Select the correct statement (s) :

Options

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

Answer

To solve the question, we need to analyze each of the given statements about atomic orbitals and determine which ones are correct. Let's go through each statement step by step.

### Step-by-Step Solution:

1. **Statement 1: An orbital with L = 0 is symmetrical about the nucleus.**
- The azimuthal quantum number (L) indicates the shape of the orbital. When L = 0, it refers to the s-orbital.
- The s-orbital is spherical in shape, meaning it is uniformly distributed around the nucleus.
- Therefore, this statement is **correct**.

2. **Statement 2: An orbital with L = 1 is spherically symmetrical about the nucleus.**
- When L = 1, it refers to the p-orbital.
- P-orbitals have a dumbbell shape and are not symmetrical in a spherical sense. They are oriented along specific axes (x, y, z).
- Thus, this statement is **incorrect**.

3. **Statement 3: 3dz² is spherically symmetrical about the z-axis.**
- The 3dz² orbital has a specific shape that includes a lobular structure along the z-axis and a donut-shaped ring around the equatorial plane.
- When considering symmetry about the z-axis, the lobes of the dz² orbital are indeed symmetrical around the z-axis.
- Hence, this statement is **correct**.

4. **Conclusion:**
- The correct statements are:
- Statement 1 (L = 0 is symmetrical about the nucleus)
- Statement 3 (3dz² is spherically symmetrical about the z-axis)

### Final Answer:
The correct statements are **Statement 1 and Statement 3**.

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