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How would you explain the fact that first ionisation enthalpy of sodium is lower than that of magnesium, but its second ionisation enthalpy is higher than that of magnesium?

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The first ionisation enthalpy of magnesium is higher than that of Na due to the higher nuclear charge and slightly smaller atomic radius of Mg than Na. After the loss of the first electron, Na+ formed has the electronic configuration of neon (2,8) which means it becomes highly stable because of achieving the nearest noble gas configuration and its quite clear that higher the stability more energy is required to remove an electron; thus more is the ionisation enthalpy. The higher stability of the completely filled noble gas configuration leads to very high second ionisation enthalpy for sodium. On the other hand, Mg+ formed after losing the first electron still has one more electron in its outermost (3s) orbital. As a result, the second ionisation enthalpy of magnesium is much smaller than that of sodium.

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