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Topic: How do I calculate the position of the nodes for this wave function?  (Read 9360 times)

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Offline 1loudninja

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Hey,

So this is what I did
1)   I set the wave function to 0
2)   I was left with the quadratic equation (27 − 18σ + 2σ2)
3)   The values for r that I got were 3.75e-10 and 1.006e-10
Are these the values I’m looking for?

pic below
« Last Edit: January 15, 2016, 08:18:21 PM by 1loudninja »

Offline Corribus

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Re: How do I calculate the position of the nodes for this wave function?
« Reply #1 on: January 15, 2016, 06:56:27 PM »
What is the definition of a node?
What men are poets who can speak of Jupiter if he were like a man, but if he is an immense spinning sphere of methane and ammonia must be silent?  - Richard P. Feynman

Offline 1loudninja

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Re: How do I calculate the position of the nodes for this wave function?
« Reply #2 on: January 15, 2016, 07:24:07 PM »
Ok, so the back of my book says a Node is "an area of an orbital having zero electron probability"

Offline mikasaur

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Re: How do I calculate the position of the nodes for this wave function?
« Reply #3 on: January 15, 2016, 07:37:57 PM »
Ok, so the back of my book says a Node is "an area of an orbital having zero electron probability"

Right. And so what does a wavefunction tell you about electron probability?

As far as higher and lower, how many nodes would you expect in an orbital with your given quantum numbers: n=3, [itex]\ell[/itex]=0, m=0?
Or you could, you know, Google it.

Offline 1loudninja

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Re: How do I calculate the position of the nodes for this wave function?
« Reply #4 on: January 15, 2016, 07:39:54 PM »
2 nodes?

Offline 1loudninja

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Re: How do I calculate the position of the nodes for this wave function?
« Reply #5 on: January 15, 2016, 07:40:57 PM »
No wait, wouldn't it be zero?? Ok,  I think you just make the equation equal to zero right? And just solve for R?

Offline Corribus

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Re: How do I calculate the position of the nodes for this wave function?
« Reply #6 on: January 15, 2016, 09:39:20 PM »
I didn't do the math but this is basically the way you would solve the problem. You should be able to tell how many roots (nodes) there are by inspection of the equation.
What men are poets who can speak of Jupiter if he were like a man, but if he is an immense spinning sphere of methane and ammonia must be silent?  - Richard P. Feynman

Offline mikasaur

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Re: How do I calculate the position of the nodes for this wave function?
« Reply #7 on: January 18, 2016, 12:59:38 AM »
No wait, wouldn't it be zero?? Ok,  I think you just make the equation equal to zero right? And just solve for R?

When n=3, [itex]\ell[/itex]=0, and m=0 we're describing the 3s orbital which, yes, has two radial nodes. Like you say, a node is where the wave function is zero. As Corribus says, you can fairly easily solve for which values of r the wavefunction is zero.
Or you could, you know, Google it.

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