The maximum probability of finding electron in the `d_(xy)` orbital is -

Options

A. along the x - axis
B. along the y - axis
C. at the angle of `45^(@)` from the x - and y - axis
D. at the angle of `90^(@)` from the x - and y - axis

Answer

To determine the maximum probability of finding an electron in the \(d_{xy}\) orbital, we need to analyze the characteristics of this specific orbital.

### Step 1: Understand the Shape of the \(d_{xy}\) Orbital
The \(d_{xy}\) orbital is one of the five \(d\) orbitals in quantum chemistry. It is characterized by its unique shape, which lies in the plane between the x and y axes. The \(d_{xy}\) orbital has a lobular shape, with lobes extending into the first and third quadrants as well as the second and fourth quadrants of the Cartesian coordinate system.

### Step 2: Identify the Orientation of the Orbital
The lobes of the \(d_{xy}\) orbital are oriented at 45 degrees to both the x-axis and the y-axis. This means that the maximum probability of finding an electron in this orbital occurs at points that are equidistant from the x and y axes, specifically along the lines where the angles are 45 degrees.

### Step 3: Determine the Maximum Probability Location
Since the lobes of the \(d_{xy}\) orbital are situated at 45 degrees to the x and y axes, the maximum probability of finding an electron in the \(d_{xy}\) orbital will occur at these angles. Thus, the maximum probability is at an angle of 45 degrees from both the x-axis and y-axis.

### Conclusion
Therefore, the maximum probability of finding an electron in the \(d_{xy}\) orbital is at an angle of 45 degrees from the x and y axes.

### Final Answer
The maximum probability of finding an electron in the \(d_{xy}\) orbital is at an angle of **45 degrees** from the x and y axes.

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