The first `(IE_1)` and second `(IE_2)` ionisation enthalpies `("kJ mol"^(-1))` of a few elements designated by Roman numerals are shown below.
`{:(,,IE_(1),IE_(2)),(,I,2372,5251),(,III,900,1760):}` `{:(,,IE_(1),IE_(2)),(,II,520,7300),(,IV,1680,3380):}`
Which of the above element is likely to be:
a metal A that forms a stable binary halide of the formula `AX_(2) ("X = halogen")`

Explanation

To determine which element is likely to be a metal \( A \) that forms a stable binary halide of the formula \( AX_2 \) (where \( X \) is a halogen), we need to analyze the given ionization enthalpies (IE) of the elements.

### Step-by-Step Solution:

1. **Understanding the Ionization Energies**:
- The first ionization energy (\( IE_1 \)) is the energy required to remove the first electron from an atom.
- The second ionization energy (\( IE_2 \)) is the energy required to remove a second electron after the first has been removed.

...