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 \(\Psi\) and \(\Psi^2\).
In quantum mechanics, the state of an electron in an atom is described by a wave function, represented by the Greek letter psi (\(\Psi\)). The wave function \(\Psi\) itself is a mathematical function (a solution to the Schrödinger equation) and does not have a direct physical meaning. However, its square, \(\Psi^2\), does have a very important physical significance. 
Step 2: Evaluating the Options. 
(A) \(\Psi^2\) represents atomic orbit: An atomic orbital is the three-dimensional region of space around the nucleus where the probability of finding an electron is maximum (typically >90%). \(\Psi^2\) is the probability density at a single point, not the entire region (orbital). So, this is incorrect. 
(B) Probability density of the electron at that point: According to Max Born's interpretation of the wave function, the value of \(\Psi^2\) at any given point in space is proportional to the probability of finding the electron at that point. More precisely, \(\Psi^2 dV\) represents the probability of finding the electron in a small volume element dV. Therefore, \(\Psi^2\) is known as the probability density. This statement is correct. 
(C) \(\Psi^2 \neq 0\) for nodes: A node is a point or a surface where the probability of finding an electron is zero. By definition, at a node, \(\Psi = 0\), and consequently, \(\Psi^2 = 0\). This statement claims the opposite and is therefore incorrect. 
(D) \(\Psi^2\) has no physical meaning: This is incorrect. As explained in (B), \(\Psi^2\) has a clear and crucial physical meaning: it represents the probability density of finding an electron. It is \(\Psi\) itself that has no direct physical meaning. 
Step 3: Final Answer. 
The correct statement is that \(\Psi^2\) represents the probability density of the electron at a point.