Consider the following schematic plots of orbital wavefunction (\(\psi_r\)) against distance (\(r\)) from the nucleus.
The figure representing two radial nodes in the orbital is
Show Hint
To count radial nodes from a graph of \(\psi_r\) vs \(r\):
- Count the number of times the curve completely cuts through the \(\psi_r = 0\) line (do not count the origin \(r=0\) or the far right end where it flattens out).
- Graph C cuts the line twice \(\rightarrow\) 2 radial nodes.
Step 1: Define a radial node. A radial node is a distance \(r\) where the radial wavefunction \(\psi_r\) becomes zero and changes sign. On a plot of \(\psi_r\) versus \(r\), it shows as a crossing of the horizontal axis. Step 2: Decide what to count. We count the number of times the curve actually crosses the zero line, but we do not count the gentle approach to zero at very large \(r\) (that is just the tail, not a node). Step 3: Look for two crossings. Two radial nodes mean the curve must cut the \(r\)-axis exactly twice before fading out. Step 4: Scan the figures. We check each plot A, B, C, D and count genuine sign changes, ignoring the asymptotic tail at infinity. Step 5: Identify the correct curve. The curve labelled C is the one that crosses the axis twice, so it has two radial nodes. Step 6: State the answer. The figure with two radial nodes is C, which is option 4. \[ \boxed{\text{Figure C}} \]
