Consider the following statements:
(a) Electron density in the `XY` plane in `3d_(x^(2)-y^(2))` orbital is zero
(b) Electron density in the `XY` plane in `3d_(z^(2))` orbital is zero.
(c ) `2s` orbital has one nodel surface
(d) for `2p_(z)` orbital, `XY` is the nodal plane.
Which of these are incorrect statements :

Options

A. a & c
B. b & c
C. Only b
D. a, b

Explanation

To solve the question, we need to analyze each of the statements provided regarding the electron density in different orbitals and their nodal surfaces.

**Step 1: Analyze statement (a)**
- Statement (a) claims that the electron density in the XY plane in the `3d_(x²-y²)` orbital is zero.
- The `3d_(x²-y²)` orbital has a characteristic shape where it has lobes along the x and y axes and a nodal plane along the line where x = y.
- In the XY plane, the lobes of the `3d_(x²-y²)` orbital are present, indicating that there is electron density in that plane.
- Therefore, statement (a) is **incorrect**.

**Step 2: Analyze statement (b)**
- Statement (b) claims that the electron density in the XY plane in the `3d_(z²)` orbital is zero.
- The `3d_(z²)` orbital has a unique shape that includes a lobular structure extending along the z-axis and a torus (doughnut shape) in the XY plane.
- This means that there is indeed electron density present in the XY plane.
- Therefore, statement (b) is **incorrect**.

**Step 3: Analyze statement (c)**
- Statement (c) states that the `2s` orbital has one nodal surface.
- The `2s` orbital has a spherical shape with one spherical nodal surface separating the inner and outer regions of electron density.
- Thus, statement (c) is **correct**.

**Step 4: Analyze statement (d)**
- Statement (d) claims that for the `2p_(z)` orbital, the XY plane is the nodal plane.
- The `2p_(z)` orbital has lobes extending along the z-axis, and the XY plane is indeed a nodal plane where there is no electron density.
- Therefore, statement (d) is **correct**.

**Conclusion:**
- The incorrect statements are (a) and (b). Therefore, the answer to the question is that statements (a) and (b) are incorrect.

### Summary of Incorrect Statements:
- (a) Electron density in the `XY` plane in `3d_(x²-y²)` orbital is zero. **(Incorrect)**
- (b) Electron density in the `XY` plane in `3d_(z²)` orbital is zero. **(Incorrect)**
- (c) `2s` orbital has one nodal surface. **(Correct)**
- (d) For `2p_(z)` orbital, `XY` is the nodal plane. **(Correct)**

### Final Answer:
The incorrect statements are (a) and (b).

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