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A nodal plane are regions where there is zero likelihood of finding an electron. In a sigma bond it is a symmetrical sphere and the electron density is cylindrically symmetrical around the axis (imagine a beach ball). In a pi bond there is electron density on either side of the internuclear axis but at the internuclear axis the nodal plane exists (two beach balls and where they touch there are no electrons).
The sigma p bonding orbital is the lowest energy orbital which means it will have zero nodes. Then there is the pi bonding orbitals (1 node), the pi anti-bonding orbitals (2 nodes) and finally the anti-bonding sigma p orbital which has three nodes.
I think it is helpful to think of nodal planes using the 3D shapes that the book has for orbitals. Knowing that nodal planes are areas where there is a zero percent chance of finding an electron, think of a sphere (sigma bond) and how there is no gaps within it. P orbitals are made up of multiple orbs/lobes and therefore there will be space in between them. Nodal planes are in these spaces.
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