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A nodal plane is a plane where the probabilty of finding an electron is zero. The s-orbitals do not have one due to the spherical shape, there are no angular nodes possible. Any s-orbital has an angular momentum number, l, of 0.
It all boils down to the wave function. Nodal planes are planes that divide lobes of electrons. It's the area where the probability of an electron is also zero. Since the s orbital is just one lobe, there's no nodal plane.
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