Which of following has maximum possibility to find `e^(Θ)` in `d_(ZX)` orbital :-

Options

A. Along x axis
B. Along z axis
C. Along zx axis plane 2D
D. At an angle of `45^(@)`from z & x axis

Answer

To determine which of the given options has the maximum probability of finding an electron in the \(d_{zx}\) orbital, we can follow these steps:

### Step 1: Understand the \(d_{zx}\) Orbital
The \(d_{zx}\) orbital is one of the five d-orbitals found in transition metals. It has a specific shape that resembles a cloverleaf, with lobes oriented along the z-axis and x-axis.

### Step 2: Visualize the Orbital
To visualize the \(d_{zx}\) orbital, we can draw the coordinate axes. The z-axis is vertical, and the x-axis is horizontal. The lobes of the \(d_{zx}\) orbital will extend in the z-direction and x-direction, forming a cloverleaf shape.

### Step 3: Identify the Regions of Maximum Electron Density
The maximum probability of finding an electron in the \(d_{zx}\) orbital occurs in the lobes of the orbital. These lobes are oriented in the xz-plane, which means that the electron density will be highest at certain angles relative to the axes.

### Step 4: Analyze the Given Options
1. **Along the x-axis**: There is no electron probability along the x-axis itself, as the lobes do not extend in that direction. Therefore, this option is incorrect.
2. **Along the z-axis**: Similar to the x-axis, there is no maximum probability along the z-axis. This option is also incorrect.
3. **In the xz-plane**: While there is some electron density in the xz-plane, the maximum probability occurs at an angle of 45 degrees from both the x and z axes, not directly along the axes. This option is partially correct but not the maximum.
4. **At an angle of 45 degrees from the z and x axes**: This option correctly identifies the maximum probability regions of the \(d_{zx}\) orbital, where the lobes are located.

### Conclusion
The correct answer is that the maximum probability of finding an electron in the \(d_{zx}\) orbital occurs at an angle of 45 degrees from both the z-axis and the x-axis.

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