What is the maximum number of electron that may be present in all the atomic orbitals with principal quantum number `3` and azimuthal quantum number` 2`?

Explanation

To determine the maximum number of electrons that may be present in all the atomic orbitals with a principal quantum number (n) of 3 and an azimuthal quantum number (l) of 2, we can follow these steps:

### Step 1: Identify the Principal Quantum Number (n)
The principal quantum number (n) indicates the energy level or shell of the electron. Here, n = 3 corresponds to the third energy level.

### Step 2: Identify the Azimuthal Quantum Number (l)
The azimuthal quantum number (l) describes the shape of the subshell. The value of l can be 0, 1, 2, or 3, which correspond to the s, p, d, and f subshells respectively. In this case, l = 2 corresponds to the d subshell.

### Step 3: Determine the Number of Orbitals in the d Subshell
For a d subshell (l = 2), there are a total of 5 orbitals. The orbitals can be represented as:
- dxy
- dyz
- dzx
- dx²-y²
- dz²

### Step 4: Calculate the Maximum Number of Electrons
Each orbital can hold a maximum of 2 electrons (due to the Pauli exclusion principle). Therefore, the total number of electrons that can occupy the 5 d orbitals is calculated as follows:
\[ \text{Maximum number of electrons} = \text{Number of orbitals} \times \text{Maximum electrons per orbital} \]
\[ \text{Maximum number of electrons} = 5 \times 2 = 10 \]

### Conclusion
Thus, the maximum number of electrons that may be present in all the atomic orbitals with principal quantum number 3 and azimuthal quantum number 2 (3D subshell) is **10**.

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