Arrange the following ions in order of their inceasing radii : `Na^(+) , Mg^(2+) , K^(+) , Al^(3+)`

Explanation

(i) The ionic radius of any cation increases as the number of energy shells increases and decreases as the magnitude of the positive charge increases.
(ii) `Mg^(2+) ( 1s^(2) 2s^(2) 2p^(6))` and `A1^(3+) (1s^(2) 2s^(2) 2p^(6))` are isoelectronic ions and each one of these has two energy shells. Since `K^(+) (1s^(2) 2s^(2) 2p^(6) 3s^(2) 3p^(6))` has three shells and `Mg^(2+) ` and `A1^(2+)` and `A1^(3+)` have two shells each, therefore ionic radius of `K^(+)` is the largest followed by `Mg^(2+) ` and then `A1^(3+)`
(iv) Now `Li^(+) (1s^(2))` has one shell and + 1 charge but `A1^(3+) (1s^(2) 2s^(2) 2p^(6))` has two shell s and + 3 charge . Since the increases in the ionic radius of `A1^(3+)` due to the presence of two shells is more than counterbalanced by the decrease in its size dut to an increases in charge from + 1 in `Li^(+) ` to 3 in `A1^(3+)` therefore the ionic radius of `A1^(3+)` is lower than that of `Li^(+)`
Thus the ionic radii of the four ions increases in the order : `A1^(3+) lt Li^(+) lt Mg^(2+) lt K^(+)`