The maximum number of electrons in `3d_(z^(2))` orbital is-

Answer

To determine the maximum number of electrons in the `3d_(z^2)` orbital, we can follow these steps:

### Step 1: Understand the d-orbitals
The d-orbitals consist of five different types: `d_xy`, `d_yz`, `d_xz`, `d_(x^2-y^2)`, and `d_(z^2)`. Each of these orbitals can hold a certain number of electrons.

**Hint:** Remember that each orbital can hold a maximum of 2 electrons due to the Pauli exclusion principle.

### Step 2: Calculate the total capacity of d-orbitals
The total number of d-orbitals is 5. Since each orbital can hold a maximum of 2 electrons, the total maximum number of electrons that can occupy all d-orbitals is:
\[ \text{Total electrons} = \text{Number of orbitals} \times \text{Max electrons per orbital} = 5 \times 2 = 10 \]

**Hint:** Think about how many orbitals are in the d-subshell and how many electrons each can hold.

### Step 3: Identify the specific orbital
In this case, we are specifically interested in the `3d_(z^2)` orbital. Like any other d-orbital, the `3d_(z^2)` orbital can also hold a maximum of 2 electrons.

**Hint:** Focus on the individual orbital you are asked about, which is `3d_(z^2)`.

### Step 4: Conclusion
Thus, the maximum number of electrons that can occupy the `3d_(z^2)` orbital is:
\[ \text{Maximum electrons in } 3d_{(z^2)} = 2 \]

**Final Answer:** The maximum number of electrons in the `3d_(z^2)` orbital is **2**.

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