Consider the following orbitals `3s, 2p_(x), 4d_(xy),4d_(z^(2)), 3d_(x^(2)-y^(2)),3p_(y),4s,4p_(z)` and find total number of orbital (s) having even number of nodal plane.

Explanation

To solve the problem, we need to analyze each of the given orbitals and determine the number of nodal planes they possess. We will then count the orbitals that have an even number of nodal planes (0, 2, 4, etc.).

### Step-by-Step Solution:

1. **Identify the Orbitals**: The orbitals given are:
- 3s
- 2p_x
- 4d_{xy}
- 4d_{z^2}
- 3d_{x^2-y^2}
- 3p_y
- 4s
- 4p_z

2. **Count Nodal Planes for Each Orbital**:
- **3s**: Spherical shape, **0 nodal planes**.
- **2p_x**: Has one nodal plane (the plane where electron density is zero), **1 nodal plane**.
- **4d_{xy}**: Has two nodal planes (the planes where electron density is zero), **2 nodal planes**.
- **4d_{z^2}**: This orbital has a more complex shape but also has **0 nodal planes**.
- **3d_{x^2-y^2}**: Similar to 4d_{xy}, it has **2 nodal planes**.
- **3p_y**: Has one nodal plane, **1 nodal plane**.
- **4s**: Spherical shape, **0 nodal planes**.
- **4p_z**: Has one nodal plane, **1 nodal plane**.

3. **List of Nodal Planes**:
- 3s: 0
- 2p_x: 1
- 4d_{xy}: 2
- 4d_{z^2}: 0
- 3d_{x^2-y^2}: 2
- 3p_y: 1
- 4s: 0
- 4p_z: 1

4. **Count the Orbitals with Even Nodal Planes**:
- Even nodal planes are 0 and 2.
- Orbitals with 0 nodal planes: 3s, 4d_{z^2}, 4s (3 orbitals)
- Orbitals with 2 nodal planes: 4d_{xy}, 3d_{x^2-y^2} (2 orbitals)
- Total: 3 (from 0 nodal planes) + 2 (from 2 nodal planes) = **5 orbitals**.

### Final Answer:
The total number of orbitals having an even number of nodal planes is **5**.

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