Slice and RF bandwidth
INCORRECT. Increasing the transmitted frequency bandwidth of the RF excitation pulse means exciting a larger range of frequencies in the patient. Since the slice-selection gradient causes a range of Larmor frequencies to exist in the patient, what would exciting a larger range do?
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Slice selection method
CORRECT. The slice thickness is governed by the following equation:
thk = BWtrans / (ω0·GS)
where thk is the slice thickness, BWtrans is the transmitted RF bandwidth (the range of frequencies it covers), γ0 is the gyromagnetic ratio and GS is the magnitude of the slice selection magnetic field gradient.
So, slice thickness is proportional to BWtrans; increasing BWtrans will yield a thicker imaging slice.
INCORRECT. The question refers to the transmitted RF bandwidth, not the RF carrier frequency. (However, if the carrier frequency was changed, the location of slice selection in the scanner would change.)
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Further reading on this topic:
Books: MRI From Picture to Proton p116, Q&A in MRI p75, MRI The Basics p100
Online: Medcyclopaedia, Basics of MRI