You want to excite spins in an xy-plane located at z = -5.0 cm. The resonance frequency at the isocenter is 63.85 MHz and your slice selection gradient is 1 G/cm. Describe in detail the RF pulse which should be used.

We need to find the frequency of the RF that needs to be turned on and off in the shape of an apodised sinc function. If the slice is to be located at Z=-5.0 cm, the slice selection gradient must be applied along the +z-axis. The frequency is calculated as follows.

ν - νo = γ z G
where:
ν = frequency for slice
νo = frequency at isocenter = 63.85 MHz
γ = gyromagnetic ratio, 42.58 MHz/T
G = slice selection gradient = 0.0001 T/cm
z = position relative to isocenter = -5 cm

ν = νo + γ z G

ν = 63.85 MHz + (42.58 MHz/T)(-5 cm)(0.0001 T/cm)

ν = 63.85 MHz - 0.21 MHz

63.829 MHz