This experiment is based on the use of the Scanning Electronic Microscope (SEM) in the Saints Center. The Bohr-Rutherford shell model of atomic structure can be used to understand how the SEM performs an elemental analysis using x-rays. The students can measure the K-alpha and K-Beta x-ray spectra from various metals. These metals can range from atomic numbers between 12 and 41. This can be used to verify Moseley's Law. Moseley's law is an empirical law concerning the characteristic x-rays that are emitted by atoms. (For more on Moseley's Law).
In performing this experiment the students would be taking several photographs/snapshots from the SEM. After taking the photographs the students will be taking measurements of the x-ray spectra of different types of elements in order to analyze the variation of the x-ray spectra with the atomic number. The students will need to be first trained on the SEM of course and then taking the photographs and spectra for a number of elements (approximately 15, taking roughly an hour). The student scan present their data as a function of atomic weight or atomic number, Z. Once this is done a Moseley Plot can be made by taking the square root of x-ray energy vs. Z, using Moseley's Law shown below. This plot should show a linear relationship between the measured quantity, square root of E, and atomic number, Z.
The energies of the x-ray spectra can be fit using this function, which is referred to as Moseley's law.
E=hv=B(Z-sigma)^2
Where B and sigma depend on the family of x-ray lines. B involves Rydberg energy and sigma is like a type of screening parameter.
Another useful equation is the Bohr equation for hydrogenic transition energies, E, that predicts the hydrogenic energy levels of a single electron orbiting a nucleus with a positive charge.
E=R(1/(nf^2)-1/(ni^2))*Z^2
Where nf is the principal quantum number of the final state and ni is of the initial state. R is the Rydberg constant and Z is the effective nuclear charge (Z-sigma).
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