Atomic Orbitals: Energies and Shapes

At A Level, an orbital is not a circular electron path. Orbital questions test (i) how many s, p and d orbitals exist, (ii) their relative energies and (iii) their shapes—including the exceptional d_z² shape. Use those ideas next in orbital filling and electron configuration. Return to the Atomic Structure hub when you need the full lesson sequence.

Definitions (Must Know)

A. Orbital

An orbital is a region of space around the nucleus in which there is a high probability of finding an electron. Each orbital can hold up to two electrons with opposite spins.

B. Shell (principal quantum number, n)

A shell is an energy level labelled by n = 1, 2, 3, ….

C. Subshell (s, p, d)

A subshell is a set of orbitals of the same type within a shell (e.g. 3p is a subshell inside the n = 3 shell).

Key Ideas (What Earns Marks)

• s, p, d subshells contain 1, 3, 5 orbitals respectively.
• Each orbital holds a maximum of 2 electrons → s holds 2, p holds 6, d holds 10.
• For the same shell (n): s < p < d in energy (s is lowest energy).
• For atomic structure questions you must know the relative order: 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p.

Detailed Explanations

A. How many orbitals exist in each subshell?

So for principal quantum numbers 1–3 (and the required 4s/4p):

You also need to know that 4s and 4p orbitals exist, and their relative energies appear in the common filling order used for electron configurations (see below).

B. Relative energies (what you need to memorise)

Two exam-safe rules for the multi-electron atoms considered here:

1. Higher n generally means higher energy.
2. For the same n: s < p < d.

The common energy order you use for electron configurations (up to 4p) is: 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p

C. Shapes (what to write in “describe the shape” questions)

• s orbital: spherical.
• p orbital: two-lobed “dumbbell” (three orientations in space, so there are 3 p orbitals in a p subshell).
• d orbitals: d_xy, d_xz, d_yz and d_(x²-y²) have four-lobed shapes. The fifth, d_z², has two lobes with a torus (ring) around the centre.

The different orientations do not create extra orbitals: a p subshell has three orbitals in total, and a d subshell has five.

Worked Examples

Common Mistakes

• Treating every orbital in one shell as identical. The shell label n = 3 groups 3s, 3p and 3d, but it does not give them one energy or shape. In a many-electron atom, these subshells have different relative energies: a 3s orbital is spherical, a 3p orbital is two-lobed, and 3d orbitals have the d shapes shown above. Orbitals within one subshell, such as the three 3p orbitals, have the same energy but point in different directions. Compare the subshell letters as well as n before describing an orbital.
• Describing orbitals as circular “electron orbits” around the nucleus.
• Saying p has 2 orbitals (p has 3 orbitals) or d has 4 orbitals (d has 5 orbitals).
• Drawing every d orbital as a four-lobed clover and forgetting the d_z² two-lobes-plus-torus shape.
• Forgetting that a d subshell exists starting at n = 3 (3d is part of the n = 3 shell).
• Mixing up filling order (4s before 3d) with removal from transition ions (4s removed first).

Check the distinction with n = 2: would a 2s orbital and a 2p orbital have the same energy and shape? Explain your answer before opening the check.

Then use the worked examples and practice below to apply orbital counts, shapes and energy order without relying on the shell number alone.

Exam Tips

• If the question says “state the number”, just write: s = 1 orbital, p = 3, d = 5.
• For “shape” questions, state spherical for s and two-lobed for p. For d, distinguish the four four-lobed orbitals from d_z² (two lobes and a torus).
• If you use the energy order in a configuration answer, always write it from low → high energy (don’t invent a new order).

Mind Stretchers