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Quantum Numbers and Atomic Orbitals in 3D – s, p, d

ChemistryAtomic Structure & Periodic TableAges 15–16

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Use with my class

Choose the four quantum numbers n, l, mₗ and mₛ and view the s, p and d orbitals of the hydrogen atom in three dimensions, as a 90% boundary surface or as a probability cloud, with radial nodes (n − l − 1) and angular nodes (l) highlighted. A radial distribution graph r²R², a box diagram of the whole shell n (2l + 1 orbitals per subshell, 2n² electrons per shell), a table of the orbitals viewed and three self-checking tasks complete the picture.

Lesson: Atomic orbitals, quantum numbers, shapes of s, p and d orbitals

What it shows

An electron in an atom is described by four quantum numbers: the principal number n sets the shell and size, l = 0 … n − 1 the subshell and shape (s, p, d, f), mₗ = −l … +l the orientation, and mₛ = ±½ the spin. A subshell has 2l + 1 orbitals and a shell holds 2n² electrons. Each orbital has n − l − 1 radial nodes (spheres) and l angular nodes (planes or cones) where the probability is zero. The model is the hydrogen atom; orbitals of larger atoms have similar shapes but different sizes and energies.

How to use

Pick n, then l and mₗ; values that are not allowed are greyed out. Rotate the orbital by dragging and compare the 90% surface with the cloud. Turn on Cut away to see the radial nodes inside, and compare them with the dips to zero in the radial distribution graph. Tap a box in the shell diagram to jump to that orbital, then try the three tasks.

Parameters you can change

  • Principal quantum number n 1–4
  • Azimuthal quantum number l 0–2
  • Magnetic quantum number mₗ -2–2
  • Spin quantum number mₛ +½ (↑), −½ (↓)
  • Orbital display 90% surface, Probability cloud
  • Show nodes
  • Cut away the front half

Questions to explore

  1. How many radial and angular nodes does a 3p orbital have, and where can you see each kind?
  2. Why can there be no 2d orbital, and how many orbitals does the shell n = 3 contain?
  3. How does the most probable distance from the nucleus change from 1s to 2s to 3s?

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