The `(IE_(1))` and the `(IE_(2))` in `kJ mol^(-1)` of a few eiements designated by Roman numberals are shown below.
`|{:(,I,II,III),(IE_(1),403,549,1142),(IE_(2),2640,1060,2080):}|`
Which of the above elements is likely to be a
(a) non-metal (b) alkali metal (c ) alkaline earth metal?

Answer

To determine which of the elements designated by Roman numerals is likely to be a non-metal, alkali metal, and alkaline earth metal based on their first and second ionization enthalpies (IE1 and IE2), we can analyze the provided data step by step.

### Step-by-Step Solution:

1. **Understanding Ionization Energies**:
- Ionization energy (IE) is the energy required to remove an electron from an atom. The first ionization energy (IE1) refers to the energy needed to remove the first electron, while the second ionization energy (IE2) refers to the energy needed to remove a second electron.
- Generally, non-metals have higher ionization energies due to their smaller atomic size and greater effective nuclear charge.

2. **Analyzing the Given Data**:
- The provided ionization enthalpy values are:
- **Element I**: IE1 = 403 kJ/mol, IE2 = 2640 kJ/mol
- **Element II**: IE1 = 549 kJ/mol, IE2 = 1060 kJ/mol
- **Element III**: IE1 = 1142 kJ/mol, IE2 = 2080 kJ/mol

3. **Identifying the Non-Metal**:
- Non-metals typically have the highest ionization energies.
- Comparing the values, **Element III** has the highest IE1 (1142 kJ/mol) and IE2 (2080 kJ/mol).
- Therefore, **Element III** is likely to be a **non-metal**.

4. **Identifying the Alkali Metal**:
- Alkali metals have low first ionization energies and a very high jump in the second ionization energy, indicating that after losing one electron, the atom achieves a stable noble gas configuration.
- **Element I** has a relatively low IE1 (403 kJ/mol) and a very high IE2 (2640 kJ/mol), showing a significant jump.
- Thus, **Element I** is likely to be an **alkali metal**.

5. **Identifying the Alkaline Earth Metal**:
- Alkaline earth metals have a first ionization energy that is lower than that of non-metals but higher than that of alkali metals. They lose two electrons to achieve a stable configuration.
- **Element II** has an IE1 of 549 kJ/mol and an IE2 of 1060 kJ/mol, which is higher than that of Element I but lower than that of Element III.
- Therefore, **Element II** is likely to be an **alkaline earth metal**.

### Summary of Findings:
- **Non-metal**: Element III
- **Alkali metal**: Element I
- **Alkaline earth metal**: Element II