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Homework Help: H NMR Fourier Transform Question work shown please help!

  1. Jan 5, 2010 #1
    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












    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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