Step 1: Understand the trend in ionisation enthalpy.
Ionisation enthalpy increases across a period from left to right because the atomic radius decreases, leading to stronger attraction between the nucleus and electrons, making it harder to remove electrons. Similarly, ionisation enthalpy decreases down a group as the atomic radius increases.
Step 2: Compare ionisation enthalpies.
- For Na (Sodium), \( \Delta H_{\text{ion}} = 497 \) kJ/mol,
- For Mg (Magnesium), \( \Delta H_{\text{ion}} = 738 \) kJ/mol,
- For Si (Silicon), \( \Delta H_{\text{ion}} = 787 \) kJ/mol.
Aluminum (Al) is placed between Mg and Si, and based on periodic trends, its first ionisation enthalpy would be closer to that of Mg. Therefore, the first ionisation enthalpy of Al is around 578 kJ/mol.
Step 3: Conclusion.
The correct ionisation enthalpy of Al is 578 kJ/mol, so the correct answer is option (B).