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Based on what we need to know about the Schrodinger's Wave Function Equation, we just know that a nodal plane is where the electron density distribution is 0. Why? I think the nodal plane represents the area where the wave function is squared(Remember the example sin graph: It can be squared and there will be a spot on the graph that is 0). Also, if you want to think of it based on the shapes, it is the rectangle that divides the shapes. This explains why the s orbital does not have a nodal plane.
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