# Graphing Hydrogen atom wave functions

1. Mar 30, 2009

### chart2006

1. The problem statement, all variables and given/known data
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.

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

3. 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.

Last edited: Mar 30, 2009
2. Mar 30, 2009

### orthovector

you need to realize that h squared is the probability density and NOT the probability....

3. Mar 30, 2009

### chart2006

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 accross 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.

Last edited: Mar 30, 2009
4. Mar 30, 2009

### turin

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?

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. Mar 30, 2009

### Redbelly98

Staff Emeritus
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 = _____?​