Which of the following species has the smallest size?
(a) `K^(o+), Sr^(2+), Ar` , (b) `Si, P, Cl` , (c ) `O, O^(ө), O^(2-)`

Explanation

`Z` for `Sr^(2+), K^(o+)` and `Ar=38, 19` and `18` respectively.
Electronic configuration of `Sr = [Kr] 5s^(2)`
Electronic configuration of `Sr^(2+) = [Kr]` (it has four shells)
Electronic configuration of `K = [Ar]4s^(1)`
Electronic configuration pf `K^(o+) = [Ar]` (it has three shells)
Inoic size of `Sr^(2+)` is smaller than that of `K^(o+)`, due to higher nuclear which compensates the effect of additional shell.
Since `K^(o+)` and `Ar` are isolectronic species with `18` electron each. `(Z)/(e^(-))` for `K^(o+) = (19)/(18) = 1.05` and `(Z)/(e^(-)` for `Ar = (18)/(19) = 1.0`. Smaller is the value of `(Z)/(e^(-))`, longer the size of that species.
So decreasing order of size is
`A gt K^(o+) gt Sr^(2+)`
(b) `Z` sor `Si, P` and `Cl = 14, 15, 17`
Decreasi9ng order of size is
`Si gt P gt Cl`
Thus, `Cl` is of the smallest size.
Moreover, along the period, size decreases from the left to the right. All of them belong to the `3rd` period.
( c) Species with more negative charge is larger than its parent atom.
Thusn the dreasing order of size is
`O^(2-) gt O^(ө) gt O`.
Thus, `O` is tyhe smallest in size.