The correct set of quantum numbers for the unpaired electron of chlorine atom is

Options

A. `n=2,l=1,m=0`
B. `n=2,l=1,m=1`
C. `n=3,l=1,m=1`
D. `n=3,l=0,m=0`

Answer

To determine the correct set of quantum numbers for the unpaired electron of a chlorine atom, we will follow these steps:

### Step 1: Identify the Atomic Number of Chlorine
Chlorine has an atomic number of 17, which means it has 17 electrons.

### Step 2: Write the Electron Configuration
The electron configuration for chlorine can be written as:
- 1s² 2s² 2p⁶ 3s² 3p⁵

### Step 3: Determine the Last Electron Added
The last electron added is in the 3p subshell. The 3p subshell can hold a maximum of 6 electrons, but chlorine has 5 electrons in this subshell.

### Step 4: Identify the Unpaired Electron
In the 3p subshell, the electrons are filled according to Hund's rule, which states that electrons will fill degenerate orbitals singly before pairing. The filling of the 3p subshell can be represented as:
- 3p: ↑ ↑ ↑ ↓ ↓ (where ↑ represents an unpaired electron and ↓ represents paired electrons)
Thus, there is one unpaired electron in the 3p subshell.

### Step 5: Assign Quantum Numbers
Quantum numbers consist of four values:
1. **Principal Quantum Number (n)**: This indicates the shell level. For the 3p subshell, n = 3.
2. **Azimuthal Quantum Number (l)**: This indicates the subshell type. For p subshells, l = 1.
3. **Magnetic Quantum Number (m)**: This can take values from -l to +l. For l = 1, m can be -1, 0, or +1. The unpaired electron is in the last orbital, which corresponds to m = +1.
4. **Spin Quantum Number (s)**: This can be either +1/2 or -1/2. We can assign +1/2 to the unpaired electron.

### Step 6: Compile the Quantum Numbers
Thus, the quantum numbers for the unpaired electron in chlorine are:
- n = 3
- l = 1
- m = +1
- s = +1/2 (not asked in the question, but included for completeness)

### Conclusion
The correct set of quantum numbers for the unpaired electron of the chlorine atom is:
- n = 3, l = 1, m = +1

### Final Answer
The correct option is **Option C: n = 3, l = 1, m = 1**.

---