Orientation of orbitals is given by

Options

A. Magnetic quantum number
B. spin quantum number
C. Azimuthal quantum number
D. Principal quantum number

Answer

To determine which quantum number describes the orientation of orbitals, we can analyze the different quantum numbers and their roles:

1. **Principal Quantum Number (n)**: This quantum number indicates the main energy level or shell of an electron in an atom. It defines the size of the orbital but does not provide information about the orientation of the orbital.

2. **Azimuthal Quantum Number (l)**: This quantum number is associated with the shape of the orbital. It can take integer values from 0 to (n-1) and helps identify the subshell (s, p, d, f). However, it does not specify the orientation of the orbital.

3. **Magnetic Quantum Number (mₗ)**: This quantum number is crucial for determining the orientation of orbitals in space. For a given value of l, the magnetic quantum number can take values ranging from -l to +l, which results in a total of (2l + 1) possible orientations. Therefore, it directly describes how orbitals are oriented in a magnetic field.

4. **Spin Quantum Number (mₛ)**: This quantum number describes the intrinsic spin of the electron within an orbital. It indicates the direction of the electron's spin (either +1/2 or -1/2) but does not relate to the orientation of the orbital itself.

Based on the analysis above, the correct answer to the question "Orientation of orbitals is given by" is:

**Answer**: Magnetic Quantum Number (mₗ)

### Step-by-Step Solution:
1. Identify the four quantum numbers: principal (n), azimuthal (l), magnetic (mₗ), and spin (mₛ).
2. Understand the role of each quantum number:
- n: size and energy level of the orbital.
- l: shape of the orbital.
- mₗ: orientation of the orbital.
- mₛ: orientation of the electron's spin.
3. Conclude that the magnetic quantum number (mₗ) is the one that specifies the orientation of orbitals.