Fourier Transform NMR Physics Work Shown

In summary: Determine the ratio S_PCr@0/ S_ATP@0, where S_PCr@0 is the contribution to the intial signal amplitude from PCr, and S_ATP@0 is the contribution to the initial signal amplitude from ATP.S_PCr@0/S_ATP@0= (PCr/ATP)*100Since S_PCr@0 is greater than S_ATP@0, the ratio will be positive.b.) If the peak in the spectrum from the unknown biochemical is centered at a frequency 100 Hz to the left of the Pi peak (where PCr is on the right of the Pi peak),
  • #1
johnq2k7
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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 z-axis (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 z-axis?


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







 
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  • #2


johnq2k7 said:
a.) At what frequency in (MHz) does the magnetization (now in the x,y plane) precess about the external magnetic field (Bo).

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

85.2 MHz is the correct answer.
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

I'm not quite sure what you're trying to do here.
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 z-axis?

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

I'm not quite sure what you're trying to do here. Basically, when you turn on the B1 field, your magnetization will precess about B1. Because you know the strength of the field, you can calculate the frequency of precession as well as the period. From this information, you should be able to calculate the time needed to move the magnetization by 90o (from the z-axis into the x,y-plane).
 
  • #3


since i know the value of B1, i can find the frequency and period .. how do i determine the time, i understand if the magnetization is rotated into the x,y plane from the z plane that is equal to angle of 90 degrees... which formula do i use to compute the time?
 
  • #4


If it takes T seconds to rotate one cycle, how much time will it take to rotate 90o (1/4 of a cycle)?
 
  • #5


Thanks for your help... please help me with this problem.. how do i go about approaching this problem



Suppose you acquire the 31P NMR signal from a region of muscle of a healthy subject using a 3 Tesla magnet. Assume that the signal has contributions from ATP,PCR, Pi, and from an unknown phosphorous containing biochemical. Assume that all decay shapes are exponential.

Note: H1- 42.575 MHz/T for y/2pi , 31P- 17.235 MHz/T for y/2pi, and 13C- 10.705 for y/2pi

31P- nucleus (chemical shifts), ATP-alpha= -7.52 ppm
ATP-beta= -16.26 ppm
ATP-gamma= -2.48 ppm
PCr= 0 ppm
Pi= 5.02 ppm
a.) Determine the ratio S_PCr@0/ S_ATP@0, where S_PCr@0 is the contribution to the intial signal amplitude from PCr, and S_ATP@0 is the contribution to the initial signal amplitude from ATP.

b.) If the peak in the spectrum from the unknown biochemical is centered at a frequency 100 Hz to the left of the Pi peak (where PCr is on the right of the Pi peak), determine the value of the chemical shift for the peak from the unknown chemical, with PCR as the reference peak.

c.) If the full width at half maximum (FWHM) of the peak from the unknown chemical is 10 Hz and its height s half that of the PCr peak, determine the concentration of the unknown chemical assuming that there is only one phosphorous nucleus per molecule.

Please help.. need a lot of help here!
 

FAQ: Fourier Transform NMR Physics Work Shown

1. What is Fourier Transform NMR Physics?

Fourier Transform NMR Physics is a branch of physics that uses the principles of Fourier Transform to analyze the signals produced by Nuclear Magnetic Resonance (NMR) spectroscopy. This technique allows for the identification and quantification of chemical compounds in a sample.

2. How does Fourier Transform NMR Physics work?

In Fourier Transform NMR Physics, a sample is placed in a strong magnetic field and exposed to radiofrequency pulses. The nuclei in the sample absorb and emit energy, producing a signal that is recorded and processed using Fourier Transform techniques. This allows for the separation and identification of different chemical compounds in the sample.

3. What are some applications of Fourier Transform NMR Physics?

Fourier Transform NMR Physics has a wide range of applications in chemistry, biochemistry, and materials science. It is commonly used in drug discovery, environmental analysis, and food safety testing. It can also be used to study the structure and dynamics of molecules, proteins, and other biomolecules.

4. What is the difference between Fourier Transform NMR and traditional NMR?

The main difference between Fourier Transform NMR and traditional NMR is the method used to acquire and process the data. In traditional NMR, the signal is recorded as a function of time, while in Fourier Transform NMR, the signal is recorded as a function of frequency. This allows for faster and more accurate analysis of the data.

5. What are the benefits of using Fourier Transform NMR Physics?

Fourier Transform NMR Physics offers several benefits compared to traditional NMR techniques. It provides higher resolution and sensitivity, allowing for the identification of smaller and more complex structures. It also allows for faster data acquisition and processing, making it a valuable tool in various fields of research and industry.

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