JEE Main · 2024 · Shift-IIeasyBOND-093

When A and B are the wave functions of atomic orbitals, then is represented by:

Chemical Bonding · Class 11 · JEE Main Previous Year Question

Question

When ψA\psi_A and ψB\psi_B are the wave functions of atomic orbitals, then σ\sigma^* is represented by:

Options
  1. a

    ψA+2ψB\psi_A + 2\psi_B

  2. b

    ψAψB\psi_A - \psi_B

  3. c

    ψA+ψB\psi_A + \psi_B

  4. d

    ψA2ψB\psi_A - 2\psi_B

Correct Answerb

ψAψB\psi_A - \psi_B

Detailed Solution

🧠 In MO theory, combining two atomic wave functions gives two molecular orbitals:

  • Bonding MO: σ=ψA+ψB\sigma = \psi_A + \psi_B (constructive interference, electron density increases between nuclei)
  • Antibonding MO: σ=ψAψB\sigma^* = \psi_A - \psi_B (destructive interference, electron density decreases/creates a node between nuclei)

The antibonding σ\sigma^* MO is represented by the difference of the two atomic wave functions.

⚡ The − sign introduces a nodal plane between the nuclei (where ψA=ψB\psi_A = \psi_B and the wave function becomes zero), which is the defining feature of an antibonding MO.

Answer: (b) ψAψB\boxed{\text{Answer: (b) } \psi_A - \psi_B}

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When A and B are the wave functions of atomic orbitals, then is represented by: (JEE Main 2024) | Canvas Classes