# Probability of finding an electron

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• physicsmaths1613
In summary, the probability of finding an electron on the z-axis is zero, as the z-axis has no volume. This is in line with the general principle that the probability of a continuous random variable having a specific value is always zero. Therefore, your instructor is correct in stating that the probability of finding the electron on the z-axis is zero.

#### physicsmaths1613

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?

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.

Paul Colby said:
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?

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##.

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.