The mass of an atom, a fundamental property, serves as a unique identier of the nucleus like a fingerprint and represents, through the binding energy, the sum of all atomic and nuclear interactions. Precise mass values are essential in many disciplines including nuclear structure and fundamental symmetries. The highest precision mass measurements are obtained with Penning trap mass spectrometers; of those, onlythe Low Energy Beam and Ion Trap (LEBIT) facility has been able to measure rare isotopes produced by projectile fragmentation. In this work, the high precision mass measurement of unstable Si-32, dm/m = 1 x10^-8, is presented and found to deviate from the literature value by four standard deviations. The measurement is combined with the mass values for the A = 32, T = 2 quintet to provide the most stringent testof the isobaric multiplet mass equation (IMME) to date. The experimental results indicate a dramatic breakdown of the quadratic form of IMME and require a large cubic term. In addition, the masses of Si-33, P-31, P-34, and S-32 were measured, which agree with earlier experimental data.Beam purity is critical to high-precision Penning trap mass spectrometry. This dissertation documents the development of in-trap cleaning of stored ion samples based on stored waveform inverse Fourier transform (SWIFT). The technique can eliminate isobaric contaminants without the need to identify individual contaminants unlike the method used in the present work. SWIFT cleaning minimizes possible systematic errors in mass determination and will increase LEBIT's measurement effciency.
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