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Atomic orbitals: 7pThe shape of the three 7p orbitals. From left to right: 7p_{z}, 7p_{x}, and 7p_{y}. For each, the copper zones are where the wave functions have negative values and the green zones denote positive values. For any atom, there are three 7p orbitals. These orbitals have the same shape but are aligned differently in space. The three 7p orbitals normally used are labelled 7p_{x}, 7p_{y}, and 7p_{z} since the functions are "aligned" along the x, y, and z axes respectively. Each 7p orbital has 12 lobes. There is a planar node normal to the axis of the orbital (so the 7p_{x} orbital has a yz nodal plane, for instance). Apart from the planar node there are also five spherical node that partition off the small inner lobes. The origin of the planar node becomes clear if we examine the wave equation which, for instance, includes an x term in the case of the 7p_{x} orbital. Clearly When x = 0, then we must have a node, and this by definition is the yz plane. The origin of the spherical nodes becomes clearer if we examine the wave equations, which include a (6720  8400ρ + 3360ρ^{2}  420ρ^{3} + 40ρ^{4}  ρ^{5}) term. When (6720  8400ρ + 3360ρ^{2}  420ρ^{3} + 40ρ^{4}  ρ^{5}) = 0, then we must have nodes. Whil not trivial, we can solve this on a casebycase basis to determine the position of the nodes.  

The Orbitron is a gallery of orbitals on the WWW The Orbitron^{TM}, a gallery of orbitals on the WWW, URL: http://winter.group.shef.ac.uk/orbitron/Copyright 20022015 Prof Mark Winter [The University of Sheffield]. All rights reserved. Document served: Sunday 21st October, 2018 