Calculating Nuclear Spin: Oxygen-17

In summary, the conversation is about determining the nuclear spin of oxygen 17, with a focus on the angular momentum of its protons and neutrons. The formula j=l+s is used to calculate the total angular momentum, with l representing the angular momentum of the individual nucleons and s representing their spin. The correct answer is 9/2, with the confusion arising from incorrect information about the spin of the neutron. It is also mentioned that an even number of neutrons and protons results in a nucleus with no spin.
  • #1
nicedazed
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0

Homework Statement



Oxygen 17, work out j (nuclear spin)Hi. Assume oxygen 17 atom. j is supposed to be 5/2. How does one work this out? from what i gather, l for protons is 1, and l for neutrons is 2. How does one work out j, and what would s be?

Partly what I'm confused about is for the protons l=1 but neutron l=2? what l do you use?

Thanks :devil:

Homework Equations

This is for the nucleus by the way. 8 protons and 9 neutrons

The Attempt at a Solution

 
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  • #2
l doesn't have to be either 1 or 2. Rather, for all nucleons l can range, in increments of 2, from 0 to n for even n and 1 to n for odd n. For example, for n=5 l can be 1, 3, or 5.

However, what you really want is j=l+s. For this question, all of the protons pair off, so they contribute no angular momentum. All but one of the neutrons pair off, and the remaining neutron determines the angular momentum of the whole nucleus. So, what is j for that neutron?
 
  • #3
Parity= (-1) ^l

l=2, to parity=+.

s=5/2 for the neutron.

so is this is the spin? what is j?

as parity =+ then j=2+(5/2)?= 9/2?

I'm sure that's not right...

if anyone can tell me what I'm doing wrong it'd be massively (unlike a photon) appreciated! I know this is a very easy question, it's just that other links such as wikipedia are confusing the hell out of me.

thanks for the reply :)
 
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  • #4
j is the total angular momentum, or "nuclear spin".

Where did you get that s=5/2 for the neutron? It's not; both the proton and the neutron has a spin of 1/2. Besides that, you have the right answer.
 
  • #5
Now it makes sense, thanks a lot. My lecture notes are slightly confusing.

There's just one thing I don't get:

Let's add a neutron: 18O. On Wikipedia, it says the spin is 0.

Once again, parity = +1. The additional spin is another +1/2.

Now, using the formula j=l+s, =2+1=3.

BUT, am I correct in thinking that because there's an even number of neutrons, they contribute no spin?

Thanks once again!
 
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  • #6
Yes, you're correct. Any nucleus with an even number of protons and even number of neutrons has no spin.
 

1. What is nuclear spin and why is it important to calculate?

Nuclear spin is a fundamental property of an atomic nucleus that describes its angular momentum. It is important to calculate because it directly affects the magnetic properties of the nucleus, which have practical applications in fields such as nuclear magnetic resonance (NMR) imaging and spectroscopy.

2. How is nuclear spin of Oxygen-17 calculated?

The nuclear spin of Oxygen-17 is calculated by considering the number of protons and neutrons in its nucleus. Oxygen-17 has 8 protons and 9 neutrons, resulting in a total spin of 5/2. This can also be represented as a quantum number, I, which in this case is 5/2.

3. What is the significance of the half-integer value for nuclear spin?

A half-integer value for nuclear spin indicates that the nucleus contains an odd number of protons and/or neutrons. This results in a non-zero total spin, which gives the nucleus a magnetic moment. This magnetic moment allows for interactions with external magnetic fields, making it useful for NMR applications.

4. How does nuclear spin affect the chemical properties of Oxygen-17?

The nuclear spin of Oxygen-17 does not directly affect its chemical properties, as it is a nuclear property and not an electronic property. However, the magnetic properties of Oxygen-17 can indirectly influence its chemical environment, which can be observed in NMR spectroscopy.

5. Are there any factors that can change the nuclear spin of Oxygen-17?

No, the nuclear spin of Oxygen-17 is a fundamental property of its nucleus and cannot be changed. However, the spin can be affected by external magnetic fields, which can cause the nucleus to undergo certain processes such as nuclear resonance or spin relaxation.

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