Consider the schematic plots of the orbital wavefunction ψ_r against distance r from the nucleus (A: monotonically decreasing; B: one sign-change; C: two ripples crossing zero twice; D: oscillatory). The figure representing two radial nodes in the orbital is:

Solution & Explanation

Concept: For the radial wavefunction ψ_r plotted against r, the number of RADIAL nodes equals the number of times the curve CROSSES the r-axis (changes sign), not merely touches it. For s orbitals, radial nodes = n − 1. Apply to the schematic plots: • Plot A — monotonically decreasing, never crosses zero → 0 radial nodes → 1s (n−1 = 0). • Plot B — one sign change (crosses zero once) → 1 radial node → 2s. • Plot C — the curve ripples and crosses the axis TWICE → 2 radial nodes → 3s (n−1 = 2). • Plot D — oscillatory p-type curve; for 3p the radial-node count would be n − l − 1 = 1, so it does not show two radial nodes here. The orbital with TWO radial nodes is plot C → answer C. Key trap: count true sign-changes (axis crossings), and note ψ may also have angular nodes which are NOT radial nodes.