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The radial probability distribution curve P(r) = 4 * pi * r² * psi² for which of the following orbitals has exactly ONE node (one zero of P(r) other than r = 0 and r = infinity)?

1. 2p
2. 2s
3. 4d
4. 3p

Correct answer: 2s

Solution

Radial nodes = n - l - 1. 2p: 2-1-1=0 nodes (no radial node, single peak). 2s: 2-0-1=1 node (one interior zero). 3p: 3-1-1=1 node. 4d: 4-2-1=1 node. If the curve shown has one radial node and the first peak is smaller than the second (typical of 2s), the answer is 2s. The 2p curve has no radial node (single hump), making it the one orbital that is definitively different. A curve with exactly one radial node that also has a significant probability near the nucleus (like 2s) most likely represents the 2s orbital.

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