![]() ![]() There are some particular angles at which the scaling factor Y(\theta,\phi) is zero in this case, \phi = \\pi/2. If they had used x = 3y instead, the 2D graph would be smaller, but it would still have the same shape. For example, in the 5d orbital you showed, the cross section was taken along the line x = y. If you switch to a different radial cross section, though, it would have a different value. For a radial line, \theta and \phi are fixed, so Y(\theta,\phi) is just a constant for any given radial cross section. Where R and Y are the radial and angular parts, respectively. In other words, you know that the wavefunction can be decomposed as The angular part is just a scaling factor. So what you're seeing in the 2D graph is just the radial part of the wavefunction. The cross section is taken along a radial line, i.e. What they're plotting on the (2D) graph in those figures is a cross section of the wavefunction. My only clue for the answer to my question is that maybe angular nodes are not represented by x-intercepts. If one radial node causes the graph to cause the x-axis twice (on each side of nucleus, as in the case of the 2s orbital) then shouldnt there be 2 nodes * 2 intercepts/node = 4 intercepts just for the angular nodes? And then 2 more intercepts for the angular nodes? But the graph hits the x-axis at 5 (instead of 6) separate points which would imply 5 nodes but this isnt the case. The number of of radial nodes is 2 (from equation n-l-1) and the number of angular nodes is l=2. Now consider the graph of Ψ for a 5d orbital. The graph intersects at two points, but these two intercepts represent the same spherical node. Take for example, the graph of Ψ for a 2s orbital as seen on the left here: ![]() ![]() I am having a hard time understanding the nodes on the graphs of Ψ for atomic orbitals. ![]()
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