P orbital lobes tangent to plane of nucleus

[qhyperbola]

I read the following on a page about atomic orbitals (p and d orbitals in particular) which seem 2 me like 3d lemniscates (figures 8 or ∞ rotated about an axis of symmetry to form tear drop pairs or toruses.
http://www.chemguide.co.uk/atoms/properties/atomorbs.html
Taking chemistry further: If you imagine a horizontal plane through the nucleus, with one lobe of the (p) orbital above the plane and the other beneath it, there is a zero probability of finding the electron on that plane. So how does the electron get from one lobe to the other if it can never pass through the plane of the nucleus? At this introductory level you just have to accept that it does! If you want to find out more, read about the wave nature of electrons.

I can visualizably understand that 4 spatial dimensions allow for a 3d object 2b rotated around a plane w/o intersecting it just like 3 dimensions allow a 2d object 2b rotated around a line w/o intersecting it. I've got no idea of whether that has anything to do w/ explaining the above statement about not crossing the plane of the nucleus. I'm wanting a qualitative, visualizable understanding if at all possible
I've also read that ψ^2 gives probability density clouds for electron position and I contemplate that this perhaps is what necessitated that Schrödinger's wave function ψ be complex valued. I can rudimentarily visualize the x (real + imaginary) and y (real plus imaginary) in terms of circles and hyperbolas. Can anybody help me out with understanding the wave nature of particles - mathematical rigor and symbolic logic are not my aptitudes - but I like to think I'm capable of understanding this stuff.

 

[Bill_K]

qhyperbola, It may be what has you confused is a phrase I see on this web page, "...spends part of its time...".

This gives the impression that the electron is constantly hopping around from one part of the orbital to another. And so to get from the +z region to the -z region it would somehow have to move along a path and thus at some point penetrate the z = 0 plane, where it is not to be found.

Ok, this is not the correct picture. There is no motion implied - the orbital simply tells us the probability of finding the electron at a particular point, and that is all.

 

[qhyperbola]

mmmm, that does clash w/ my preconceived notion of a wave function as describing ...well... a waving motion or oscillation of position over time. So, is there perhaps an imaginary valued probability of finding a particle on the plane between lobes - ( e^1.57i or e^.785i) - or am I making this harder than it is by persisting in thinking of an electron as point-like?

 

[Bill_K]

An atomic orbital is a standing wave, and standing waves (by definition!) do not move. The only oscillation is in time: for a state of energy E the wavefunction varies as exp(iEt/ħ). But it stands still while doing so.

So, is there perhaps an imaginary valued probability of finding a particle on the plane between lobes - ( e^1.57i or e^.785i)

Nope, for the state we're talking about, the wavefunction is zero on the plane z = 0.

 

[qhyperbola]

I'll post again in another day after taking some time to reckon this out. so the wave function is zero at the z=0 plane, and with an s orbital the wave funtion will be symmetric about the origin but at the origin (or nucleus point) this wave function will be zero? like in the sense of sin(x)/x which looks tike it has its peak at at x=0, y= 1, but is actually undefined. And this wave function exp(iEt/ħ) is being defined for t seconds measured as complex radians. I'm hoping that I can understand lobed (p, d, and f) orbitals this in terms of a circle, hyperbola, and lemniscates of bernoulli. Thank you for your help btw - I'm liking pf a lot.