Objective: The tools and data provided here are intended to assist students in their understanding of the quantization of the energy levels of single-electron atoms, and the spectral lines that arise from this quantization.
Data: The pull down menu in the upper left is for selection of a specific atom. The atoms are hydrogen (H), singly ionized helium (He+), doubly ionized lithium (Li2+), and triply ionized beryllium (Be3+). Spectral data of differing completeness for four single-electron atoms is provided in the left hand table. The data is drawn from the spectroscopic data provided by the National Institute of Science and Technology (NIST).
The Spectrum Display Tool: This tool is at the top of the screen. The range of wavelengths displayed is controlled by the pull down menu on the right below the Spectrum Display. Selecting a spectral line (clicking on it): (i) displays the wavelength selected below the Spectrum Display Tool; (ii) highlights the corresponding entry in the Data Table; and, (iii) highlights the corresponding energy on the central graph.
The Asymptote Tool: This tool is used on the central graph. The pull-down menu beneath this tool sets the range of energies displayed. This graph shows a plot of the spectral line energies as a function of “line number” N. The Asymptote Tool is a line that can be dragged up and down on this energy graph to determine the limiting energy of transitions for the different spectral series for each case. (For H, these are the Lyman, Balmer, Paschen, Brackett, and Pfundt Series.) These limiting energies are the energies for the orbitals of the one-electron atom.
The Energy Transition Tool: This tool is on the far right. The range of energies displayed is set by the left pull-down menu beneath the Tool. There are two modes for this tool determined by the pull-down menu in the lower right hand corner.
(i) Add Energy Levels: Once the orbital energies have been determined using the Asymptote Tool, these energies can be used to set the energy levels in the Transition Tool. Clicking on an energy on the scale of the tool will cause a horizontal line to appear. If the energy selected is an orbital energy, then this line will remain after the cursor is removed, otherwise it will vanish.
(ii) Add Energy Transitions: After the energy levels have been properly placed on the graph, an arrow can be drawn between levels corresponding to a transition. This tool is linked to the lowermost spectrum display. When the arrow is drawn between energy levels, the spectral line appears in the lower spectrum display for comparison with the upper spectrum display.
Suggested investigations:
(1) Distinction between Spectral Lines and Energy Levels: The difference between
energy levels and spectral lines can be emphasized to students through use
of the Energy Transition Tool.
(2) The Z2 dependence of energy levels for a single-electron atom can be investigated.
(3) The Li2+ and Be3+ spectral series are incomplete. This provides an opportunity
for students to make predictions based on (2) for the observable spectral lines.