Find total number of orbitals in S atom, for which `|m| le 1` and which contains at least one electron.
(Atomic number of S= 16). 

Answer

To find the total number of orbitals in a sulfur (S) atom for which \(|m| \leq 1\) and which contains at least one electron, we can follow these steps:

### Step 1: Determine the Electron Configuration of Sulfur
The atomic number of sulfur (S) is 16, which means it has 16 electrons. The electron configuration of sulfur is:
- 1s²
- 2s²
- 2p⁶
- 3s²
- 3p⁴

### Step 2: Identify the Relevant Orbitals
We need to consider the orbitals where the magnetic quantum number \(m\) satisfies the condition \(|m| \leq 1\). The possible values of \(m\) for different types of orbitals are:
- For s orbitals: \(m = 0\)
- For p orbitals: \(m = -1, 0, +1\)

### Step 3: Count the Orbitals
Now we will count the orbitals that meet the criteria:

1. **1s Orbital**:
- \(m = 0\) (1 orbital)
- Electrons: 2 (1s²)

2. **2s Orbital**:
- \(m = 0\) (1 orbital)
- Electrons: 2 (2s²)

3. **2p Orbitals**:
- \(m = -1, 0, +1\) (3 orbitals)
- Electrons: 6 (2p⁶)

4. **3s Orbital**:
- \(m = 0\) (1 orbital)
- Electrons: 2 (3s²)

5. **3p Orbitals**:
- \(m = -1, 0, +1\) (3 orbitals)
- Electrons: 4 (3p⁴)

### Step 4: Total Count of Orbitals
Now, we will sum the orbitals that have at least one electron:
- 1s: 1 orbital
- 2s: 1 orbital
- 2p: 3 orbitals
- 3s: 1 orbital
- 3p: 3 orbitals

Total = \(1 + 1 + 3 + 1 + 3 = 9\) orbitals.

### Final Answer
The total number of orbitals in a sulfur atom for which \(|m| \leq 1\) and which contains at least one electron is **9**.

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