Graphing Hydrogen atom wave functions

In summary, the conversation discusses a homework assignment involving graphing functions, states, and levels using Excel. The equations provided for the assignment are for wave functions and involve variables such as n and l. The person is unsure of how to begin and what variables to use for a and r. It is suggested to convert the equations into dimensionless form and plot using dimensionless variables, such as y. It is also mentioned that Excel allows for the use of undefined variables and there is a free alternative program called Open Office.
  • #1
chart2006
12
0

Homework Statement


I have a series of functions, states, and levels that I'm suppose to graph using excel. Only problem is I'm not even sure of what to do. I'm completely confused/lost.


Homework Equations


n=1 l=0 [tex]R(r)=\frac{2}{a_0^{3/2}}e^{-r/a_0}[/tex]
n=2 l=0 [tex]R(r)=(2-\frac{r}{a_0})\frac{e^{-r/2a_0}}{(2a_0)^{3/2}} [/tex]
n=2 l=1 [tex]R(r)=\frac{r}{a_0}\frac{e^{-r/2a_0}}{\sqrt{3}(2a_0)^{3/2}} [/tex]
n=3 l=0 [tex]R(r)=\frac{1}{(a_0)^{3/2}}\frac{2}{81\sqrt{3}}(27-18\frac{r}{a_0}+2\frac{r^2}{a_0^2})e^{-r/3a_0}[/tex]
n=3 l=1 [tex]R(r)=\frac{1}{(a_0)^{3/2}}\frac{4}{81\sqrt{6}}(6-\frac{r}{a_0})\frac{r}{a_0}e^{-r/3a_0} [/tex]
n=3 l=2 [tex]R(r)=\frac{1}{(a_0)^{3/2}}\frac{4}{81\sqrt{30}}\frac{r^2}{a_0^2}e^{-r/3a_0}[/tex]


The Attempt at a Solution



As for attempting this I'm not even sure of how to begin. I'd have to state some variable with excel but in this form and introducing the state of the atom into the function. What am i suppose to use for 'a' or 'r'? Will excell allow me to graph a wave function using so many undefined variables? In other words I haven't a clue as to what to do here. Any insight would be greatful.
 
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  • #2
you need to realize that h squared is the probability density and NOT the probability...
 
  • #3
I know that h squared is the probability density and not the probability but i still don't see what the relationship is with the functions given. Maybe they are something covered in a later chapter but I don't recognize them at least from the information covered thus far. I've looked through the chapter in my book but no help. I'm still unsure as to how to graph the functions. How do I apply both 'n' and 'l' into the function in order to graph it on excel. I've come across a few other equations to solve for 'n' but nothing for 'l.' How do I implement 'l' which is the orbital quantum number into the functions? The only reason I know what 'l' even is is because I found it in 3 chapters ahead. This is by far not my strong area so I'm completely in the dark here.
 
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  • #4
chart2006 said:
I have a series of functions, states, and levels that I'm suppose to graph using excel.
...
n=1 l=0 [tex]R(r)=\frac{2}{a_0^{3/2}}e^{-r/a_0}[/tex]
n=2 l=0 [tex]R(r)=(2-\frac{r}{a_0})\frac{e^{-r/2a_0}}{(2a_0)^{3/2}} [/tex]
...
I'd have to state some variable with excel but in this form and introducing the state of the atom into the function. What am i suppose to use for 'a' or 'r'?
A common graphing practice is to convert equations into dimensionless form, and then plot in the dimensionless variables. Hint: how can you make a dimensionless variable from a and r?

chart2006 said:
Will excell allow me to graph a wave function using so many undefined variables?
Actually, yes. You can set up a cell to contain the value of a parameter, and you can do this for as many parameters that you like. Then, in the function cells, just reference the parameters by referencing the cells. A word of caution: use the fixed reference (to do this, I think you put a "$" in front of the row number and column letter, e.g. $B$13), otherwise you may accidentally reference different cells for different instances of the function. It all depends on how much you want to learn about excel and how you decide to lay out the problem.

BTW, I will briefly mention that there is a FREE open office alternative to excel that basically works like excel ...
 
  • #5
turin said:
A common graphing practice is to convert equations into dimensionless form, and then plot in the dimensionless variables. Hint: how can you make a dimensionless variable from a and r?

I will add to turin's excellent suggestion: for these plots, let "y" be a03/2 · R

So, for example, the n=1 l=0 equation is
a03/2 · R = _____?​
 

What is a hydrogen atom wave function?

A hydrogen atom wave function is a mathematical representation of the probability of finding an electron in a particular location around the nucleus of a hydrogen atom. It describes the behavior and properties of the electron in the atom.

Why is graphing hydrogen atom wave functions important?

Graphing hydrogen atom wave functions allows us to visualize and better understand the behavior of electrons in hydrogen atoms. It also helps us to predict the behavior of other atoms and molecules.

What do the peaks and valleys on a graph of a hydrogen atom wave function represent?

The peaks and valleys on a graph of a hydrogen atom wave function represent areas of high and low electron density, respectively. The higher the peak, the higher the probability of finding an electron in that location.

Can we graph the wave function of any atom?

No, the wave function of any atom can only be graphed for systems with one electron, such as the hydrogen atom. For atoms with more than one electron, the wave function becomes more complex and cannot be easily graphed.

How does the principal quantum number affect the shape of a hydrogen atom wave function?

The principal quantum number, denoted as "n", determines the overall size and energy of the electron in the atom. As n increases, the size of the orbital and the distance of the electron from the nucleus also increase, resulting in a larger and more spread out wave function.

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