To determine the incorrect statement among the provided options regarding ionization energies, we will analyze each statement step by step.
### Step 1: Analyze the First Statement
**Statement:** The first ionization energy of aluminum is less than the first ionization energy of magnesium.
- **Explanation:**
- Aluminum (Al) has an atomic number of 13, with an electronic configuration of [Ne] 3s² 3p¹.
- Magnesium (Mg) has an atomic number of 12, with an electronic configuration of [Ne] 3s².
- The first ionization energy of aluminum is indeed less than that of magnesium because the 3p orbital of aluminum is higher in energy and more shielded than the 3s orbital of magnesium, making it easier to remove an electron from aluminum.
- **Conclusion:** This statement is **correct**.
### Step 2: Analyze the Second Statement
**Statement:** The second ionization energy of magnesium is greater than the second ionization energy of sodium.
- **Explanation:**
- Sodium (Na) has one valence electron in its outer shell (3s¹), and after losing one electron, it achieves a stable electronic configuration (Neon).
- Magnesium (Mg) has two valence electrons (3s²). After losing one electron, it still has one more electron to remove, which requires more energy.
- Therefore, the second ionization energy of sodium will be greater than that of magnesium because sodium becomes stable after losing one electron, while magnesium requires more energy to remove the second electron.
- **Conclusion:** This statement is **incorrect**.
### Step 3: Analyze the Third Statement
**Statement:** The first ionization energy of sodium is less than the first ionization energy of magnesium.
- **Explanation:**
- Sodium has one valence electron (3s¹), while magnesium has two (3s²).
- The first ionization energy of magnesium is higher than that of sodium because magnesium has a greater nuclear charge, which holds its electrons more tightly.
- **Conclusion:** This statement is **correct**.
### Step 4: Analyze the Fourth Statement
**Statement:** The third ionization energy of magnesium is greater than the third ionization energy of aluminum.
- **Explanation:**
- The third ionization energy refers to the energy required to remove the third electron from an atom.
- Magnesium, after losing two electrons, has a stable noble gas configuration (Neon), and removing a third electron requires significantly more energy.
- Aluminum, after losing two electrons, still has one more electron in the 3p orbital, which is easier to remove compared to magnesium's tightly held electrons.
- **Conclusion:** This statement is **correct**.
### Final Conclusion
The only incorrect statement among the options is **the second statement**, which claims that the second ionization energy of magnesium is greater than that of sodium.
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