Which of the following orbitals are valid?
`1s, 2p_(x),3d_(x^(2)-z^(2)),4p_(z),2p_(y),3d_(x^(2)),2d_(x^(2)-y^(2)),4d_(z^(2))`

Explanation

To determine which of the given orbitals are valid, we need to analyze each orbital based on the rules of quantum mechanics and the allowed quantum numbers for each type of orbital (s, p, d).

### Step-by-Step Solution:

1. **1s Orbital**:
- The 's' subshell can hold one orbital. The principal quantum number (n) for the 1s orbital is 1.
- **Validity**: Valid.

2. **2p_(x) Orbital**:
- The 'p' subshell can hold three orbitals (px, py, pz). The principal quantum number (n) is 2.
- **Validity**: Valid.

3. **3d_(x²-z²) Orbital**:
- The 'd' subshell can hold five orbitals. The principal quantum number (n) is 3. The d orbitals are valid for n=3.
- **Validity**: Valid.

4. **4p_(z) Orbital**:
- The 'p' subshell can hold three orbitals. The principal quantum number (n) is 4.
- **Validity**: Valid.

5. **2p_(y) Orbital**:
- Similar to the 2p_(x) orbital, the 'p' subshell can hold three orbitals. The principal quantum number (n) is 2.
- **Validity**: Valid.

6. **3d_(x²) Orbital**:
- The 'd' subshell can hold five orbitals. However, the correct notation for the d orbitals includes (x²-y²) and (z²). There is no standalone (x²) orbital in the d subshell.
- **Validity**: Invalid.

7. **2d_(x²-y²) Orbital**:
- The 'd' subshell starts from n=3. There is no 2d subshell; hence, this notation is incorrect.
- **Validity**: Invalid.

8. **4d_(z²) Orbital**:
- The 'd' subshell can hold five orbitals. The principal quantum number (n) is 4, which is valid for the d subshell.
- **Validity**: Valid.

### Summary of Validity:
- Valid orbitals: **1s, 2p_(x), 3d_(x²-z²), 4p_(z), 2p_(y), 4d_(z²)**
- Invalid orbitals: **3d_(x²), 2d_(x²-y²)**