Fourier Transform NMR Physics... Work Shown... Please Help!!!!!!!
Suppose you would like to detect the NMR signal from water within an area of the brain using a 2 Tesla Magnet. Intially, the magnetization from the protons in water has a magnitude (length) represented by Mo and oriented in a direction parallel to the zaxis (defined as the direction of the external magnetic field (Bo)). In order to observe the NMR signal this magnetization is rotated into the x,y plan (using the B1 magnetic field).
a.) At what frequency in (MHz) does the magnetization (now in the x,y plane) precess about the external magnetic field (Bo).
b.) If the magnitude of B1 is 1.5 mT, how long does it take for the magnetization to rotate into the x,y plane from it's intial position parallel to the zaxis?
My work:
f0= (y/2pi) (Bo)
since (y/2pi) is equal to 42.6 MHz/T for H1
therefore, f0= (42.6 MHz/T) (2T)= 85.2 MHz
exp (t_(1/2)/ T2*)= 1/2
t_(1/2) / T2*= ln 2
t_(1/2)= T2*(ln(2))
# of cycles= t_(1/2)/ T_period = t_(1/2)*(f0)= T2*(ln(2))*f0= 50x10^3 us (ln 2) (85.2 MHz)
= 3 x10^6 cycles
b.) B1= 1.5mT
# of cycles = 3 x 10^6
f0= 85.2 x 10^6 =8.52 x 10^7 Hz= 8.52 x 10^7 cycles/sec
# of cycles/f0= 3x 10^6 cycles/ (8.52 x 10^7 cycles/sec)
= 3.52 x 10^2 sec
Please help me with these questions, I showed my work.. need help
