JEE Main · 2019 · Shift-ImediumATOM-036

The electrons are more likely to be found:

Structure of Atom · Class 11 · JEE Main Previous Year Question

Question

The electrons are more likely to be found:

image

Options
  1. a

    Only in the region a

  2. b

    In the region a and b

  3. c

    In the region a and c

  4. d

    Only in the region c

Correct Answerc

In the region a and c

Detailed Solution

🧠 Finding the Dense Regions Wave mechanics tells us that electrons don't just "sit" in a circle. They exist in regions of probability. The radial probability distribution (4πr2ψ24\pi r^2 \psi^2) specifically maps where you are most likely to find an electron at a certain distance (rr) from the nucleus.

🗺️ Reading the Peaks and Valleys For a 2s orbital:

  • Radial Nodes: nl1=201=1n - l - 1 = 2 - 0 - 1 = 1. There is exactly one point where the probability drops to zero.
  • Regions on Graph:
    • Region a (Peak 1): The "inner" probability density. Small, but very close to the nucleus (penetration effect).
    • Region b (Valley): The radial node. Probability =0= 0.
    • Region c (Peak 2): The "outer" probability density. Large and broad, representing where the valence electron spends most of its time.

Electrons inhabit the high-probability zones, which are the peaks. Thus, they are most likely found in a and c.

The Node-Counter Shortcut Any "s" orbital has nn regions of electron density (peaks) separated by n1n-1 nodes. For 2s, that's 22 regions and 11 node. Identifying the peaks on any probability graph is as simple as counting the "bumps."

⚠️ Common Traps Don't confuse probability density (ψ2\psi^2) with radial probability (4πr2ψ24\pi r^2 \psi^2). The density ψ2\psi^2 is maximum at the nucleus for s-orbitals, but the volume element (r2\propto r^2) makes the radial probability zero at r=0r=0. Always check if the graph starts at the origin!

Answer: (c)\boxed{\text{Answer: (c)}}

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