To determine the possible correct set of quantum numbers for the unpaired electron of a chlorine (Cl) atom, we will follow these steps:
### Step 1: Determine the Atomic Number and Electronic Configuration
- The atomic number of chlorine (Cl) is 17. This means it has 17 electrons.
- The electronic configuration of chlorine can be written as:
\[
\text{Cl: } 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^5
\]
### Step 2: Identify the Valence Electrons
- The valence electrons for chlorine are found in the outermost shell, which is the third shell (n=3).
- The configuration shows that there are 2 electrons in the 3s subshell and 5 electrons in the 3p subshell.
### Step 3: Identify the Unpaired Electron
- In the 3p subshell, there are 5 electrons. According to Hund's rule, these electrons will occupy the orbitals singly before pairing up.
- Therefore, the unpaired electron is one of the electrons in the 3p subshell.
### Step 4: Determine the Quantum Numbers for the Unpaired Electron
- The quantum numbers for an electron are represented as (n, l, m_l, m_s):
- **Principal Quantum Number (n)**: For the 3p orbital, \( n = 3 \).
- **Azimuthal Quantum Number (l)**: For p orbitals, \( l = 1 \).
- **Magnetic Quantum Number (m_l)**: For p orbitals, \( m_l \) can take values of -1, 0, or +1. Since we are looking for an unpaired electron, we can choose one of these values. Let's choose \( m_l = 0 \) for simplicity.
- **Spin Quantum Number (m_s)**: The spin can be either +1/2 or -1/2. We can choose \( m_s = +1/2 \) for the unpaired electron.
### Step 5: Compile the Quantum Numbers
- Therefore, the quantum numbers for the unpaired electron in chlorine can be summarized as:
\[
(n, l, m_l, m_s) = (3, 1, 0, +\frac{1}{2})
\]
### Step 6: Check the Given Options
- Now, we need to compare our derived quantum numbers with the provided options to find the correct one.
### Conclusion
- The correct set of quantum numbers for the unpaired electron of the chlorine atom is:
\[
(3, 1, 0, +\frac{1}{2})
\]
