0:00
Hi there.
00:01
So for this problem, we are told that mri relies on only a tiny majority of the nuclear magnetic moments aligning with this stern -up field.
00:12
So we need to consider the common target nucleus hydrogen.
00:17
The difference between the aligned and the anti -aligned states of a diapole in a magnetic field is two times the magnetic moment.
00:29
So can be used to find the magnetic moment for the proton, provided that the current mass and gyretic magnetic ratio that we know for the proton is equal to 5 .6.
00:52
So using boltzmann distribution and show that for a magnetic field that is equal to one tesla and a reasonable temperature, the number.
01:04
Of align it exceeds the number of anti -align it by less than 1 over 100%.
01:16
So what we are going to do in here is to calculate the ratio of align divided by the ratio of anti -align.
01:36
So using the bolsman distribution, we will have that this is equal to the s -belign.
01:43
Exponential of minus the energy align divided by the bolzman constant times the temperature and we have something similar for the case of the anti -align.
02:06
Now when we simplify this we're going to find that this is the exponential of minus the difference in the energy divided by the bolzman constant times the temperature.
02:19
Now we can write this in terms of the magnetic field and the magnetic moment.
02:26
We know that that is two times the magnetic moment times the magnetic field, divided by boltman -compson times the temperator...