Arrange the elements of second period in order of increasing second ionization enthalpies.

Explanation

The electron configuration of the ions obtained after removal of first electron from the elements of 2nd `(1s^(2) 2s^(2) 2p^(3), F^(+) (1s^(2) 2s^(2) 2p^(4))` and `(Ne^(+) (1s^(2) 2s^(2) 2p^(5))`
The following conclusions can be drawn from the above configuration
(i) `Li^(+)` has nole gas viz. He gas configuration therefore `Delta_(i)H_(2)`of Li is the highest in the second period
(ii) Since `B^(+)` the electron has to be removal from a more stable fully filled 2 s-orbital while in `Be^(+)` it has to be lost from the less stable half-filled 2s-orbital and furthermore, the loss of an electron from `Be^(+)` gives more stable `Be^(2+)` ion with noble gas configuration therefore `Delta_(i)H_(2)` of Be is lower than that of B.
(iii) Since more energy is required to remove an s-electron than a p-electron of the same energy level therefore more energy is required to remove a 2s-electron from `B^(+) (1s^(2) 2s^(2))` than a 2p- electron from `C^(+) (1s^(2) 2s^(2) 2p^(1))`. In other words `Delta_(i)H_(2)` of C is lower than that of B.
(iv) As we move from C to N O, the nuclear charge increases by one unit at time therefore their `Deltai H_(2)` also increase accordingly. In other words `Delta_(i)H_(2)` of highest than that of N which in turn is higher than that of C.
(v) In case of `O^(+) (1s^(2) 2s^(2) 2p^(3))` and electron is to be from an exactly half- filled 2p- orbital but in case of `F^(+) (1s^(2) 2s^(2) 2p^(4))` this is not so. However, loss of an electron from `F^(+)` gives an exactly half-filled 2p- orbital (i.e, `F^(2+) (1s^(2) 2s^(2) 2p^(3))` therefore `Delta_(i)H_(2)` of F should be lower than that of O.
(vi) Like `O^(+) (1s^(2) s^(2) 2p^(3))` and `F^(+) (1s^(2) 2s^(2) 2p^(4))` in case of `Ne^(+) (1s^(2) 2s^(2) 2p^(5))` also an electron is to be removed from a 2p-orbital . Since Ne has the highest nuclear nuclear charge in 2nd period `Delta_(i)H_(2)` of Ne is expected to be much higher than that of O ro E.
From the above discussion it follows that `Delta_(i)H_(2)` of the elements of 2nd period increase in the order.
`Be lt C lt B lt N lt F lt O lt Ne lt Li`