${IP}_{2}$ for an element is invariably higher than ${IP}_{1}$ because

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Effective nuclear charge is less for cation

Size of the cation is higher than neutral atom

Nuclear charge is high in cation

Change in bond energy

answer is B.

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Detailed Solution

When an electron is removed from an atom, it becomes a cation, and the size of the cation is smaller than neutral atom. Cation is positively charged and has higher nuclear charge, thereby it is harder to remove a negatively charged electron from a positively charged ion.

When an electron removes from an element X, then it becomes positively charged and its ionization potential is denoted as ${IP}_{1}$ . The removal of second electron from cation is called second ionization potential which is denoted as ${IP}_{2}$ and it is always higher than ${IP}_{1}$ because the electron is removed from cation.

Hence, option(b) is correct.

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