H NMR Fourier Transform Question work shown

[johnq2k7]

Consider the following H1 NMR signal from the human brain obtained at 1.5 T
S(t)= S(0) { 3 exp (-iw_NAA*t)* exp (-t/T2_NAA*) + exp(-iw_Cr*t)*exp(-t/T2_Cr*) +
exp(-iw_Cho*t)*exp(-t/T2_Cho*)}

where the 3 terms shown rep. the contributions from the major peaks of total creatine (Cr), choline containing compounds (Cho) and (NAA).

Given: y/2pi of H1 is 42.575 MHz/T
Major Ch3 peak Chemical Shift
-Cho 3.22
-Cr 3.03
-NAA 2.02

Creatine contains one CH3 group, therefore 3 H1 protons, NAA contains one CH3 group therefore 3 H1 protons, Choline contains 3 CH3 groups, therefore 9 H1 protons


a.) Determine the ratio of the area under the NAA peak to the area under the Cho peak
b.) Based on info and given chem. structures, determine ratio of conc. of NAA to that of Cho.
c.) If full-width at half max. is 5 Hz for NAA and 10 Hz for other two peaks, determine ratio of peak heigh of NAA to that of Cho
d.) use info from previous part c, to determine full-width at one-fifth max. of NAA peak


Work Shown:

a.) I'm not sure how to determine the area in this case, do you have to find the frequency of the NAA and Cho peak

therefore, f= (y/2pi)(1.5 T)= 42.575 * 1.5= 63.86 Mhz/T = 63.86 x 10^6 Hz/T

f_NAA= (chem. shift)(f)(10^-6)
f_Cho= (chem.shift) (f) (10^-6)

however, given the ratio of CH3 groups is 1 to 3.. we know S(0)NAA/S(0)Cho= 1/3

however, i don't know how to determine the ratio of the area with the provided info

b.) is the ratio of the conc. simply 1/3 since intial amp. is 1 and 3 for # of CH3 groups and 3 and 9 H1 protons respectively

c.) since the formula for FWHM= 1/(pi*T2*)... in units Hz
if FWHM of NAA is 5Hz and other two peaks are 10 Hz
how do u determine ratio of peak height...
if formula for height is... Height= S(0)T2*

d.) how do u determine the FW at 1.5 max. I'm confused.. do u the height or width info... if so how..


please help me with this problem

 

[Jhero]

a.) To determine the ratio of the area under the NAA peak to the area under the Cho peak, you need to integrate the signal over the respective peaks. This can be done by using a software program or by hand using a mathematical function that represents the signal. Once you have the integrated values, you can calculate the ratio of the areas.

b.) The ratio of the concentration of NAA to that of Cho can be determined by using the ratio of the number of CH3 groups and H1 protons. Since NAA has 3 CH3 groups and 3 H1 protons, and Cho has 9 CH3 groups and 9 H1 protons, the ratio would be 1/3.

c.) To determine the ratio of the peak height, you can use the formula for peak height, which is Height= S(0)*T2*. In this case, you would use the T2* values for each peak, which are given in the equation. So for NAA, the peak height would be S(0)*T2_NAA*, and for Cho, it would be S(0)*T2_Cho*. The ratio of these two heights would give you the ratio of the peak heights.

d.) To determine the full-width at one-fifth max of the NAA peak, you would use the same formula for FWHM, but instead of using the FWHM value, you would use one-fifth of that value. So it would be 1/5 * FWHM = 1/5 * (1/(pi*T2_NAA*)), which would give you the full-width at one-fifth max for the NAA peak.