Spin of a nucleus within an external magnetic field.

[Matt1025723598]

When a nucleus is placed inside an external magnetic field, it aligns itself parallel to the field, as that is the most stable position for it to be in. In more technical terms: it acquires an alpha spin.
When you shine radio waves at this nucleus, it absorbs energy and flips over anti-parallel to the external magnetic field. It acquires a beta spin. It then releases energy and flips back to the alpha spin state, parallel to the external magnetic field.

My question is simply: why? Why does the nucleus flip over when you give it radio wave energy? Why not just stay in the stable position? What does the nucleus benefit by doing this?

I am never getting a straight answer to this question. My chemistry textbook, ChemGuide, KhanAcademy, Youtube, etc. all say the same thing: that the nucleus "now has enough energy to be in the unstable beta spin state". Never explaining why that occurs. Like, we just have to accept it without question.

I have high school level physics/chemistry knowledge. A+ grades. Wikipedia is not an option for me at all; I tried my hardest to read Wikipedia but it's just too ridiculously difficult to understand.

 

[DrClaude]

The simple answer is that the interaction with the electromagnetic wave leads to a reorientation of the spin of the nucleus. It is not significantly different from a pendulum that starts swinging when you give it a push, although many details of the process can only be understood using quantum mechanics.

By the way, let me make a couple of corrections to what you wrote.

When a nucleus is placed inside an external magnetic field, it aligns itself parallel to the field, as that is the most stable position for it to be in. In more technical terms: it acquires an alpha spin.

This is not completely correct. In any sample, some of the nuclei will have opposite spins. The number will vary depending on the strength of the field and the temperature of the sample.

What does the nucleus benefit by doing this?

I personally don't like discussions of inanimate objects "wanting" or "benefiting" from something. In this particular case, you can't see the nucleus as an isolated system, you have to consider the nucleus plus the EM field and look at what happens there.

 

[Matt1025723598]

The simple answer is that the interaction with the electromagnetic wave leads to a reorientation of the spin of the nucleus. It is not significantly different from a pendulum that starts swinging when you give it a push, although many details of the process can only be understood using quantum mechanics.

Let me see if I understood this correctly. The bottom position is the only stable position for the pendulum. You give it energy (pushing it, kinetic energy) and now it swings into an unstable position (gains potential energy, loses kinetic) and so it must come back down to a stable position (loses the potential, gains partially the kinetic energy I initially gave it). The nucleus is stable, you give it energy and I'm assuming that it must use that energy somehow, and so (correct me if I'm wrong, just an assumption) physicists conjured up the term "spin" and said that the particle uses the energy to change its.. 'spin', before going back to its initial spin and releasing the same amount of energy it absorbed. In a similar fashion, an electron must somehow use the energy it absorbed, so it jumps up into a higher energy orbital, before returning back down. Is it because there's no other way to "use" that energy other than to, respectfully: 1. swing up, 2. change spin, 3. jump up an orbital. ?
Is it like everything must change/do something when handed energy, before going back to its initial state and releasing the energy it was handed? Is that why the textbooks use the term "orientation" very lightly when referring to "spin"? Because it's just a convenient made up term to describe where the energy is going and not an actual orientation in space? Educators always say "let's just say spin is its orientation in space", they're not explicitly calling it an orientation
Sorry this is so long, I just really need to nail this down before moving onwards.

 

[DrDu]

The spin of a nucleus is a quantum mechanical object, hence its precise direction is not sharp. However, if instead you consider the expected or average position of an ensemble of many spins, which is sufficient especially to explain NMR, as there a huge number of spins is considered, then things become a lot easier. Namely, the mean orientation ( I shall simply speak of the orientation, dropping the word mean in the following) will follow classical equations of motion. Namely, if you apply a radio wave, this wave also has a magnetic field. The orientation of the spin will then start to precess around the new position of the field, which changes in time with the frequency of the radio wave. Hence, once you switch off the radio wave, the orientation of the spins will no longer coincide with the initial equilibrium orientation.

 

[DrClaude]

The nucleus is stable, you give it energy and I'm assuming that it must use that energy somehow, and so (correct me if I'm wrong, just an assumption) physicists conjured up the term "spin" and said that the particle uses the energy to change its.. 'spin', before going back to its initial spin and releasing the same amount of energy it absorbed.

Not exactly. Spin is an intrinsic property of fundamental particles, for which there is no classical analog. It is a kind of angular momentum, just like rotation is a kind of angular momentum. In the absence of an external field, the spin has no particular orientation. Then you put the nucleus in an external magnetic field, and it will align itself with this external field, similar to a compass needle aligned itself with the Earth's magnetic field (with the caveat that the spin can also be anti-aligned).

To use a classical analogy, if you were to give a push to the needle, it would stop pointing in the direction of the field, which I guess you would not find weird. Same thing happens with the spin changing orientation due to the EM wave. In the case of the compass, the needle will eventually return to point in the direction of the Earth's magnetic field, losing through friction the extra energy gained by the push. For the spin, it eventually returns to the ground state through emission of a photon.

Is it like everything must change/do something when handed energy, before going back to its initial state and releasing the energy it was handed?

Again, not exactly. What you have is an interaction between the system and some external agent, like you pushing the pendulum. Through that interaction, energy is exchanged between two. In the cases you are considering here, the interaction is limited in time (you do not keep pushing the pendulum as you would, for instance, do for a kid on a swing), and there are dissipative forces that will eventually bring the system back to its original (ground) state.

Is that why the textbooks use the term "orientation" very lightly when referring to "spin"? Because it's just a convenient made up term to describe where the energy is going and not an actual orientation in space? Educators always say "let's just say spin is its orientation in space", they're not explicitly calling it an orientation

@DrDu gave a good answer to that. I will add that it is an orientation in space, as angular momentum is a vector quantity. But since it is purely quantum mechanical, there are some peculiarities, e.g., spin is quantized. You cannot say that the spin angular momentum points in a precise direction, like you would do for a classical vector, because of the Heisenberg uncertainty principle, but you can give its direction with respect to a particular axis (allowing, for instance, to describe a spin-1/2 particle as being in a "spin up" or "spin down" state, aligned or anti-aligned with the magnetic field in the NMR case).

 

[DrDu]

You can even simulate the dynamics of the spin vector yourself:
http://demonstrations.wolfram.com/MagneticResonanceAndBlochEquations/

 

[Matt1025723598]

Thank you guys so much! :)

 

[Tom.G]

These may help too. Both are fairly readable.
http://www.bu.edu/chemistry/files/cic/nmr/documents/CICNMR_basicconcepts.pdf
http://chem.ch.huji.ac.il/nmr/techniques/1d/pulseq.htm (and the links within it)

Cheers,
Tom

 

[Jake Osborne]

That was a good question and interesting discussion. High school chemistry is really advanced these days