Pascal's triangle strikes again

ryos · 2006-03-01 05:12:33

So, I'm sitting (lying, actually) peacefully, studying H NMR spectroscopy for my Organic Chemistry class, when I come to the topic of splitting. Basically, NMR spectrometers apply a magnetic field to the substance under study, and different hydrogens emit peaks of RF radiations at slightly different frequencies based on the structure of the molecule; this lets us infer a lot of information about the a molecule's structure.

Anyway, hydrogens that are vicinal to each other split the peaks of their neighbors. The "mini-peaks" are not the same height as each other, but rather are governed by a ratio of heights. Here are the height ratios listed in a table of my book for multiplets from a doublet to a septet:

       1:1
      1:2:1
     1:3:3:1
    1:4:6:4:1
  1:5:10:10:5:1
1:6:15:20:15:6:1

Does that look familiar to anyone else? Score one for Pascal!

krassi_holmz · 2006-03-01 05:17:03

Wanna know something other?
Pascal's Δ

Last edited by krassi_holmz (2006-03-01 05:17:49)

MathsIsFun · 2006-03-01 08:47:42

Or my version: Pascal's Triangle

John E. Franklin · 2006-03-01 13:43:44

On the web page krassi h. pointed out, their is a mistake in the diagram of pascal's triangle. The 186 in the bottom row should be a 286 I think.

John E. Franklin · 2006-03-01 13:56:10

I really enjoyed MIF's pages on Pascal's triangle! My favorite part was the picture of the marbles in a tetrahedron. Wonderful implications, how the diagonal rows are possibly for each successive dimension that we cannot visualize in our 3-D world, at least that's what we can see with our eyes.
Diagonal rows:
1. all ones (0-D ?)
2. 1-D (counting numbers along a line)
3. 2-D triangle (like bowling pins)
4. 3-D triangle (like the marbles MIF has depicted)
5. 4-D triangle I am guessing, how could we prove this?????

John E. Franklin · 2006-03-01 13:59:46

What is vicinal hydrogens?? Is it in close proximity to each other??

John E. Franklin · 2006-03-01 14:21:31

I found this, but wish it explained more.
http://www.wfu.edu/~ylwong/chem/nmr/h1/splitting.html

John E. Franklin · 2006-03-01 14:56:17

And this is fun to read... http://www.shu.ac.uk/schools/sci/chem/t … c/nmr1.htm

ryos · 2006-03-01 16:42:04

"Vicinal" hydrogens are separated by three bonds. So, in this structure: H3--C--C--H3 (ethane), 3 hydrogens are vicinal to three others.

So yes, they're close together, but not so much in space as in bonds (though it usually means in space, too).

John E. Franklin · 2006-03-01 17:40:30

Thanks for the info, ryos, and Boy, this chemistry reading is really fascinating.
And difficult.

krassi_holmz · 2006-03-01 17:43:35

Ya, It's difficult-not so easy as math!!!

Math Is Fun Forum

#1 2006-03-01 05:12:33

Pascal's triangle strikes again

#2 2006-03-01 05:17:03

Re: Pascal's triangle strikes again

#3 2006-03-01 08:47:42

Re: Pascal's triangle strikes again

#4 2006-03-01 13:43:44

Re: Pascal's triangle strikes again

#5 2006-03-01 13:56:10

Re: Pascal's triangle strikes again

#6 2006-03-01 13:59:46

Re: Pascal's triangle strikes again

#7 2006-03-01 14:21:31

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#8 2006-03-01 14:56:17

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#9 2006-03-01 16:42:04

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#10 2006-03-01 17:40:30

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#11 2006-03-01 17:43:35

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