Problem 4: Nuclear Magnetic Resonance Sim-based Problem [4 pts] [Problem solving template not needed, but show your work and explain your reasoning] The magnetic dipole moment, a, is a useful model for explaining the behavior of not just loops of current rotating in uniform B-elds, but other objects like nuclei and atoms. We treat certain nuclei or atoms as dipole moments as they feel a similar torque that wants to align the moment with the direction of the magnetic eld. However, these dipole moments are not caused by some current loop. Rather, it is due to a fundamental property of particles called spin. The potential energy of the moment due to spin depends on its relative direction with an external magnetic eld in the same way as for the current loops we studied in class: namely U -ri - I} . Another important difference is the fact that the possible energy states for nuclear or atomic dipole moments are quantized into only two states: aligned (0 degrees) or anti-aligned (180 degrees). Current loops, in contrast, can exist over a continuum of angles from 0 to 180 degrees. Nuclear Magnetic Resonance: If we apply a uniform magnetic eld across a region of nuclei with non-zero dipole moments, we can establish these two states. Then we can use radio waves to flip the moments into the higher antialigned states. See the sim here: https:phet.colorado.edufsimsicheergjimrillatestfmri.html?simulation=mri The key, though, is that the energy of the radio wave must match the change in potential energy to ip a dipole moment from the aligned to the anti-aligned state in order to be efciently absorbed. The energy of the radiowave is given by 5' hf , where f is the frequency, and h is the plank constant. h = 6.626 x 10\"34 J5. Once in the higher-state, the dipole moments will eventually relax back into the lower energy state and release energy in the form of a radiowave. We can detect those emitted waves to use the NMR phenomenon to image tissue. This technique is known as Magnetic Resonance Imaging. For the problem, run the \"Simplied NMR simulation" at the link above. To start, set the eld strength, radiowave source power, and radiowave source frequency to their lowest values. The sample atom should be set to "hydrogen". Now turn the magnetic field to 1.0 T. On the right hand side, there is a diagram illustrating the potential energy difference for aligned and anti-aligned moments caused by the B-eld. Now set the radiowave source power to 25% and then adjust the radiowave source frequency such that it matches the potential energy difference. There is a wavy double-sided arrow that illustrates the energy of the radiowaves for a given frequency. When the energy matches the potential energy gap, you'll see dipole moments kicked to the higher energy state. You should also see such states decay and emit radiowaves. Based on this simulation. estimate the dipole moment of the "hydrogen" nuclei in this sim. (This is beyond the intro to NMR explored in this problem, but to actually image using NMR, there are a number of strategies. One strategy is to scan through different combinations of spatial patterns of B-eld strengths and radiowave source frequencies. Based on the radiowaves detected from these scans. one can use special algorithms to produce an image. You can play around with the MRI part of the sim to get a sense of how this might work. For example, can you modify the X-Y B-eld gradients to get only certain portions to emit radiowaves?)