STATEMENT-1: Orbital having xz plane as node may be `3d_(xy)`
STATEMENT-2: `3d_(xy)` has zero radial node.

Options

A. If both the statement are TRUE and STATEMENT-2 is the correct explanation of STATEMENT-1
B. If both the statements are TRUE but STATEMENT-2 is NOT the correct explanation of STATEMENT-1
C. If STATEMENT-1 is TRUE and STATEMENT-2 is FALSE
D. If STATEMENT-1 is FALSE and STATEMENT-2 is TRUE

Answer

To determine the validity of the given statements, we will analyze each statement step by step.

### Step 1: Analyze Statement 1
**Statement 1:** "Orbital having xz plane as node may be \(3d_{xy}\)."

- The \(3d_{xy}\) orbital is a type of d-orbital.
- D-orbitals have specific shapes and orientations in space. The \(3d_{xy}\) orbital has lobes that lie in the xy-plane, and it has nodal planes.
- A nodal plane is a plane where the probability of finding an electron is zero. For the \(3d_{xy}\) orbital, the nodal planes are indeed the xz and yz planes.

**Conclusion for Statement 1:** This statement is correct because the \(3d_{xy}\) orbital does have the xz plane as a nodal plane.

### Step 2: Analyze Statement 2
**Statement 2:** "\(3d_{xy}\) has zero radial node."

- To find the number of radial nodes, we use the formula:
\[ \text{Number of radial nodes} = n - l - 1 \]
where \(n\) is the principal quantum number and \(l\) is the azimuthal quantum number.
- For the \(3d_{xy}\) orbital:
- The principal quantum number \(n = 3\) (since it is a 3d orbital).
- The azimuthal quantum number \(l = 2\) (for d-orbitals).
- Plugging in the values:
\[ \text{Number of radial nodes} = 3 - 2 - 1 = 0 \]

**Conclusion for Statement 2:** This statement is also correct because the \(3d_{xy}\) orbital indeed has zero radial nodes.

### Step 3: Determine the Relationship Between Statements
- Both statements are correct.
- However, Statement 2 does not explain Statement 1. Statement 1 discusses the nodal planes (spatial nodes), while Statement 2 discusses radial nodes (which are different).

### Final Conclusion
Both statements are true, but Statement 2 is not the correct explanation for Statement 1. Therefore, the correct answer is that both statements are true, but Statement 2 does not explain Statement 1.