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 can follow these steps:

### Step 1: Determine the Atomic Number and Electronic Configuration
The atomic number of chlorine (Cl) is 17. This means that a chlorine atom has 17 electrons. The electronic configuration can be written as:
- 1s² 2s² 2p⁶ 3s² 3p⁵

### Step 2: Identify the Unpaired Electrons
From the electronic configuration, we can see that:
- The 1s, 2s, and 2p orbitals are fully filled.
- The 3s orbital has 2 electrons (fully filled).
- The 3p orbital has 5 electrons.

In the 3p orbital, there are 5 electrons. The distribution of these electrons in the 3p subshell (which can hold a maximum of 6 electrons) is as follows:
- 3p: ↑↓ ↑ ↑ ↑ ↑ (where ↑ represents an electron and ↓ represents a paired electron)

From this arrangement, we can see that there is 1 unpaired electron in the 3p orbital.

### Step 3: Assign Quantum Numbers to the Unpaired Electron
Quantum numbers are defined as follows:
1. **Principal Quantum Number (n)**: Indicates the energy level of the electron.
2. **Azimuthal Quantum Number (l)**: Indicates the shape of the orbital. For p orbitals, l = 1.
3. **Magnetic Quantum Number (m)**: Indicates the orientation of the orbital. For l = 1, m can be -1, 0, or +1.

Since the unpaired electron is in the 3p orbital:
- The principal quantum number (n) for the 3rd energy level is **3**.
- The azimuthal quantum number (l) for p orbitals is **1**.
- The magnetic quantum number (m) can be either -1, 0, or +1. For this unpaired electron, we can choose **+1** (though -1 or 0 would also be valid).

### Step 4: Identify the Correct Option
Now we can compare the quantum numbers we derived with the options provided:
- Option 1: n = 2, l = 1, m = 0 (Incorrect)
- Option 2: n = 2, l = 1, m = 1 (Incorrect)
- Option 3: n = 3, l = 1, m = 1 (Correct)
- Option 4: n = 3, l = 0, m = 0 (Incorrect)

Thus, the correct set of quantum numbers for the unpaired electron of a chlorine atom is:
**n = 3, l = 1, m = 1.**