The graph between ||2 and r (radial distance) is shown below. This represents:

🧠 Reading the Cloud Density The plot of $|\psi|^2$ vs $r$ represents probability density. Key features to look for:

1. The Starting Point: Does it start high or at zero?
2. The Nodes: How many times does it touch the x-axis?

🗺️ The Graph Signature

1. The Intercept: The graph starts at its maximum value at $r=0$. This is the unique signature of s-orbitals.
2. The Node Count: The graph crosses zero exactly once. $\text{Radial Nodes} = n - l - 1 = 1$
3. Solving for $n$: Since $l=0$ (s-orbital), then $n - 0 - 1 = 1 \implies n = 2$.
4. Identity: The graph represents the 2s orbital.

⚡ The Origin Rule

• s-orbitals: Start high (non-zero probability at nucleus).
• p, d, f orbitals: Start at zero ($0$ probability at nucleus). This instantly eliminates 2p.

⚠️ Common Traps Forgetting to count the zero-point as a node. A 1s orbital would never touch the axis; a 2s touches it once.

$\boxed{\text{Answer: (c)}}$