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Chemistry Forums for Students => Undergraduate General Chemistry Forum => Topic started by: 1loudninja on January 15, 2016, 06:30:47 PM

Title: How do I calculate the position of the nodes for this wave function?
Post by: 1loudninja on January 15, 2016, 06:30:47 PM: 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
Title: Re: How do I calculate the position of the nodes for this wave function?
Post by: Corribus on January 15, 2016, 06:56:27 PM: What is the definition of a node?
Title: Re: How do I calculate the position of the nodes for this wave function?
Post by: 1loudninja 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"
Title: Re: How do I calculate the position of the nodes for this wave function?
Post by: mikasaur on January 15, 2016, 07:37:57 PM: Quote from: 1loudninja 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"

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?
Title: Re: How do I calculate the position of the nodes for this wave function?
Post by: 1loudninja on January 15, 2016, 07:39:54 PM: 2 nodes?
Title: Re: How do I calculate the position of the nodes for this wave function?
Post by: 1loudninja 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?
Title: Re: How do I calculate the position of the nodes for this wave function?
Post by: Corribus 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.
Title: Re: How do I calculate the position of the nodes for this wave function?
Post by: mikasaur on January 18, 2016, 12:59:38 AM: Quote from: 1loudninja 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?

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.