dot{A}):(a) 1212.7 ;(b) 4340.5 ;(c) 4861.3 ;(d) 6562.8 ;(e) 10,938$
Three lines result from transitions to $n_{\text {finul }}=2$ (visible series). The other two result from transitions in different series, one with $n_{\text {final }}=1$ and the other with $n_{\text {final }}=3$. Identify $n_{\text {initial }}$ for each line.

Key Concepts

Quantized Energy Levels

In atomic physics, electrons in an atom occupy discrete energy levels that are defined by quantum numbers. These levels are not continuous, and each has a specific energy value, meaning that electrons must be promoted or demoted between these levels via absorption or emission of quantized energy amounts.

Electron Transitions

Electron transitions occur when an electron moves from one energy level to another, resulting in the absorption or emission of a photon whose energy corresponds to the difference between the initial and final states. These photon energies determine the wavelengths of the spectral lines observed in atomic spectra.

Rydberg Formula

The Rydberg formula is a mathematical expression used to predict the wavelengths of spectral lines produced by transitions between different energy levels in the hydrogen atom. It relates the inverse of the wavelength to the difference of the inverses of the squares of the initial and final quantum numbers, making it a fundamental tool in understanding emission and absorption spectra.

Spectral Series

Hydrogen spectral lines are organized into series based on the final energy level (n_final) reached during an electron transition. Examples include the Lyman series (with n_final = 1, typically in the ultraviolet range), the Balmer series (with n_final = 2, visible spectrum), and series with higher n_final values such as the one with n_final = 3 (which appears in the infrared region). Each series has characteristic wavelengths corresponding to transitions terminating at a specific energy level.

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