The incorrect statement among the following is :
(A)

Options

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

Answer

To solve the question regarding which statement among the given options is incorrect, we will analyze each statement one by one.

### Step 1: Analyze the First Statement
**Statement:** The ionization energy of aluminum will be less than that of magnesium.

- **Electronic Configuration:**
- Aluminum (Al): 1s² 2s² 2p⁶ 3s² 3p¹ (Total 13 electrons)
- Magnesium (Mg): 1s² 2s² 2p⁶ 3s² (Total 12 electrons)

- **Ionization Energy Comparison:**
- Aluminum has one electron in the 3p orbital, while magnesium has a filled 3s orbital.
- Since filled orbitals are more stable than partially filled ones, magnesium will have a higher ionization energy than aluminum.

**Conclusion:** This statement is **correct**.

### Step 2: Analyze the Second Statement
**Statement:** The second ionization potential of magnesium is greater than that of sodium.

- **Ionization Potentials:**
- Sodium (Na) after losing one electron becomes Na⁺ (10 electrons): 1s² 2s² 2p⁶ (Noble gas configuration).
- Magnesium (Mg) after losing one electron becomes Mg⁺ (11 electrons): 1s² 2s² 2p⁶ 3s¹.

- **Comparison:**
- Na⁺ has a noble gas configuration, making it more stable and thus harder to remove another electron compared to Mg⁺, which has an unpaired electron.

**Conclusion:** This statement is **incorrect**.

### Step 3: Analyze the Third Statement
**Statement:** The first ionization energy of sodium is less than that of magnesium.

- **Comparison:**
- Sodium has one electron in its outermost shell (3s¹), while magnesium has two (3s²).
- It is easier to remove one electron from sodium than from magnesium, which has a higher ionization energy due to its filled orbital.

**Conclusion:** This statement is **correct**.

### Step 4: Analyze the Fourth Statement
**Statement:** The third ionization energy of magnesium is greater than that of aluminum.

- **Comparison:**
- After losing two electrons, Mg²⁺ has the configuration of 1s² 2s² 2p⁶ (10 electrons).
- After losing two electrons, Al²⁺ has the configuration of 1s² 2s² 2p⁶ 3s² (11 electrons).
- Removing an electron from Mg²⁺ (which has a stable noble gas configuration) requires more energy than removing it from Al²⁺.

**Conclusion:** This statement is **correct**.

### Final Conclusion
The only incorrect statement among the options is the **second statement**: "The second ionization potential of magnesium is greater than that of sodium."

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