Question

The figures below show: Which of the following points in Figure 2 most accurately represents the nodal surface shown in Figure 1?

• A. C
• B. D
• C. B
• D. A

Hint:

Nodes are identified where the wave function becomes exactly zero, not where probability is merely low.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
A nodal surface (radial node) is a region where the probability density (\( \Psi^2 \)) and the wave function (\( \Psi \)) are zero.
For a 2s orbital, the number of radial nodes = \( n - l - 1 = 2 - 0 - 1 = 1 \).
Step 2: Detailed Explanation:
Figure 1 shows the physical representation of the 2s orbital with one spherical nodal surface (the white ring between shaded areas).
Figure 2 shows the plot of the radial wave function \( \Psi_{2s}(x) \) against distance \( x \) from the nucleus.
- Point A represents a region of high positive wave function value (near the nucleus).
- Point B is where the curve intersects the x-axis, meaning \( \Psi = 0 \). This corresponds to the radial node.
- Point C represents the maximum negative value of the wave function after the node.
- Point D represents the tail of the wave function as it asymptotically approaches zero at large distances.
Since a node is defined as where \( \Psi = 0 \), point B is the correct representation.
Step 3: Final Answer:
Point B accurately represents the nodal surface.