A Semiclassical Method to Predict Helium-like Energy Levels

Overview

Objectives/Goals The objective of my project is to develop a modified Bohr#s model using a semi-classical approach (using the Bohr theory and Coulomb repulsion energy) that can be easily understood by any high school students with simple geometry and pre-calculus math level to predict the energy levels and emission spectra of Helium-like atoms (ex: Helium and Lithium+1). Methods/Materials For materials, I used a spectrometer, a diffraction grating, and gas discharge tubes to measure the emission spectra lines. I also used the NIST database to get the energy levels for Helium-like atoms. Use my method to predict the emission lines and the energy levels, and then compare it to experimental lines and real energy levels from NIST database. Results The calculated energy levels of Helium and Lithium+1 was found surprisingly close to the NIST database. As for the spectral lines, the calculated and the experimental result was a little off. This is due to the fact that my method is based on Bohr's model, which did not include elements of Quantum Mechanics: the 2nd quantum number, spins of electrons, possibilities of transitions...etc. Conclusions/Discussion Because my model is simple (based on Bohr model, without Quantum Mechanics elements), it can be used to predict a approximate value of energy levels and spectral lines of Helium-like atoms, but not the exact value. This can be used as a tool for any high-school student with pre-calculus math level to predict energy levels, spectral lines, and somewhat have an understanding of Helium-like atoms without dealing with Quantum Mechanics which require Calculus-level math skills.

Competition history

• CSEF 2009 Physics & Astronomy · Entry S1912

Resources

• CSEF project summary ↗

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