Select the correct statement(s):

Options

A. An orbital with l = 0 is symmetrical about the nucleus
B. An orbital with l = 1 is spherically symmetrical about the nucleus
C. `3d_(z^(2))` is spherically symmetrical about the z-axis
D. All are correct

Explanation

To solve the question of selecting the correct statements regarding atomic orbitals, we will analyze each option step by step.

### Step 1: Understanding the Quantum Numbers
The azimuthal quantum number \( l \) defines the shape of the orbital:
- \( l = 0 \) corresponds to the **s orbital** (spherical shape).
- \( l = 1 \) corresponds to the **p orbital** (dumbbell shape).
- \( l = 2 \) corresponds to the **d orbital** (more complex shapes).

### Step 2: Analyzing Each Statement
1. **Statement A**: "n orbital with \( l = 0 \) is symmetric about nucleus."
- Since \( l = 0 \) corresponds to the s orbital, which is indeed spherical and symmetric about the nucleus, this statement is **correct**.

2. **Statement B**: "n orbital with \( l = 1 \) is symmetric about nucleus."
- The p orbital (where \( l = 1 \)) has a dumbbell shape and is symmetric about the nucleus in the sense that it has equal probability density in opposite lobes. Therefore, this statement is also **correct**.

3. **Statement C**: "3d \( z^2 \) is spherically symmetrical about the z-axis."
- The \( d_{z^2} \) orbital has a unique shape that includes a lobe along the z-axis and a torus around the xy-plane. While it has symmetry about the z-axis, it is not spherically symmetrical. Thus, this statement is **incorrect**.

### Step 3: Conclusion
Based on the analysis:
- Statement A is correct.
- Statement B is correct.
- Statement C is incorrect.

Thus, the correct answer is that statements A and B are correct, while C is incorrect. Therefore, the final answer is **A and B are correct**.

### Final Answer
The correct statements are A and B.

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