Question

Which of the following is the CORRECT statement about \(\Psi^2\)?

• A. \(\Psi^2\) represents atomic orbit
• B. Probability density of the electron at that point
• C. \(\Psi^2 \neq 0\) for nodes
• D. \(\Psi^2\) has no physical meaning

Hint:

Distinguish carefully between the wave function (\(\Psi\)) and the probability density (\(\Psi^2\)).

• \(\Psi\): Wave function. Can be positive, negative, or zero. No direct physical meaning.
• \(\Psi^2\): Probability density. Must be positive or zero. Represents the probability of finding an electron per unit volume at a specific point.

An orbital is the region where the total probability (\(\int \Psi^2 dV\)) is high.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
In the quantum mechanical model of the atom, $\Psi$ represents the wave function (amplitude of the electron wave), while its square, $\Psi^{2}$, has a strict statistical interpretation.
Step 2: Key Formula or Approach:
Recall the Born Interpretation of quantum mechanics, which links the mathematical wave function to the physical probability of locating a particle.
Step 3: Detailed Explanation:
(A) Atomic orbit: An orbit is a classical 2D circular path (Bohr model). $\Psi^{2}$ defines an "orbital" (a 3D region of space), not an orbit. (Incorrect)
(B) Probability density: According to Max Born, the value of $\Psi^{2}$ at any given point in space around the nucleus gives the probability density of finding an electron at that exact point. (Correct)
(C) Nodes: A node is specifically defined as a region where the probability of finding an electron is exactly zero. Therefore, at nodes, $\Psi^{2} = 0$. (Incorrect)
(D) Physical meaning: While the wave function $\Psi$ itself has no direct physical meaning (it can be positive, negative, or complex), $\Psi^{2}$ is always positive and has a very profound physical meaning: probability density. (Incorrect)
Step 4: Final Answer:
$\Psi^{2}$ represents the probability density of the electron.