Sketch the 3dxy and 3dz² orbitals
Represent the orientation of the two d orbitals named in the syllabus and distinguish their defining shapes.
Section 28 · Chemistry of transition elements
A Level; Cambridge International Chemistry 9701, 2028–2030 syllabus, Topic 28. Use the first-row transition elements titanium to copper and the species explicitly named in the syllabus. Where redox potentials or stability constants are needed, use the values supplied in the question. Colour descriptions can depend on conditions and concentration. Written practice is self-checked
Before you begin
- Use electron configurations, oxidation numbers, ionic equations, equilibrium expressions and the AS redox and bonding models.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Where do the four lobes of 3dxy point?
What you will learn
- Sketch four lobes for a 3dxy orbital between the x and y axes
- Sketch the 3dz² orbital with two lobes on z and a torus in the xy plane
- Label axes and avoid confusing orbital orientation with electron paths
Orient 3dxy between the coordinate axes
The 3dxy orbital has four lobes in the xy plane. Each lobe points between the x and y axes, rather than lying along either axis. Label x and y in the plane and z perpendicular to it.
An orbital sketch represents a region of high probability density. It is not a path traced by an electron. Keep the four lobes and their orientation clear even in a simple line drawing.
Show the distinctive 3dz² shape
The 3dz² orbital has two lobes directed along the positive and negative z directions and a doughnut-shaped ring, or torus, around the nucleus in the xy plane.
A good sketch labels all three axes, places the two lobes on z, and shows the torus perpendicular to z. Do not draw the four diagonal lobes of dxy for this orbital.
Pause and explain
Which extra feature belongs in a sketch of 3dz²?
Worked example
Describe the features a sketch must show to distinguish 3dxy from 3dz².
Show the worked solution
- Place the coordinate axes first.
- Put four dxy lobes between x and y in the xy plane.
- Put two dz² lobes on z and a torus in the xy plane.
Answer 3dxy has four lobes between x and y in the xy plane. 3dz² has two lobes along z plus a torus in the xy plane.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Give a three-step sketch plan for 3dxy.
Give me a hint
Start with axes, then place the lobes in the correct plane and orientation.
Compare my reasoning
- Draw and label x, y and z.
- Keep the orbital in the xy plane.
- Place four lobes between the x and y axes.
Draw labelled axes and four lobes in the xy plane, each between x and y.
Look for these in your work
- Axes labelled
- Correct plane
- Lobes between axes
A 3dz² sketch shows four lobes in the xy plane. State two changes needed.
Give me a hint
Recall the two axial lobes and the torus.
Compare my reasoning
- Remove the four-lobe arrangement.
- Add two lobes along positive and negative z.
- Add a torus in the xy plane.
Redraw two lobes along z and a torus in the xy plane; the four-lobe pattern is not dz².
Look for these in your work
- Incorrect arrangement identified
- Axial lobes added
- Torus placed correctly
A learner labels a dxy sketch with x and y axes but no z axis. Why should the sketch add z even though all four lobes lie in the xy plane?
Give me a hint
The third axis makes the orientation of the orbital plane unambiguous.
Compare my reasoning
- State that z is perpendicular to the xy plane.
- Label its direction through the nucleus.
- Use the same coordinate frame to compare dz².
Add z perpendicular to the xy plane. This makes the orbital orientation explicit and allows a clear comparison with dz², whose lobes lie along z.
Look for these in your work
- Third axis relation stated
- Plane orientation clear
- Comparison supported
Common mistakes
- Drawing dxy lobes directly on the x and y axes
- Omitting the torus from dz²
- Putting the dz² lobes in the xy plane
- Describing an orbital as a fixed electron orbit
What can you explain now?
Where do the four lobes of 3dxy point?
Compare with the explanation
Between the x and y axes in the xy plane
The dxy lobes are oriented between, not along, those axes.
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Make it stick
What is the plane and lobe orientation of dxy, and what two parts make the dz² sketch distinctive?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.