Sciencemadness Discussion Board

Inorganic Chemistry

Argon - 29-1-2004 at 00:16

Hi, I am new user. 4th year student at UBC chem. I need help with some stuff and I was wondering if you pros can help.

Regarding NMR Multiplicity Splitting Pattern of Nuclear Spin I = 1

I can't seem to find a Pascal
s Triangle equivlaent for nucleart spin 1.


| (1)
| | | (111)
| || ||| || | (12321)

What is next?

I am a fish - 29-1-2004 at 02:09

A nucleus with I = 1 can have I<sub>z</sub> = -1, 0 or 1. When adding another particle to the system, the total I<sub>z</sub> can either be unchanged, can decrease by 1 or increase by 1. Therefore to calculate the next line, you must add each number to the numbers on either side of it (taking numbers outside the triangle to be 0), and place this sum directly below the original number.

0 0 0 0 1 0 0 0 0
0 0 0 1 2 1 0 0 0
0 0 1 2 3 2 1 0 0
0 1 3 6 7 6 3 1 0


[Edited on 29-1-2004 by I am a fish]

chemoleo - 29-1-2004 at 02:47

Fish was too fast - but he is correct, I checked.
Let's make this interesting - what if you have a spin quantum number of 3/2, or 5/2? :P

Damn - I have to deal with things like that every day now :( in fact in a few days i will be assigning the backbone of my protein by NMR - that's gonna be fun!

I am a fish - 29-1-2004 at 09:22

Quote:
Originally posted by chemoleo
Fish was too fast - but he is correct, I checked.
Let's make this interesting - what if you have a spin quantum number of 3/2, or 5/2? :P


The same principle applies...

Taking the I = 3/2 case as an example:

You calculate the allowed values of I<sub>z</sub>:

I<sub>z</sub> = (-3/2, -1/2, 1/2, 3/2)

Therefore when calculating the values for the next line, you add four consecutive numbers (again taking values outside the triangle to be implicit zeros) and place the sum beneath the middle of each set:


------------------------1------------------------
------------------1---1---1---1------------------
--------1---1---2---3---4---3---2---1---1--------
--1---2---4---7---10--12--12--10--7---4---2---1--

and so on...
Quote:
Damn - I have to deal with things like that every day now :( in fact in a few days i will be assigning the backbone of my protein by NMR - that's gonna be fun!