Choose the correct statement (s) :

Options

A. The shape of an atomic orbital depends upon azimuthal quantum number
B. The orientation of an atomic orbital depends upon the magnetic quantum number
C. The energy of an electron in an atomic orbital of multi-electron depends upon principal quantum number only
D. The number of degenerate atomic orbitals of one type depends upon the value of azimuthal quantum number

Answer

To solve the question, we need to analyze each statement regarding atomic orbitals and quantum numbers.

### Step-by-Step Solution:

1. **Understanding the Quantum Numbers**:
- **Principal Quantum Number (n)**: Indicates the energy level and size of the orbital. It can take positive integer values (1, 2, 3,...).
- **Azimuthal Quantum Number (l)**: Determines the shape of the orbital. Its values range from 0 to (n-1). For example, if n=2, l can be 0 (s orbital) or 1 (p orbital).
- **Magnetic Quantum Number (m)**: Specifies the orientation of the orbital in space. Its values range from -l to +l.

2. **Analyzing Each Statement**:
- **Statement 1**: "The shape of an atomic orbital depends upon azimuthal quantum number."
- This statement is **correct** because the azimuthal quantum number (l) determines the shape of the orbital (s, p, d, f).

- **Statement 2**: "The orientation of an atomic orbital depends upon magnetic quantum number."
- This statement is **correct** because the magnetic quantum number (m) defines the orientation of the orbital within a given shape.

- **Statement 3**: "The energy of an electron in an atomic orbital of a multi-electron atom depends upon principal quantum number only."
- This statement is **incorrect**. In multi-electron atoms, the energy of an electron also depends on the azimuthal quantum number (l). For example, in the second energy level (n=2), the 2s orbital has lower energy than the 2p orbital.

- **Statement 4**: "The number of degenerate atomic orbitals of one type depends upon the value of azimuthal quantum number only."
- This statement is **correct**. The number of degenerate orbitals (orbitals with the same energy) for a given l value is determined by the magnetic quantum number (m). For example, for l=1 (p orbitals), there are three degenerate orbitals corresponding to m = -1, 0, +1.

3. **Conclusion**:
- The correct statements are **1, 2, and 4**.

### Final Answer:
The correct statements are: **1, 2, and 4**.

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