How many electrons in p-subshell of argon (Z = 18) have same spin ?

Answer

To determine how many electrons in the p-subshell of argon (Z = 18) have the same spin, we will follow these steps:

### Step-by-Step Solution:

1. **Determine the Electron Configuration of Argon:**
- The atomic number of argon (Z = 18) indicates it has 18 electrons.
- The electron configuration can be written as:
\[ \text{1s}^2 \text{2s}^2 \text{2p}^6 \text{3s}^2 \text{3p}^6 \]

2. **Identify the Electrons in the p-subshell:**
- In the electron configuration, the p-subshells are found in the 2p and 3p levels.
- For argon, the p-subshells contain:
- 2p: 6 electrons
- 3p: 6 electrons

3. **Count the Total Electrons in the p-subshells:**
- Total electrons in the p-subshells:
\[ 6 \text{ (from 2p)} + 6 \text{ (from 3p)} = 12 \text{ electrons} \]

4. **Determine the Spin of Electrons:**
- According to the Pauli Exclusion Principle, each orbital can hold a maximum of 2 electrons with opposite spins.
- The p-subshell can hold a maximum of 6 electrons (3 orbitals, each can hold 2 electrons).
- For the 2p and 3p subshells, the electrons will fill according to Hund's rule, which states that electrons will fill degenerate orbitals singly first before pairing up.

5. **Count the Electrons with the Same Spin:**
- In the 2p subshell (6 electrons), they will fill as follows:
- 2 electrons will pair up in each of the 3 orbitals (2p_x, 2p_y, 2p_z).
- In the 3p subshell (6 electrons), they will also fill similarly:
- 2 electrons will pair up in each of the 3 orbitals (3p_x, 3p_y, 3p_z).
- Therefore, for each p subshell (2p and 3p), there are 3 orbitals, and in each orbital, there can be 1 electron with spin up (+1/2) and 1 electron with spin down (-1/2).

6. **Final Count of Electrons with Same Spin:**
- In total, there are 6 electrons in the p-subshells (3 from 2p and 3 from 3p) that can have the same spin.
- Thus, the total number of electrons in the p-subshells of argon that have the same spin is:
\[ 6 \text{ (3 from 2p + 3 from 3p)} \]

### Final Answer:
The number of electrons in the p-subshell of argon that have the same spin is **6**.

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