What is a Boundary Surface Diagram?
A boundary surface diagram is one of the good diagrammatic representations of the shape of atomic orbitals. It is a resultant solution of the Schrödinger wave equation.
As we all know that the momentum and exact position of an electron cannot be determined (as per the Heisenberg uncertainty principle), so we calculate the probability density of finding the electron in a specific region.
A boundary surface diagram can be explained either as a boundary surface or as a contoured surface that is drawn in a space for an orbital, where the value of probability density |ψ|2 is constant.
Note: The constant probability density of the boundary surface diagram is considered an acceptable and good approximation of orbital shape if the boundary surface encloses the volume or region with a probability density having more than 90%. It means that the boundary surface enclosing a constant probability density of 50% (for suppose) won't be considered good.
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Features of the Boundary Surface Diagram
Size of the Surface Diagram
The boundary surface diagram of the orbital increases either in volume or size with an increase in the principal quantum number (n).
Shape of the Surface Diagram
The orbital boundary surface diagram is independent of the principal quantum number.
For example, the boundary surface diagram of an s orbital is spherical, and so, it will remain spherical for 1s, 2s, 3s, 4s, or for any other general ns. It should be noted that the shape does not depend on the principle quantum number (n).
Nodes in the Surface Diagram
Nodes are the regions having very low probability density, which goes to zero, typically. There exist (n-1) nodes in the s-orbital’s boundary surface diagram with the principal quantum number 'n.' Such nodes are also noticed in the surface diagram of p, d, f orbitals.
Shapes of the Orbitals
Probability Density
ψ provides us the wave amplitude. The value of ψ contains no physical significance.
Wheres, |Ψ|2 provides us the region, where the probability of finding an electron is maximum. It is known as a probability density.
Nodal Surfaces
The region where this function of probability density reduces to zero is known as simply nodes or nodal surfaces.
There are two types of Nodes, which are given below:
Angular nodes and,
Nodal Planes
Angular nodes or nodal planes take place when the probability density wave function for the electron is given as zero along the directions specified by a specific angle, where the number of angular nodes is l.
Therefore we can say that
The number of angular nodes is l,
The number of radial nodes is n-l-1,
Total number of nodes = No.of radial nodes + No.of angular nodes = n – 1.
Nodal Region or Radial Nodes
Radial nodes or the nodal region takes place when the probability density of the wave function for an electron is zero on a spherical surface of the radius. Thus, the number of radial nodes is = n – l – 1
Shapes of Boundary Surface Diagrams
It is a surface in space, where the density of probability is constant for a given orbital. This provides a good representation of the orbital shape. Also, this shape encloses the region or volume, where the probability of finding electrons is high.
Shape of S-Orbital
All the s-orbitals will be Spherical in shape.
The size of s orbital increases with an increase in n, which means 4s > 3s > 2s > 1s, and the electron is located further away to the point of the nucleus as the principal quantum number increases.
The probability of finding out the electron at a given distance is equal in all directions.
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Shape of P-orbitals
It holds 3 possible orientations.
Each p orbital contains 2 sections, which are known as lobes that are on either side of the plane, passing via the nucleus.
The probability density function can be given as zero on the plane, where the 2 lobes touch each other.
The shape, energy, and size of the 3 orbitals are similar, whereas just the orientation is different.
They are provided with the designations 2px, 2py, 2pz.
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Shape of D-Orbitals
It contains 5 orientations.
The shapes of the first 4D orbitals are the same as each other, whereas that of the 5th one is different from the others. But, all the 5 3d orbitals are equivalent in energy.
The 5 d-orbitals are designated as dxy, dyz, dxz, dx2-y2, dz2.
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Difference between boundary Surface and Orbital Diagrams
A boundary is a surface or line marking the extent of some feature. Hence, it is not similar to an orbital.
An orbital can be given as a volume around an atomic nucleus, where an electron can be found with a given permitted energy state.
Even though the textbook illustrations depict the orbitals as zones having clear boundaries, it is NOT accurate.
In fact, there are no boundaries defined for the orbitals, in the sense of demarcating a volume within which the electron will always be found.
FAQs on Boundary Surface Diagram
1. What is a boundary surface diagram in Chemistry?
A boundary surface diagram is a visual representation of an atomic orbital. It outlines the three-dimensional space around an atom's nucleus where there is a high probability (typically 90-95%) of finding an electron. It essentially gives the orbital its characteristic shape, like a sphere for an s-orbital or a dumbbell for a p-orbital.
2. Why can't a boundary surface diagram show a 100% probability of finding an electron?
An electron's position is described by a wave function that theoretically extends to infinity. This means there is always a small, non-zero chance of finding the electron very far from the nucleus. To draw a finite shape, we must set a practical boundary, like 90% probability, because a 100% probability region would be infinitely large and impossible to draw.
3. How do the boundary surface diagrams for s, p, and d orbitals differ?
The shapes of these orbitals are very distinct and describe where an electron is likely to be found:
- s-orbitals have a simple spherical shape.
- p-orbitals have a dumbbell shape, consisting of two lobes on opposite sides of the nucleus.
- d-orbitals have more complex shapes, most with a cloverleaf or double-dumbbell appearance (four lobes).
4. What do the positive (+) and negative (-) signs on the lobes of a p-orbital diagram mean?
These signs do not represent electrical charge. They represent the mathematical phase of the electron's wave function (ψ), similar to how a wave has crests and troughs. The phase is important for understanding how atomic orbitals overlap to form chemical bonds.
5. What is a node, and how can you see it in a boundary surface diagram?
A node is a region in an orbital where the probability of finding an electron is zero. In a boundary surface diagram, a node is the space where lobes are separated. For example, a p-orbital has a nodal plane that passes through the nucleus, separating its two lobes.
6. How is the diagram for a 2s orbital different from a 1s orbital?
While both are spherical, the 2s orbital is larger than the 1s orbital. The most important difference is that the 2s orbital contains a radial node—a spherical shell within the orbital where the electron probability drops to zero. The 1s orbital does not have any nodes.
7. What is the main difference between an orbit and an atomic orbital?
An orbit (from the older Bohr model) is a fixed, two-dimensional circular path an electron is supposed to follow. An atomic orbital is a modern, quantum mechanical concept representing a three-dimensional region of space where there is a high probability of finding an electron, not a defined path.
