The plots of radial distribution functions for various orbitals of hydrogen atom against 'r' are given below. The…

🧠 Charting the Humps The Radial Distribution Function (RDF) represents the probability of finding an electron in a thin shell at distance $r$. The number of peaks (humps) in an RDF plot is exactly equal to $(n - l)$.

🗺️ The Peak Count

1. Quantum Numbers: For 3s, $n=3$ and $l=0$.
2. Peaks: $n - l = 3 - 0 = mathbf{3 ext{ peaks}}$.
3. Nodes: $n - l - 1 = mathbf{2 ext{ nodes}}$ (where the plot touches the x-axis).
4. Conclusion: The only plot with 3 distinct peaks and 2 nodes is Option (c).

⚡ The Peak Magnitude Rule Each successive hump in an RDF plot is larger than the previous one because as the radius ($r$) grows, the volume of the shell ($4pi r^2$) grows, catching more probability mass.

⚠️ Common Traps Don't confuse RDF ($4pi r^2 psi^2$) with Probability Density ($\psi^2$). RDF always starts at zero (at origin, volume is zero), while 3s density starts at its maximum.

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