The nucleus of a hydrogen atom, a proton, has a magnetic moment. In a magnetic f

Question

The nucleus of a hydrogen atom, a proton, has a magnetic moment. In a magnetic field, the proton has two states of different energy; spin up and spin down. This is the basis of proton NMR. The relative populations can be assumed to be given by the Boltzmann distribution, where the difference in energy between the two states is delta E = g mu B, g = 2.79 for protons, and mu = 5.05 times 10^-24 J/T. For a 300MHz NMR instrument, B = 7T. Compute the relative population difference, |N_uparrow - N_downarrow|/(N_uparrow + N_downarrow) at room temperature for this machine. Describe how the population difference changes with temperature. What is the partition function?

Explanation / Answer

6a) we know that relative population difference is E/E= hcut **B/2KT

using given values we get E =2.79*5.05*10^-34*7* 3.33 [T=1/300Mhz

or E= 328*10^-34

then E/E = 6.62*10^-34/2*3.14*26.75*10^-7/2*1.38*10^-23=10.21*10^-18

b)

From the principle of NMR the population density increases with temperature

c)Using the probability density the partition function is defined as

ensemble density = 1/Q exp(-H/KT) where Q is the partition function

or Q=exp(-H/KT) /ensemble density

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