In case of `D_(x^(2)-y^(2)` orbital :

Options

A. Probability of finding the electron along x-axis zero
B. Probability of finding the electron along y-axis zero
C. Probability of finding the electron is maximum along `x` and `y`-axis
D. Probability of finding the electron is zero in `x-y` plane

Answer

To solve the question regarding the `d_(x^2 - y^2)` orbital, we will analyze the characteristics of this specific orbital step by step.

### Step 1: Understanding the Orbital
The `d_(x^2 - y^2)` orbital is one of the five d-orbitals in quantum chemistry. It is characterized by its unique shape and orientation in three-dimensional space.

**Hint:** Remember that d-orbitals have specific shapes and orientations that influence where electrons are likely to be found.

### Step 2: Analyzing the Probability Density
In quantum mechanics, the probability density of finding an electron in a particular region of space is given by the square of the wave function associated with that orbital. For the `d_(x^2 - y^2)` orbital, the probability density is influenced by the values of x and y.

**Hint:** The probability density is derived from the wave function, which can be visualized as regions where the electron is likely to be found.

### Step 3: Identifying Key Characteristics
For the `d_(x^2 - y^2)` orbital:
- The probability of finding an electron along the x-axis is maximum.
- The probability of finding an electron along the y-axis is also maximum.
- The probability of finding an electron in the xy-plane (where both x and y are non-zero) is zero.

**Hint:** Focus on how the orbital's shape affects the probability distribution in different planes.

### Step 4: Conclusion
Based on the characteristics of the `d_(x^2 - y^2)` orbital:
- The probability of finding an electron is maximum along the x and y axes.
- Therefore, the correct answer to the question is that the probability of finding the electron is maximum along the x and y axes.

**Final Answer:** The answer is option C: Probability of finding the electron is maximum along x and y axes.