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### Topic: how to determine l a nucleus  (Read 10790 times)

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#### tisu85

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##### how to determine l a nucleus
« on: October 04, 2006, 03:08:12 AM »
i have a homework problem that asks me to calculate the magnetic dipole moment for 37Cl with J= l - 1/2
I know that in order to find the moment, i need to find J
However , i don't know how to find l for a certain nucleus
Can you guys help me with this??

#### Mitch

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##### Re: how to determine l a nucleus
« Reply #1 on: October 04, 2006, 03:36:51 AM »
Use the shell model. Does 37Cl have an odd proton or an odd neutron.
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#### ethylenediamine

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##### Re: how to determine l a nucleus
« Reply #2 on: October 08, 2006, 12:25:44 AM »
I tried the calculation for 137-Cesium, but I used this equation:

[J/(J+1)] [(l+1)g_l -0.5g_s],                     where g_l = l u_0, and g_s = 5.5845 u_0 (protons)

I find that l=4, because the last proton is in the g 7/2 state.

I would then get, [(7/2)/(9/2)][5*4-0.5*5.5845]u_0 = 13.3 u_0, but I thought the answer was 1.8 u_0. Am I wrong.  How come when I look online, at:

I see 2.84 as the listed value? Are they assuming J = l+1/2, even though I am calculating for J=l-1/2?
« Last Edit: October 08, 2006, 01:01:19 AM by ethylenediamine »

#### Mitch

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##### Re: how to determine l a nucleus
« Reply #3 on: October 08, 2006, 12:58:10 AM »
If you use gl = 1 u0 (protons), you seem to get the right answer so try that.
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#### ethylenediamine

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##### Re: how to determine l a nucleus
« Reply #4 on: October 08, 2006, 01:03:13 AM »
But gl = l u0 , as in "l" the alphabet not "1" Wouldn't that mean we should use the angular momentum value: 4???
« Last Edit: October 08, 2006, 01:12:44 AM by ethylenediamine »

#### Mitch

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##### Re: how to determine l a nucleus
« Reply #5 on: October 08, 2006, 01:52:44 AM »
Just try it, see what you get for the values.
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#### tisu85

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##### Re: how to determine l a nucleus
« Reply #6 on: October 08, 2006, 01:51:52 PM »
so , is it gl always equal to 1 times u0 (nuclear magneton)
The book says it is l times u0
i m confused

#### ethylenediamine

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##### Re: how to determine l a nucleus
« Reply #7 on: October 08, 2006, 02:00:50 PM »
How would the quadrupole moment be found? Does it have anything to do with j? Or does it have to do with the magic numbers?

#### Mitch

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##### Re: how to determine l a nucleus
« Reply #8 on: October 08, 2006, 06:26:52 PM »
so , is it gl always equal to 1 times u0 (nuclear magneton)
The book says it is l times u0
i m confused

Does it work?
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#### toluene

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##### Re: how to determine l a nucleus
« Reply #9 on: October 09, 2006, 02:30:09 AM »
I've tried setting gl = l as well as gl = 1. The latter seems to work better when you compare your answer to Fig. 6.6 in the text.

#### Mitch

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##### Re: how to determine l a nucleus
« Reply #10 on: October 09, 2006, 02:57:27 AM »
Yeah, there should be no overall problem; the answers are literally in Figure 6.6