# Probability of finding electron.

1. May 15, 2013

### nil1996

The picture shows the first few hydrogen atom orbitals (energy eigenfunctions). These are cross-sections of the probability density that are color-coded (black=zero density, white=highest density).

according to the picture -Do s orbital electrons have highest probability density in the nucleus?

(i am totally new to quantum mechanics.So please tell if i am wrong.)

Last edited: May 15, 2013
2. May 15, 2013

### Staff: Mentor

If you take the radial part of the wave function only, then yes, the probability density $|\psi|^2$ is maximum at $r=0$ for s electrons. But that doesn't mean that the expectation value $\langle r \rangle$ is 0. A measurement will most likely find the electron at a certain distance from the nucleus.

Another way to see it is to consider the radial distribution too. As s orbitals are spherical, the surface of the sphere increases as $r$ increases, so the probability of finding the electron at a certain distance of the nucleus goes through a maximum away from the nucleus.