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

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
The atomic number (Z) of chlorine is 17. This means that a chlorine atom has 17 electrons.

### Step 2: Write the Electronic Configuration
The electronic configuration of chlorine can be written as:
1s² 2s² 2p⁶ 3s² 3p⁵

### Step 3: Identify the Unpaired Electron
In the electronic configuration, we can see that the 3p subshell has 5 electrons. The distribution of electrons in the p subshell can be represented as:
- 3p: ↑↓ ↑↓ ↑ ↑
Here, the first four electrons are paired, and the fifth electron is unpaired.

### Step 4: Determine the Principal Quantum Number (n)
The unpaired electron is in the 3p subshell. The principal quantum number (n) for this electron is 3.

### Step 5: Determine the Azimuthal Quantum Number (l)
For p orbitals, the azimuthal quantum number (l) is 1.

### Step 6: Determine the Magnetic Quantum Number (m_l)
The magnetic quantum number (m_l) can take values from -l to +l. Since l = 1, the possible values for m_l are -1, 0, and +1. The unpaired electron in the 3p subshell can be assigned m_l = +1.

### Step 7: Determine the Spin Quantum Number (m_s)
The spin quantum number (m_s) can be either +1/2 or -1/2. For the unpaired electron, we can assign it a spin of +1/2.

### Final Set of Quantum Numbers
Putting all this information together, the correct set of quantum numbers for the unpaired electron of a chlorine atom is:
- n = 3
- l = 1
- m_l = +1
- m_s = +1/2

Thus, the final answer is: **(3, 1, +1, +1/2)**.

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