Orbitals with larger principal quantum number (n) have a smaller size.

Question

BlackTom AI · Accepted Answer

The statement to evaluate is: 'Orbitals with larger principal quantum number (n) have a smaller size.'

First, consider what 'size' of an orbital means in quantum mechanics. The radial extent of an orbital—the region where there is a significant probability of finding the electron—depends on the principal quantum number n. In hydrogen-like atoms, as n increases, the average distance of the electron from the nucleus grows, so the orbital's radial size increases rather than decreases.

Specifically, for a given l (angular momentum quantum number), the most probable radius scales roughly with n^2 (the Bohr model gives R_n ∝ n^2 a0 in a simple hydrogenic picture). Although different orbitals with the same n but different l have different shapes and radial distributions, the general trend is that higher-n orbitals are more extended in space.

Therefore, the claim that larger n leads to smaller orbital size contradicts the fundamental behavior of atomic orbitals: increasing n increases the radial reach and overall spatial extent of the orbital.

A potential source of confusion might be comparing orbitals with the same energy in multi-electron atoms or considering effective nuclear charge, but the standard principle remains: higher n corresponds to larger, more diffuse orbitals.

In summary, the assertion is incorrect because the principal quantum number n sets the overall size scale of the orbital, and larger n produces larger, not smaller, orbitals.

CHEM1012 (L2) Online Quiz #1

Orbitals with larger principal quantum number (n) have a smaller size.

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