for `3d_(z^2)` orbital the value of l and m respectively are

Options

A. `2,0`
B. `2, +1`
C. `2, -1`
D. 2, +2

Answer

To determine the values of the azimuthal quantum number (l) and the magnetic quantum number (m) for the 3d_(z^2) orbital, we can follow these steps:

### Step 1: Identify the Principal Quantum Number (n)
The notation "3d" indicates that the principal quantum number (n) is 3. The "d" indicates that we are dealing with a d orbital.

### Step 2: Determine the Azimuthal Quantum Number (l)
The azimuthal quantum number (l) defines the shape of the orbital. For d orbitals, the value of l is always 2. Therefore, for the 3d orbital:
- **l = 2**

### Step 3: Determine the Magnetic Quantum Number (m)
The magnetic quantum number (m) can take values from -l to +l, including zero. For l = 2, the possible values of m are:
- m = -2, -1, 0, +1, +2

Since we are specifically looking for the 3d_(z^2) orbital, we identify that the magnetic quantum number (m) corresponding to the d_(z^2) orbital is:
- **m = 0**

### Conclusion
Thus, for the 3d_(z^2) orbital, the values of l and m are:
- **l = 2**
- **m = 0**

### Final Answer
The values of l and m for the 3d_(z^2) orbital are (2, 0).

---