The incorrect among the following is:

Options

A. The first ionization potential of Al is less than the first ionization potential of Mg
B. The second ionizaztion potential of Mg is greater than the second ionization potential of Na
C. The first ionization potential of Na is less than the first ionization potential of Mg
D. The third ionization potential of Mg is greater than the third ionization potential of Al

Answer

To solve the question regarding the incorrect statement among the given options, we will analyze each statement one by one based on the concepts of ionization energy and electronic configurations.

### Step-by-Step Solution:

1. **Understanding Ionization Energy:**
- Ionization energy (or ionization potential) is the energy required to remove an electron from an atom in its gaseous state.
- Generally, the higher the nuclear charge and the more stable the electron configuration, the higher the ionization energy.

2. **Analyzing Option 1:**
- **Statement:** The first ionization potential of aluminum is less than that of magnesium.
- **Electronic Configuration:**
- Magnesium (Mg): 1s² 2s² 2p⁶ 3s²
- Aluminum (Al): 1s² 2s² 2p⁶ 3s² 3p¹
- **Comparison:**
- Removing an electron from Mg (3s²) involves breaking a completely filled subshell.
- Removing an electron from Al (3p¹) involves breaking an incompletely filled subshell.
- **Conclusion:** It is easier to remove an electron from Al than from Mg, thus this statement is **correct**.

3. **Analyzing Option 2:**
- **Statement:** The second ionization potential of magnesium is greater than that of sodium.
- **Electronic Configuration:**
- Sodium (Na): 1s² 2s² 2p⁶ 3s¹
- Magnesium (Mg): 1s² 2s² 2p⁶ 3s²
- **Comparison:**
- For Mg, the second ionization involves removing an electron from the 3s subshell (3s² → 3s¹).
- For Na, the second ionization involves removing an electron from a fully filled subshell (2p⁶).
- **Conclusion:** Removing an electron from a fully filled subshell requires more energy, thus the second ionization potential of sodium is greater than that of magnesium. Therefore, this statement is **incorrect**.

4. **Analyzing Option 3:**
- **Statement:** The first ionization potential of sodium is less than that of magnesium.
- **Comparison:**
- Sodium (Na) removes an electron from 3s¹, while magnesium removes from 3s².
- **Conclusion:** Since removing an electron from sodium (which has one electron in the outer shell) requires less energy than from magnesium (which has two), this statement is **correct**.

5. **Analyzing Option 4:**
- **Statement:** The third ionization potential of magnesium is greater than that of aluminum.
- **Comparison:**
- For Mg, the third ionization involves removing an electron from a filled 2p subshell (2p⁶).
- For Al, it involves removing from 3s¹.
- **Conclusion:** Removing an electron from a filled subshell requires more energy than from an incompletely filled subshell. Thus, this statement is **correct**.

### Final Conclusion:
The incorrect statement among the options provided is:
- **Option 2:** The second ionization potential of magnesium is greater than that of sodium.