The first `(IE_(1))` and second `(IE_(2))` ionisation energies `(kJ mol^(-1))` of a new element designated by roman numericals are shown below:
`{: (,(IE_(1)),(IE_(2))),(I,2372,5251),(II,520,7300),(III,900,1760),(IV,1680,3380):}`
Which of these elements is likely to be (a) a reactive metal, (b) a reactive non-metal, (c) a noble gas and (d) a metal that forms a binary halide of the formula, `AX_(2)`.

Explanation

(a) Since element II has a very low `Delta_(i)H_(1)` but a very high `Delta_(i) H_(2)` therefore it has only electron in the valence shell and hence is liekely to be a reactive metal (i.e. an alkali metal)
(b) Since the `Delta_(i)H_(1)` of element IV is very high and its `Delta_(i)H_(2)` is not so high (actually almost double) it is likely to be a reactive non- metal (i.e., a halogen)
( c) Among the elements listed `Delta_(i)H_(1)` of element I is the highest and its `Delta_(i) H_(2)` is also not so high therefore it must be a noble gas.
( d) The `Delta_(i) H_(1)` of elements III is higher than that of the element II but unlike element II its `Delta_(i) H_(2)` is only about twice such it will form a stable binary halide to the formula `AX_(2)` where is the metal X is the halogen