Nuclear Spin of Sodium 23 Explained

In summary, the conversation discusses the calculation of the nuclear spin of Sodium 23 using the shell model. However, the observed spin of 3/2 does not match the predicted spin of 0 or 1/2 from the model. The possibility of nuclei deformation and its effect on the energy levels is suggested as a possible explanation. Reference is also made to the observed spin of 5/2 for Ti-47, which does not match the predicted spin of 1f7/2.
  • #1
bluesquare
4
0
i am actually calculating the nuclear spin of Sodium 23. Here we have 11 protons and 12 neutrons. Now both the nuclei are short of the magic numbers. When I use the shell model for protons and neutrons separately, I found 3 protons in the 1d5/2 sub-shell and 4 neutrons in the same 1d5/2 sub-shell. So because of two pairings, neutrons give spin as 0 and because of a pairing in protons, one proton is left out which should give spin as 1/2. But in the book its, I=3/2. Please can anyone explain the fact how the spin of Na nucleus is 3/2. Thank you in advance.
 
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  • #2
Hi bluesquare,

Looking at wikipedia (http://en.wikipedia.org/wiki/File:Shells.png), would the shell model not lead to a spin of 5/2?
However, I remember that deformation of the nuclei can re-order the level.
Could that not be an explanation why the sheel model does not lead to the experimental spin?

m
 
  • #3
Yeah I know that we have deformities but I am unable to find it anywhere. Can you site any reference. Meanwhile i tried to calculate the spin of Ti -47 and from the shell model i got the spin as 1f7/2.. But when i checked in it is actually 5/2..So i am like ...

thank you for the reply though.
 
  • #4
"For 23Na, the observed spin must be explained by coupling of equivalent nucleons or by deformation." -- Burcham
 
  • #5
The approach you are using predicts that the only allowed nuclear spins are 0, 1/2 and 1 - you allow exactly one unpaired nucleon per shell. This is not borne out by data, so the shell model must be oversimplified. The oversimplification is that the shells in fact do depend on the other nuclei, and that moves the energy levels around, so you have the shell order change slightly.
 

1. What is the nuclear spin of sodium 23?

The nuclear spin of sodium 23 is 3/2. It is represented by the symbol I, and is a quantum mechanical property of the nucleus of an atom.

2. How is the nuclear spin of sodium 23 determined?

The nuclear spin of sodium 23 is determined by the number of protons and neutrons in the nucleus of the atom. In the case of sodium 23, there are 11 protons and 12 neutrons, giving it a nuclear spin of 3/2.

3. What is the significance of the nuclear spin of sodium 23?

The nuclear spin of sodium 23 has important implications in nuclear magnetic resonance (NMR) spectroscopy, a technique used to study the structure and properties of molecules. It also affects the chemical and physical properties of sodium 23 in various compounds.

4. How does the nuclear spin of sodium 23 affect its behavior in a magnetic field?

The nuclear spin of sodium 23 causes it to behave as a small magnet in a magnetic field. This allows for the observation of NMR signals, which can be used to determine the chemical structure and dynamics of molecules containing sodium 23.

5. Can the nuclear spin of sodium 23 change?

No, the nuclear spin of an atom is a fundamental property that cannot be changed. However, the orientation of the spin can be altered by external magnetic fields, which is the basis of NMR spectroscopy.

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