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Both Na and K are Group 1 metals, meaning they possess 1 electron in their valance shell of electrons. K is further down in group 1 because it has more electron shells. K also has more protons than Na, this would lead one to assume that the nuclear force of attraction between the positive nucleus and the valance shell of electrons would be stronger (since opposite charges attract), however, due to the greater number of shells between the nucleus and the outer shell, more shielding of the nuclear attraction occurs. This means less energy is required to break the forces of attraction between the nucleus and outer shell electron in Potassium compared to Sodium. Thus increasing the reactivity.
Due to both potassium and sodium possessing one electron in their outer shell, they are both Group 1 elements. The reactivity of this group increases as you go down as the atoms become larger, and the outer electron will move further away from the nucleus and the force of attraction between the outer electron decreases and nucleus. As potassium is larger than sodium, potassium's electron is further away from the nucleus thus, the outer electron is lost easier. This requires less energy and therefore can be said to be more reactive.
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