Consider the following orbitals (i)`3p_(x)` (ii)`4d_(z^(2))` (iii)`3d_(x^(2)-y^(2))` (iv)`3d_(yz)`
Then, calculate value of "`x+y-z`" here x is total number of gerade orbital and y is total number of ungerade orbitals and z is total number of axial orbitals in given above orbitals.

Explanation

To solve the problem, we will analyze each of the given orbitals and categorize them into gerade and ungerade orbitals, as well as identify the axial orbitals.

### Step-by-Step Solution:

1. **Identify the Orbitals**:
- The orbitals given are:
- (i) `3p_x`
- (ii) `4d_{z^2}`
- (iii) `3d_{x^2-y^2}`
- (iv) `3d_{yz}`

2. **Define Terms**:
- **Gerade Orbitals**: These are symmetric with respect to inversion through the origin.
- **Ungerade Orbitals**: These are not symmetric with respect to inversion.
- **Axial Orbitals**: These are orbitals that lie along the principal axes (x, y, z).

3. **Analyze Each Orbital**:
- **(i) `3p_x`**:
- This orbital is not symmetric with respect to inversion (positive phase on one side and negative on the other).
- **Classification**: Ungerade
- **Axial**: Yes (along the x-axis)

- **(ii) `4d_{z^2}`**:
- This orbital is symmetric with respect to inversion (both lobes are positive).
- **Classification**: Gerade
- **Axial**: Yes (along the z-axis)

- **(iii) `3d_{x^2-y^2}`**:
- This orbital is symmetric with respect to inversion (positive lobes in the x and y directions).
- **Classification**: Gerade
- **Axial**: Yes (along the x and y axes)

- **(iv) `3d_{yz}`**:
- This orbital is not symmetric with respect to inversion (positive and negative lobes).
- **Classification**: Ungerade
- **Axial**: No (lobes are in the yz plane, not along an axis)

4. **Count the Orbitals**:
- **Total Gerade Orbitals (x)**:
- `4d_{z^2}` and `3d_{x^2-y^2}` → 2
- **Total Ungerade Orbitals (y)**:
- `3p_x` and `3d_{yz}` → 2
- **Total Axial Orbitals (z)**:
- `3p_x`, `4d_{z^2}`, and `3d_{x^2-y^2}` → 3

5. **Calculate x + y - z**:
- Substitute the values:
- x = 2 (gerade)
- y = 2 (ungerade)
- z = 3 (axial)
- Calculation:
\[ x + y - z = 2 + 2 - 3 = 1 \]

### Final Answer:
The value of \( x + y - z \) is **1**.