What is a boundary surface?
Boundary surface diagram is a good diagrammatical representation of shapes of atomic orbitals. It is the resultant of the solution of Schrödinger wave equation.
As we know that the exact position and momentum of an electron cannot be determined (according to Heisenberg uncertainty principle), so we calculate the probability density of finding an electron in a particular region. Boundary surface diagram is a boundary surface or a contour surface drawn in a space for an orbital on which the value of probability density |ψ|2 is constant. The boundary surface diagram of constant probability density is considered as a good and acceptable approximation of the shape of an orbital if the boundary surface encloses the region or volume with probability density of more than 90%. This means that the boundary surface enclosing a constant probability density of let’s say 50% won’t be considered good.
Why the boundary surface diagram is not taken with constant probability density of 100%?
The answer is at any distance from the nucleus, the probability density of finding an electron is never zero. It will always have some finite value, so it is not possible to draw a boundary surface diagram which encloses a region with 100% probability density.
Feature of boundary surface diagram
- Shape of the surface diagram:
The boundary surface diagram of an orbital is independent of principle quantum number.
For e.g.: The boundary surface diagram of s orbital is spherical, so it will be spherical for 1s, 2s, 3s and 4s or for any general ns. The shape doesn’t depend on the principle quantum number (n).
- Size of the surface diagram:
The boundary surface diagram of an orbital increase in size or volume with increase in principle quantum number (n).
- Nodes in the surface diagram
Nodes are the region with very low probability density typically which goes to zero. There are (n-1) nodes in the boundary surface diagram of s-orbital with ‘n’ principle quantum number. This kind of nodes is also observed in the surface diagram of p, d and f orbitals.
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