# Probability of finding an electron

Let us assume that we have an electron belonging to the px orbital. In that case what would be the probability of finding it on the z axis? Would it be zero? My teacher says so, but I think that because we can't predict the boundary where there is 100% possibility of finding an electron, we can't find a point where the probability of finding it is 0. Who is correct?

Paul Colby
Gold Member
You instructor is correct if I understand your question. The electron wave function is spread over a volume. Any finite volume the electron will have some chance of being found there. [edit: the smaller the volume the smaller the probability] The z-axis has no volume so the probability is zero.

You instructor is correct if I understand your question. The electron wave function is spread over a volume. Any finite volume the electron will have some chance of being found there. [edit: the smaller the volume the smaller the probability] The z-axis has no volume so the probability is zero.
Does that mean that the probability of finding the electron on the x axis is 0 too, as it has no volume like the Z axis?

Paul Colby
Gold Member
Yes, written out ##P_{\Delta V}=\int\int\int_{\Delta V} \vert \psi(x)\vert^2 d^3x## if ##\Delta V=0## then ##P=0##.

mathman
This discussion is a special case of an obvious principle. The probability of a random variable, with a continuous distribution, having a specific value, is 0.