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What you say is true for a 2px prbital, i.e. where the principal quantum number n=2. Let's consider hydrogen. When l=2, as befits a p-orbital, n=2 is the smallest value for the principal quantum number n for which the radial equation has a solution. That means it is the smallest n such that there is a solution with energy -13.6/n^2. Since it is the lowest energy for which the radial equation (with l=1) has a solution, the radial part of the wave function has no node. In contrast, 3p orbitals do have radial nodes, but 3d orbitals don't, for the same reason.

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Q: Why is there no nodal region in px orbital?
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