To gain some appreciation for the numerical work done by computers interfaced to NMR spectrometers, perform the following calculations.

(a) The total FID F(t) of a signal containing many frequencies, each corresponding to a different nucleus, is given by 

where, for each nucleus j, S_0j is the maximum intensity of the signal, ν_Lj is the Larmor frequency, and T_2j is the spin–spin relaxation time. Plot the FID for the case

(b) Explore how the shape of the FID curve changes with changes in the Larmor frequency and the spin–spin relaxation time.

(c) Use mathematical software to calculate and plot the Fourier transforms of the FID curves you calculated in parts (a) and (b). How do spectral linewidths vary with the value of T₂? 

Transcribed Image Text:

F(t)=So; cos(27v₁;t)e-¹/T₂j