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Atomic orbitals: 4d wave functionThis page addresses the 4d_{xy}, 4d_{xz}, 4d_{yz}, and 4d_{x2y2} wave functions. See the 4d_{z2} page for information about its wave function. Schematic plot of the 4d_{xy} wave function ψ_{4dxy}. The blue zones are where the wave function has negative values and the red zones denote positive values. The graph on the left is a plot of values along a single line along the x=y line drawn through the nucleus while the surface plot on the right shows values of ψ_{4dxy} on the xy plane drawn through the nucleus. The plot above is labelled for the 4d_{xy} orbital but the form of the plots for the 4d_{xz}, 4d_{yz}, and 4d_{x2y2} orbitals is similar, differing only in orientation. See the 4d_{z2} page for comparable information about its wave function. In general, apart from the two nodal planes, dorbitals have a number of radial nodes that separate the largest, outer, component from the inner components. The number of radial nodes is related to the principal quantum number, n. In general, a nd orbital has (n  3) radial nodes, so 4dorbitals have (4  3) = 1 radial node. The equations for the 4d orbitals (ψ_{4d}) show that in addition to a radial dependency, there is a dependency upon direction. This is why d orbitals are not spherical. This behaviour is unlike that of the s orbitals for which the value of the wave function for a given value of r is the same no matter what direction is chosen.  

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: Saturday 21st July, 2018 