Probability of finding an electron

[physicsmaths1613]

Let us assume that we have an electron belonging to the p_x 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]

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.

 

[physicsmaths1613]

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]

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.