The radial wave function R(r) for a certain atomic orbital is plotted against the distance r from the nucleus. The graph starts at the origin ( R = 0 when r = 0 ), rises to a positive maximum, crosses the r -axis exactly once, reaches a negative minimum, and then asymptotically approaches zero as r . Which of the following atomic orbitals is represented by this graph?

Step-by-step solution

The graph of the radial wave function R(r) starts at the origin, meaning R(0) = 0 . This indicates that the orbital is not an s-orbital, so the azimuthal quantum number l > 0 . The graph crosses the r -axis exactly once, which means the orbital has exactly 1 radial node. The number of radial nodes is given by the formula n - l - 1 . Setting n - l - 1 = 1 , we get n - l = 2 . Checking the given options: For 2s: l = 0 (incorrect, as l > 0 is required). For 3d: n = 3, l = 2 n - l - 1 = 0 radial nodes. For 4f: n = 4, l