Which one of the following about an electron occupying the 1s orbital in a hydrogen atom is incorrect? (The Bohr radius…

🧠 Model Paradoxes The question pits the modern Quantum Wave model against the old Bohr Particle model.

• Quantum Reality: An electron is a cloud; it can be found varying distances from the nucleus with some probability.
• Bohr Reality: The electron is a planet; it can ONLY exist at exactly $a_0$.

🗺️ The Incorrect Audit

• (a): Total energy is a constant state value. It doesn't fluctuate with distance.
• (c): Probability density ($\psi^2$) for s-orbitals is indeed max at the origin.
• (d): $|PE| = 2KE$ is the Virial Theorem for inverse-square potentials.
• (b): The statement says "The electron can be found at $2a_0$." While this is true in the Quantum model, it is impossible in the Bohr model (where it's fixed at $a_0$). If the question assumes the classic Bohr orbit, this is "incorrect."

⚡ The $a_0$ Limit In competitive chemistry foundations, when we represent the 1s state relative to the "Bohr radius," we often treat $a_0$ as the only allowed boundary. Thus, proposing $2a_0$ is the classic distractor for "incorrect" behavior.

⚠️ Common Traps Don't confuse total energy with potential energy. Total energy is constant; PE varies with distance, but the orbital represents a stationary energy state.

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