First and second ionisation enthalpies (in \(\mathrm{kJ} /\) mol) of few elements are given below: \begin{tabular}{|c|c|c|} \hline Element & \(\boldsymbol{I E}_{\mathbf{1}}\) & \(\boldsymbol{I E}_{2}\) \\ \hline (i) & 520 & 7300 \\ \hline (ii) & 900 & 1760 \\ \hline (iii) & 1680 & 3380 \\ \hline (iv) & 2080 & 3963 \\ \hline \end{tabular} Which of the above elements will form halides with formula \(M X_{2} ?\) (a) (i) and (ii) (b) (i) and (iii) (c) (ii) and (iii) (d) (i) and (iv)

Ionization energy refers to the amount of energy needed to remove an electron from an atom or ion in its gaseous state. It's a crucial factor in understanding how elements react and the types of compounds they form. The first ionization energy (IE1) corresponds to the energy required to remove the first electron, while the second ionization energy (IE2) is the energy required to remove the second electron.

The trend of ionization energy across the periodic table is such that it generally increases from left to right and decreases from top to bottom. This behavior is due to the effective nuclear charge and the distance of the valence electron from the nucleus. A higher effective nuclear charge, often found in elements towards the right of the periodic table, translates to a stronger attraction between the nucleus and the valence electrons, thus requiring more energy to remove an electron. Conversely, as the atomic size increases, the outer electrons are farther from the nucleus and are held less tightly, making them easier to remove.

When comparing IE1 and IE2 for a given element, a significant increase from IE1 to IE2 typically indicates that the removed electron is coming from a more stable, closer shell after a valence electron has been removed. This stability is due to a fully or half-filled electron configuration that atoms naturally prefer. Therefore, elements with a massive jump from IE1 to IE2 will likely form ions with a +1 charge rather than a +2, affecting the types of compounds they can form, such as halides.

Valence electrons are the electrons in the outer shell of an atom that are involved in forming chemical bonds. They are the ones typically lost, gained, or shared when atoms interact to form compounds. The number of valence electrons an element has can determine its reactivity and the type of ions it will form.

Elements in the same group of the periodic table have the same number of valence electrons and thus exhibit similar chemical properties. For example, the elements of Group 1 have one valence electron and are highly reactive, tending to lose this electron to form +1 cations. Meanwhile, Group 17 elements have seven valence electrons and typically gain one electron to achieve a full octet, forming -1 anions.

When considering halide formation, elements with one or two valence electrons are good candidates since they can lose these electrons to form halides like MX or MX2, where M signifies the metal and X signifies the halogen. Understanding the concept of valence electrons and how they interact is crucial in predicting the types of ionic compounds an element can form.

The formation of halides occurs when halogen atoms gain electrons to form anions, which then combine with metal cations to produce salts. The formula of the resulting halide, such as MX or MX2, depends on the charges of the ions involved.

For a metal to form a halide with the formula MX2, it must be able to lose two electrons and form a divalent cation (M^2+). This is usually reflected by a smaller increase in the second ionization energy, IE2, after IE1. In halide formation, the halogen, a highly electronegative element, will attract the shed electrons from the metal. Halogens, needing only one electron to complete their valence shell, can stabilize a +1 cation to form MX. If the metal can lose two electrons (thanks to a manageable IE2), it can bond with two halogen atoms to form an MX2 structure.

In the context of our exercise, analyzing the ionization energies of the elements helps us predict their ability to form either a +1 or +2 cation. Elements that can form +2 cations are those whose IE2 values are not excessively higher than their IE1. These are the elements most likely to form MX2 type halides when they react with halogens. Understanding the interaction between ionization energy and halide formation enables us to predict the chemical formulas of compounds that will form between metals and halogens, which is vital in fields like inorganic chemistry and materials science.