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Atomic orbitals: 7s wave function

Schematic plot of the 7s wave function ψ7s. Blue represents negative values for the wave function and red represents positive values. Click on the "Show nodal structure" button to get a clearer view of the nodal structure for this orbital.

The graph on the left is a plot of values along a single line drawn through the nucleus while the surface plot on the right shows values of ψ7s on a slice drawn through the nucleus.

Further, the equation for the 7s orbital of any given atom depends only upon the distance from the nucleus, that is, the radius, r. This means there are no directional properties - the value of the wave function for a given value of r is the same no matter what direction is chosen. This is why the orbital appears spherical.

The equation for the 7s orbital (ψ7s) shows that on moving away from the nucleus, the function starts from a high point but moves across to negative values, back again to positive, back again to negative, back again to positive, back again to negative, and back again to positive before approaching zero from the positive side. The points at which the function crosses the axis at zero are referred to as nodes. Since the axis is crossed at the same six radii in any direction, we see there are nodal surfaces. In this case they are radial nodes since the nodal surfaces are represented by spheres.

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Document served: Sunday 19th November, 2017