Questions: Atomic Orbitals

Question 1

A hydrogen orbital has quantum numbers n=3, ℓ=1. How many angular nodes does this orbital have?

• A. 0
• B. 1
• C. 2
• D. 3

Answer: (B)

The angular quantum number ℓ directly gives the number of angular nodes. Since ℓ=1, there is 1 angular node, producing the two-lobe p-orbital shape. The total node count is n−1=2, so there is also 1 radial node — but that is a different kind of node.

Question 2

In a hydrogen atom, the 3s orbital has lower energy than the 3p orbital because it is closer to the nucleus.

• T. True
• F. False

Answer: False

In hydrogen (one electron), all orbitals with the same principal quantum number n have exactly the same energy — they are degenerate. The 3s, 3p, and 3d orbitals all sit at E = −13.6/9 eV. Energy degeneracy within a shell is broken only in multi-electron atoms, where electron shielding makes s orbitals lower in energy than p orbitals of the same n.

Question 3

An atomic orbital is sometimes described as 'the electron's path around the nucleus.' Why is this description wrong, and what does an orbital actually represent?

Model answer: An orbital is not a path but a wavefunction ψ (or probability density |ψ|²) that describes the probability of finding the electron at each point in space. Electrons have no definite trajectory — the orbital shape shows where the electron is most likely to be found if measured.

This targets the classical-orbit misconception. Unlike a planetary orbit, the electron exists in a quantum superposition without a definite position. The orbital's shape (sphere for s, lobes for p) represents regions of high probability density |ψ|², not a physical track. This distinction is foundational to all quantum chemistry.