NMR Diastereotopic Proton Splitting

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echandler
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This is one of those questions that probably has a very simple answer, but I can't find it anywhere, and as much as I think about it, the more confused I get.

Can diastererotopic protons have different number of split peaks in their overall signal like on a CH2R group, for example, one proton splits as a doublet and the other splits as a triplet?

My mind keeps bouncing back and forth between "No because their bonding relationship to other nuclei is the same" and "Yes, because their spatial location is different, and then through space coupling may have an effect," which is usually followed by "that would result in a furthing splitting of the first multiplet, not change the number of the multiplet." I think I'm too deep in it to think clearly.

Thanks in advance.
 
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To get a triplet, you need two neighbouring equivalent protons. The equivalency of the protons does not depend on the non-equivalency of the two diastereotopic protons you are considering.