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### Topic: Standard Deviation and value of <r>  (Read 5739 times)

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#### soaring206

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##### Standard Deviation and value of <r>
« on: April 24, 2005, 08:22:11 PM »
I'm having a lot of trouble with two of my homework problems tonight.  I have been completely through my textbook and all over the internet, but I can't find what I'm looking for anywhere.  I have no idea where to even begin on the following two problems, so if someone could just give me a push in the right direction (like an equation or something), I'd greatly appreciate it!

1. Calculate the root-mean-square (standard deviation) displacement of the nuclei of 12C16O in the ground state and compare it to the equilibrium bond length of 112.832 pm.  (HINT: <x>=0) Use ?=(k?/?2)1/2 and k=1903 kg/s2.

2. Calculate the value of <r> for the n=2, l=1, ml=0 state and the n=2, l=0, ml=0 state of the hydrogen atom.

Any help at all would be appreciated...thank you so much in advance!

#### Mitch

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##### Re:Standard Deviation and value of <r>
« Reply #1 on: April 24, 2005, 08:24:46 PM »
2. Do you know the wavefunction for that state?
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#### soaring206

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##### Re:Standard Deviation and value of <r>
« Reply #2 on: April 24, 2005, 08:43:28 PM »
Unfortunately, no...that's all the information given to me in the question.

#### Mitch

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##### Re:Standard Deviation and value of <r>
« Reply #3 on: April 24, 2005, 10:05:12 PM »
Open your book. The wavefunctions are there.
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#### soaring206

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##### Re:Standard Deviation and value of <r>
« Reply #4 on: April 24, 2005, 10:36:10 PM »
Oh, right...sorry.

n=2. l=1, ml=0
1/8(2Z3/?a3)1/2(Zr/a)e-Zr/2acos?

n=2, l=0, ml=0
1/8(2Z3/?a3)1/2(2-Zr/a)e-Zr/2a

a=4??0?2/?e2

#### Mitch

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##### Re:Standard Deviation and value of <r>
« Reply #5 on: April 24, 2005, 11:20:17 PM »
Now just take the integral of (phi<r>phi*) and you'll be set.
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#### soaring206

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##### Re:Standard Deviation and value of <r>
« Reply #6 on: April 25, 2005, 12:05:59 AM »
Hmm...thanks Mitch.  I feel dumb...can't believe I didn't realize that.  Lol.

Any ideas on the first one perchance?