# Area under the graph of squared wave function

I was given a graph of square of the wave function of a hydrogen atom, against the distance of the electron from the nucleus (denoted by r).

What I know is that the square of the wave function gives the probability of finding an electron at a particular position, but could anyone explain to me that why does the area under this graph has to do with the probablity of locating an electron? Because I thought that on the graph where the highest value of square of wave function is, the corresponding value of r will be the answer. Isn't that so??

• Think about this first: what is the probability of finding a point particle at one particular point in space? – Wouter Nov 9 '13 at 14:03

There is a tutorial on this particular issue at University of St Andrews. You will notice that the probability density they use there contains a factor of $r^2$. This has to do with the use of spherical coordinates, much in the same way that you need to multiply by $r^2 \sin \theta$ when you perform a spherical integral in three dimensions. Refer to calculus books if you don't know what I am talking about here.