Which of the following statements are correct?

Options

A. Radial wave functions gives the shape of the orbital
B. Radial wave function depends upon n and l.
C. 3p orbital has two spherical nodes
D. 3d orbital has no sperical node

Answer

To determine which of the statements provided in the question are correct, we will analyze each statement based on our understanding of atomic orbitals, radial functions, and angular functions.

### Step-by-Step Solution:

1. **Understanding Radial and Angular Functions**:
- The wave function of an atomic orbital can be expressed as a product of a radial function and an angular function.
- The radial function depends on the distance from the nucleus (denoted as \( r \)).
- The angular function depends on the direction in space.

**Hint**: Remember that the wave function is a combination of both radial and angular components.

2. **Radial Function and Orbital Shape**:
- The radial function gives the shape of the orbital. This means that the radial part of the wave function is responsible for the distribution of electron density around the nucleus.

**Hint**: Focus on how the shape of orbitals is influenced by the radial function.

3. **Dependence on Quantum Numbers**:
- The radial wave function depends on the principal quantum number \( n \) and the azimuthal quantum number \( l \).
- As \( n \) increases, the average distance of the electron from the nucleus increases.
- The value of \( l \) indicates the type of orbital (s, p, d, etc.) and affects the shape of the orbital.

**Hint**: Recall the significance of \( n \) and \( l \) in determining the properties of orbitals.

4. **Nodes in Orbitals**:
- The number of spherical nodes in an orbital can be calculated using the formula: Number of nodes = \( n - l - 1 \).
- For a 3p orbital:
- \( n = 3 \) and \( l = 1 \) (since p corresponds to \( l = 1 \)).
- Number of nodes = \( 3 - 1 - 1 = 1 \) spherical node.
- For a 3d orbital:
- \( n = 3 \) and \( l = 2 \) (since d corresponds to \( l = 2 \)).
- Number of nodes = \( 3 - 2 - 1 = 0 \) spherical nodes.

**Hint**: Use the formula for nodes to verify the number of nodes in different orbitals.

5. **Evaluating the Statements**:
- **Statement 1**: Radial function gives the shape of the orbital. (Correct)
- **Statement 2**: Wave function is a product of radial function and angular function. (Correct)
- **Statement 3**: 3p orbital has 2 spherical nodes. (Incorrect; it has 1 spherical node)
- **Statement 4**: 3d orbital has 0 spherical nodes. (Correct)

**Hint**: Carefully check each statement against your calculations and understanding of orbital theory.

### Conclusion:
Based on the analysis:
- The correct statements are **Statement 1**, **Statement 2**, and **Statement 4**.
- The incorrect statement is **Statement 3**.

### Final Answer:
The correct statements are:
- Statement 1: Radial function gives the shape of the orbital.
- Statement 2: Wave function is a product of radial function and angular function.
- Statement 4: 3d orbital has 0 spherical nodes.