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I know s-orbitals are the only ones without a nodal plane so the electron density is symmetric but I don't really understand the significance of this or what it really means when applying this information?
A nodal plane is an area where there is no electron density. s-orbitals do not have nodal planes which means that the distribution of electrons is even over the entire orbital. Other types of orbits have nodal planes and therefore the distribution of electrons is not even (therefore its nonsymmetric).
S-orbitals do not have nodal planes, so they have even electron density distribution, making the shell symmetric. Every other orbital has at least one nodal plane, meaning there is zero electron density distribution and making the shell not symmetric. This explains why the p-orbitals have a dumbbell shape and d-orbitals have a four lobe shape. In between the lobes, there is an area where there is zero electron density distribution. The s-orbital has no nodal planes and therefore has the symmetric spherical shape.
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