For which of the following options m=0 for all orbitals ?

Options

A. `2s ,2p_(x) , 3d _(xy)`
B. `3s,2p_(z) ,3d_(z^2)`
C. `2s,2p_(z) , 3d _(X^2 -y^2)`
D. `3s , 3p_(x) , 3d _(yz)`

Answer

To solve the question "For which of the following options m=0 for all orbitals?", we need to analyze the magnetic quantum number (m) for different types of orbitals. The magnetic quantum number (m) can take values from -l to +l, where l is the azimuthal quantum number associated with the type of orbital.

### Step-by-Step Solution:

1. **Understanding Quantum Numbers**:
- The magnetic quantum number (m) indicates the orientation of the orbital in space.
- The value of m can range from -l to +l, including 0.

2. **Identify the Quantum Number (l) for Each Subshell**:
- For **s orbitals** (l = 0): The only value of m is 0.
- For **p orbitals** (l = 1): The possible values of m are -1, 0, +1. Here, m = 0 corresponds to the pz orbital.
- For **d orbitals** (l = 2): The possible values of m are -2, -1, 0, +1, +2. Here, m = 0 corresponds to the dz² orbital.

3. **Analyzing the Given Options**:
- **Option 1: 2s, 2px, 2pz, 3dz²**
- 2s: m = 0
- 2px: m = -1 (not 0)
- 2pz: m = 0
- 3dz²: m = 0
- **Conclusion**: This option is incorrect because 2px has m ≠ 0.

- **Option 2: 3s, 3p, 3dz²**
- 3s: m = 0
- 3p: m can be -1, 0, +1 (but not all are 0)
- 3dz²: m = 0
- **Conclusion**: This option is incorrect because 3p has m ≠ 0.

- **Option 3: 2s, 2pz, 3dx²-y²**
- 2s: m = 0
- 2pz: m = 0
- 3dx²-y²: m = 0
- **Conclusion**: This option is correct because all orbitals have m = 0.

- **Option 4: 3s, 3px, 3p**
- 3s: m = 0
- 3px: m = -1 (not 0)
- 3p: m can be -1, 0, +1 (but not all are 0)
- **Conclusion**: This option is incorrect because 3px has m ≠ 0.

4. **Final Answer**:
- The correct option where m = 0 for all orbitals is **Option 3: 2s, 2pz, 3dx²-y²**.