This question is in context of nmr. I know that prior to application of magnetic field and RF energy, protons are found in -1/2 and 1/2 spin values. What decides whethere a particular proton has positive or negative values. I know these values are not intrinsic to a proton since applying energy can cause them to change their spins so what decides whether proton has one value over other in first place.

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    $\begingroup$ Contrary to what Einstein may say, God throws a die. $\endgroup$
    – Jan
    Feb 12 '17 at 19:22
  • $\begingroup$ lol okay... One question. Does this have to do with pauli exclusion principle as well? I always think this would be dealing with electrons only. $\endgroup$
    – TLo
    Feb 12 '17 at 19:26
  • $\begingroup$ @Jan ALL particles of matter are subject to the Pauli exclusion principle, whereby two identical particles can never have the same exact quantum state including spin. Electrons are just the best known case because forcing them into different quantum states directly affects chemical properties; but the principle applies to protons and neutrons (and the quarks that make them up) too. What doesn't follow the Pauli exclusion principle? An entirely different class of particles that carry forces instead of making up matter, like pi mesons. $\endgroup$ Feb 18 '17 at 3:59
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    $\begingroup$ @OscarLanzi Okay, I should stop posting comments about things I know too little about. (But there was something that differentiated electrons and the like from protons and the likes, wasn’t there?) $\endgroup$
    – Jan
    Feb 20 '17 at 10:15
  • $\begingroup$ Two identical fermions, not two identical particles, surely? (Granted, electrons, protons, and neutrons are all fermions.) $\endgroup$
    – orthocresol
    Mar 16 '17 at 12:55

Spin is an intrinsic property of any nucleus, and can be 0, 1/2,1, 3/2, 2........ A nucleus of spin I can adopt 2n+1 stable states or orientations. For 1H, I=1/2, and this means it can adopt two possible stable spin states; +1/2 or -1/2. The energy levels of these two spin states are different (and proportional to the strength of the magnetic field); one is slightly higher than the other, and so there is a population difference between the two states. However, the energy difference is incredibly small, and difference in populations (called the Bolztzmann distribution) is only about one in a million. The individual nuclei can hop back and forth between the two states quite readily, provided there is sufficient energy transfer (into or out of) the system. Indeed, this is the basis of the NMR experiment - we can manipulate spins between the two spin states with relative ease.

For a nucleus with a spin greater than 1/2, there are more than 2 stable spin states that the nucleus can exist in. Deuterium (2H) has I=1, and can adopt one of 3 stable spin states. The distribution of spins amongst these states is approximately equal (less the BD of approx one in a million). Any individual nucleus will switch between these states. Lutetium176 has a spin of 7, and so can adopt 15 different stable spin states.


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