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Why does the first ionization enthalpy increase as we go from left to right across a given period of the periodic table?

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This is an account of following facts

(i) Atomic size α \(\frac{1}{I.E}\)

On moving across the period, atomic size decreases hence, ionization energy increases.

(ii) L.E. a Nuclear charge. On moving across the period, nuclear charge increases and electrons get added up in the same shell.

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