In which of the following pairs is the probability of finding the electron in only xy - plane is zero for both orbitals ?

Options

A. `3d_(xy),4d_(x^(2)-y^(2))`
B. `2P_(z),3d_(z^(2)`
C. `4d_(zx),3P_(z)`
D. None of these

Answer

To solve the question, we need to determine which pair of orbitals has a probability of finding the electron in the xy-plane equal to zero for both orbitals. Let's analyze the options step by step.

### Step 1: Understand the Orbitals
1. **3d_xy Orbital**: This orbital has a specific orientation in the xy-plane. It is shaped like a four-leaf clover and has lobes in the xy-plane. Therefore, the probability of finding an electron in the xy-plane is not zero.

2. **4d_x^2 - y^2 Orbital**: This orbital is oriented along the x and y axes, with lobes extending along these axes. It also has a nodal plane in the xy-plane, meaning the probability of finding an electron in the xy-plane is zero.

### Step 2: Analyze the Second Pair
1. **2Pz Orbital**: This orbital is oriented along the z-axis. It has no electron density in the xy-plane, so the probability of finding an electron in the xy-plane is zero.

2. **3d_z^2 Orbital**: This orbital has a lobular shape with a "doughnut" around the z-axis and has a nodal plane in the xy-plane. Therefore, the probability of finding an electron in the xy-plane is also zero.

### Step 3: Analyze the Third Pair
1. **4d_zx Orbital**: This orbital has lobes oriented along the zx-plane. Therefore, it has electron density in the xy-plane, meaning the probability of finding an electron in the xy-plane is not zero.

### Conclusion
From the analysis:
- The first pair (3d_xy and 4d_x^2 - y^2) does not have both probabilities equal to zero.
- The second pair (2Pz and 3d_z^2) has both probabilities equal to zero.
- The third pair (4d_zx) does not have both probabilities equal to zero.

Thus, the answer to the question is **Option B: 2Pz and 3d_z^2**.