In which of the following set of orbitals, nodal plane is absent ?

Options

A. `4s, 4d_(z^(2))`
B. `4s, 4d_(x^(2)-y^(2))`
C. `4p_(z), 4s`
D. `4d_(yz), 4d_(zx)`

Explanation

To determine in which set of orbitals the nodal plane is absent, we will analyze each option provided in the question. A nodal plane is defined as a plane where the probability of finding an electron is zero, meaning there is no electron density in that plane.

### Step-by-Step Solution:

1. **Understanding the Orbitals**:
- Orbitals can be classified into different types based on their shapes: s, p, d, and f orbitals.
- S orbitals are spherical, while p orbitals are dumbbell-shaped, and d orbitals have more complex shapes.

2. **Analyzing Option A: 4s and 4dz²**:
- The **4s orbital** is spherical in shape. In a spherical orbital, there are no planes where the electron density is zero; hence, there is no nodal plane.
- The **4dz² orbital** has a unique shape resembling a donut with a lobe above and below the donut. Similar to the 4s orbital, there are no planes where the electron density is zero. Therefore, there is no nodal plane in this orbital as well.

3. **Analyzing Option B: 4s and 4dx²-y²**:
- The **4s orbital** again has no nodal plane.
- The **4dx²-y² orbital** has a dumbbell shape with a nodal plane present along the z-axis where the electron density is zero. Thus, this option cannot be correct.

4. **Analyzing Option C: 4s and 4pz**:
- The **4s orbital** has no nodal plane.
- The **4pz orbital** has a shape that indicates a nodal plane along the xy-plane where the electron density is zero. Therefore, this option cannot be correct.

5. **Analyzing Option D: 4dyz and 4dzx**:
- The **4dyz orbital** and **4dzx orbital** both have shapes that indicate the presence of nodal planes. Specifically, both orbitals have nodal planes where the electron density is zero along the x and y axes. Thus, this option cannot be correct.

### Conclusion:
After analyzing all the options, the only set of orbitals where the nodal plane is absent is **Option A: 4s and 4dz²**.

### Final Answer:
**Option A: 4s and 4dz²**

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