Electron Spin Resonance Sara Lim & Elizabeth Ann Pollock University of Rochester PHY 243: Advanced Lab Professor Regina Demina

External Magnetic Field Zeeman Effect Energy Splitting: Landé Factor: Apply an external magnetic field  For a Spin ½ system with a free electron (and zero angular momentum), g= 2

Spin in an External Magnetic Field In an external magnetic field, the spin is either parallel or anti-parallel to applied magnetic field  m = +1/2,-1/2  the energy levels: or

Resonance An electromagnetic field can induce magnetic dipole moment transitions if its frequency is near the energy difference: When the levels have spacing ΔE||H the oscillatory magnetic field exerts a torque on the dipoles  some of them reverse orientation, ie, they change energy levels: RESONANCE Precessing

Set-up

Samples

Differences in samples Valance electron acts analogously to H atom which has a free electron, so applying a magnetic field and sweeping allows observance of resonance It is harder to observe resonance by sweeping magnetic field because ‘subshell’ of molecule is filled, so only a few electrons are free in copper sulfate complex. They are held closer to the complex, so they alternate spin up/down given the relaxation time. The inverse of the relaxation time- the time to reach equilibrium in spin states- is the width of the absorption peak.

DPPH Calculations (in cgs units) Values obtained in lab (via gaussmeter and wavemeter)

Errors/Uncertainty Error in B-field - study with function generator - Imperfect B-field

Problems - Oscilloscope dials - Do not apply more than 20 amps when sweeping the applied B field because the fuse will blow!