Consider a 2-D object consisting of two triangle compartments, as shown in Figure P9.4. Suppose a solution containing a 511 KeV gamma ray emitting radionuclide with concentration f = 0.5….

## Derive a more general formula for MZ (t). You can assume that the transverse magnetization has completely dephased before each RF pulse, that is, Mxy(TR) = 0.

The following equations from Example 12.4 give the components of M after an α pulse (assuming the system is in equilibrium just before the α pulse):

Suppose that we now excite the sample with a train of α pulses, separated by a time T_{R}. The equilibrium condition is true when T_{R} is long compared with T_{1} and we can assume that M_{Z} just before the pulse is equal to

Mo. Derive a more general formula for M_{Z} (t). You can assume that the transverse magnetization has completely dephased before each RF pulse, that is, M_{xy}(T_{R}) = 0. (Hint: In this more general formula, M_{O} will be replaced with the steady-state value of the longitudinal magnetization. Define M_{Z} after the (n + 1)^{th} pulse to be , and M_{Z} after the n^{th} pulse to be . Relate these two quantities with an equation. Derive another (very simple) equation from the steady-state condition. You now have enough information to solve the problem.)