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ELECTRON SPIN RESONANCE Nathan Farwell and Dylan Prendergast. ABSTRACT. METHODS. DISCUSSION. Classically the Lande g-factor should be 1. In the case of an electron orbiting a proton we have and asasdfdfasdfa which yields asdfasdfad which when compared to asdfasdf tells us g=1.
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ELECTRON SPIN RESONANCENathan Farwell and Dylan Prendergast ABSTRACT METHODS DISCUSSION Classically the Lande g-factor should be 1. In the case of an electron orbiting a proton we have and asasdfdfasdfa which yields asdfasdfad which when compared to asdfasdf tells us g=1. This is not the case however. Because of the electrons ½ spin system, we have a Lande g-factor of 2.002. SYSTEM SETUP . In this experiment we examine the aspects of microwave spectroscopy. We investigated namely the Lande g-factor for several compounds (DPPH, Copper sulfide, and Manganese Chloride). By exposing these compounds to electromagnetic radiation of a constant frequency and then placing them in a magnetic field, we can observe the change in magnetic dipole orientation that will occur in the compound. In our experiments we found a g-factor very close to this accepted value for the sample DPPH. We were unable to find resonance with both samples Copper Sulfide and Manganese Chloride. DPPH calculation using asdfasdfasdfasdf h= 4.135 x10^-15 eV*s μB= 5.8x10^-11 MeV/T v= 8.871Hz +- .005Hz H= 3.14kG +- .03kG g= 2.0184 +- .0163 PROCEDURE The system is set up using a series of wave guides to guide the electromagnetic radiation originating from the klystron throughout the setup. The first thing we need to find in order to experimentally calculate the Lande g-factor for our samples is the frequency emitted by the klystron. The instrument we use to find this is the wavemeter as seen in the above diagram. By adjusting the nearby tunable short we can find resonance, by hooking in an oscilloscope and watching the readings, in the system. Adjusting the wavemeter until the system is no longer resonating will allow us to find the constant frequency of the klystron. Next will need to put the sample into the sample cavity and create a magnetic field around it of the appropriate strength that will allow us to induce dipole transitions. By hooking up an oscilloscope to the sides of the Magic Tee, (see below) we can watch the system as we sweep over different magnetic fields for the time when the change in the dipole causes interference. We then use a Gaussmeter to find the magnetic field necessary to facilitate this transition. We now have all the information we need to calculate the Lande g-factor for the sample we are investigating using . INTRODUCTION All materials exhibit magnetic properties. We can see easily in compounds where the electrons in the compound have a magnetic moment. With charged particles with angular momentum the magnetic moment is equal to: Where g is the Lande g-factor. In our experiment we know that an electromagnetic field can induce dipole transitions if its frequency is near to the energy difference or When we expose our samples to electromagnetic radiation of a constant frequency v (achieved by using a locked in klystron in a wave guide system) and then expose them to the proper magnetic field H, we can then calculate g, the Lande factor using the formula Where aasdfasdfsasdfasdfadfasdfasdf is the Bohr magneton and h is Planks constant. CONCLUSION Although we were unable to take measurements for the Lande g-factor for all the samples we were able to accuratly calculate it for DPPH. Our experimental result of 2.0184 is very close to the accepted and well within our error. We have shown the Lande g-factor to not be 1 as it is classically predicted but to be equal to ≈2 which results from the electron ½ spin system.
