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As lithium is smaller in size than that of sodium, then sodium should loose electron more easily than lithium

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    $\begingroup$ Sodium does lose electron more easily than lithium; check the ionization energies and you'll see just that. Electrode potentials are more complicated. $\endgroup$ Dec 11 '19 at 16:07
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Of course, the Lithium atom is smaller than Sodium. But the Sodium nucleus attracts its outer electron much stronger than Lithium, at it has 11 protons, and Lithium only 3. So both effects (size and charge) have to be taken into account. Apparently the size effect is not dominant.

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