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The s- orbital is symmetrical because it has no nodal planes. Therefore, there it has a symmetric e- potential distribution. The p- orbital has two lobes on either side of the nucleus, creating a nodal plane with a px, py, pz axes.
Electrons in the s-orbital are equally likely to be found at any point in the sphere, therefore s-orbitals have symmetric probability distributions. A p-orbital shape itself is not asymmetric, but because the shape is not a sphere, an electron is more likely to be found further from the nuclear, so the probably distribution is not symmetrical.
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