Figure 1. electron probability density for 2 s orbital
Figure 2. wave function for 2s orbital
Which of the following point in Figure 2 most accurately represents the nodal surface as shown in Figure 1?

Solution

Chemistry ma’am · 3 steps

A node is where ψ itself becomes zero, so look for where the curve crosses the x-axis.

1. What a node means. On a nodal surface the electron probability density ψ² is zero, so ψ must be zero there too. For a 2s orbital, n - l - 1 = 2 - 0 - 1 = 1 radial node, which is the one spherical surface drawn in Figure 1.
2. Read the graph. In Figure 2, ψ₂ₛ starts positive near the nucleus and turns negative further out. To change sign it must pass through zero once, and that crossing is the radial node.

   Point	Value of ψ₂ₛ	Is it the node?
   A	largest positive value, at the nucleus	No, density is highest here
   B	zero, curve crosses from + to −	Yes, ψ = 0 and ψ² = 0
   C	most negative value	No, ψ² is large here
   D	small but still negative	No, ψ reaches zero only at infinite distance

3. So. Point B is where ψ₂ₛ changes sign through zero, so it matches the spherical nodal surface. The answer is (b).

The idea to keep. A radial node is where the wave function changes sign, so ψ = 0 there. On any ψ versus r graph, count the x-axis crossings (not the minima) to find the nodes. There are n - l - 1 of them.

Answer from the NTA final answer key. Solution by PrepWiser.