[Winga]

What is the difference between the probability of finding an electron (psi²) and probability density?

They look similar to each other, but their graphs are different.

[Juan R.]

I do not understand you.

Can you explain that are asking?

[Winga]

I am talking about the radial part.

Probability of finding the e- = psi²
Probability density = r²[R_nl(r)]²

[Mitch]

What level are you at in Quantum Mechanics? There is a whole sect of modern quantum chemists who try to describe everything by using density probabilities that way you get around the need to know every wavefunction for every electron. Maybe you could quote a book and some equations and pages for us.

[Winga]

I think I am at basic level.

I just wonder the probability density use for.

The psi² has already told us the probability of finding the e-, so, what can the probability density tell us?

[Yggdrasil]

Here's a very basic answer to the question.

The probability of finding an electron in a given space a distance r from the nucleus is given by [Psi(r)]².  However, to find the probablity of finding an electron over ALL points r away from the nucleus, you need to correct for the different areas.  For example, the spherical shell 1nm away from the nucleus will have about 4x less surface area than the spehrical shell 2nm away from then nucleus.  Therefore, the probability of finding an electron in the spherical shell a distance r from the nucleus is your probability function [Psi(r)]² multiplied by the surface area of the spherical shell, 4(pi)r².  Since chemists are somewhat lazy, they ignore the 4(pi) and just write the radial distribution function as r²[Psi(r)]².

[Winga]

I got it!
Thank you!

[Juan R.]

What is the difference between the probability of finding an electron (psi²) and probability density?

They look similar to each other, but their graphs are different.

Now i understand!

Well, i was confused by your distinction between probability and probabiity density. I now see that you are talking of probability density in cartesian and in radial (spherical) coordinates.

It is not true that psi² was a probability. It is a density of probability. But whereas radial density probability is the density of probability of finding electron at a radius r (i.e. in any direction), psi² is the density in a point (x, y, z) or in radial coordinates (r, theta, phi).

In fact, the probability of finding and electron between (x, y, z) and (x + dx, y + dy, z + dz) is

dP = psi² dx dy dz.

Initially you talked about probability. psi² is not a probability. The probability P is found by integrating above expression.