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Which of the following conclusions can be correctly drawn from solutions of the Schrodinger wave equation?

1. For all orbitals, the radial wave function psi approaches zero as r increases to infinity
2. The radial probability density psi² for the 1s orbital is maximum at the nucleus
3. The radial distribution function 4*pi*r²*psi² for the 1s orbital is minimum at the nucleus
4. In the plot of radial wave function psi for the 3s orbital, psi changes sign at nodes

Correct answer: In the plot of radial wave function psi for the 3s orbital, psi changes sign at nodes

Solution

Statement A is true (psi -> 0 as r -> infinity for all bound states). Statement B is true (psi² for 1s is maximum at r=0). Statement C: RDF = 4*pi*r²*psi² is zero at r=0 (due to r² factor), not merely 'minimum' — it equals zero, which IS the minimum. C is technically correct. Statement D: at radial nodes psi=0 and psi does change sign (from positive to negative or vice versa) — D is correct. The most unambiguously correct statement per standard interpretation is D (psi changes sign at nodes). A, B, and D are all correct; C is also correct (zero is the minimum value). Given the phrasing, D is the most precise and intended answer.

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