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Structure of Atom question

2019 · 10 Apr · Shift 1 · Q3
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Structure of Atom question

2019 · 10 Apr · Shift 1 · Q3

JEE MainChemistryStructure of AtomMCQ+4 / −1
The graph between ∣ψ∣2{\left| \psi \right|^2}∣ψ∣2 and r (radial distance) is shown below. This represents : JEE Main 2019 (Online) 10th April Morning Slot Chemistry - Structure of Atom Question 142 English
  1. A
    3s orbital
  2. B
    2s orbital
  3. C
    2p orbital
  4. D
    1s orbital
View written solutionFree

Correct answer: B

  1. We are asked to identify an orbital from the graph of ∣ψ∣2|\psi|^2∣ψ∣2 versus radial distance rrr.

  2. Key idea:

    • The number of radial nodes helps identify the orbital.
    • For a hydrogen-like orbital: number of radial nodes=n−l−1\text{number of radial nodes} = n - l - 1number of radial nodes=n−l−1 where:
    • nnn = principal quantum number
    • lll = azimuthal quantum number
  3. Now check each option:

    A: 3s3s3s orbital

    • For 3s3s3s, n=3n=3n=3, l=0l=0l=0
    • Radial nodes: 3−0−1=23-0-1 = 23−0−1=2
    • So its ∣ψ∣2|\psi|^2∣ψ∣2 vs rrr graph should show two radial nodes.

    B: 2s2s2s orbital

    • For 2s2s2s, n=2n=2n=2, l=0l=0l=0
    • Radial nodes: 2−0−1=12-0-1 = 12−0−1=1
    • So its graph should show one radial node.

    C: 2p2p2p orbital

    • For 2p2p2p, n=2n=2n=2, l=1l=1l=1
    • Radial nodes: 2−1−1=02-1-1 = 02−1−1=0
    • So it has no radial node.
    • Also, for a ppp orbital, ψ=0\psi=0ψ=0 at r=0r=0r=0.

    D: 1s1s1s orbital

    • For 1s1s1s, n=1n=1n=1, l=0l=0l=0
    • Radial nodes: 1−0−1=01-0-1 = 01−0−1=0
    • So it has no radial node.
    • Also, ∣ψ∣2|\psi|^2∣ψ∣2 is maximum at r=0r=0r=0 and then decreases smoothly.
  4. From the given graph, the wave function probability density ∣ψ∣2|\psi|^2∣ψ∣2 shows one radial node (it becomes zero once and then rises again).

  5. Therefore, the orbital represented is: 2s orbital\boxed{2s\text{ orbital}}2s orbital​

  6. Option-wise conclusion:

    • A: Incorrect
    • B: Correct
    • C: Incorrect
    • D: Incorrect
  7. Comparison with stored correct answer:

    • Stored correct answer = B
    • Derived answer = B
    • Hence, they agree.
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