`IE_(2)` for an element is inveriably higher than `IE_(1)` because

Options

A. The size of cations is smaller than its atom.
B. It is difficult to remove electron from cations.
C. Ionisation energy is endothermic.
D. All of the above

Answer

To understand why the second ionization energy (IE₂) of an element is invariably higher than the first ionization energy (IE₁), we can follow these steps:

### Step-by-Step Solution:

1. **Definition of Ionization Energy**:
- Ionization energy is the energy required to remove an electron from an isolated gaseous atom. The first ionization energy (IE₁) refers to the energy needed to remove the first electron, while the second ionization energy (IE₂) is the energy required to remove a second electron after the first has already been removed.

2. **Example with Sodium (Na)**:
- Let's take sodium (Na) as an example. Sodium has an atomic number of 11, meaning it has 11 electrons and 11 protons in its neutral state. The first ionization process can be represented as:
\[ \text{Na} \rightarrow \text{Na}^+ + e^- \]
- The energy required for this process (IE₁) is approximately 495.8 kJ/mol.

3. **Formation of Sodium Cation (Na⁺)**:
- After the first electron is removed, sodium becomes a cation (Na⁺) with 10 electrons and still 11 protons. The effective nuclear charge (the net positive charge experienced by electrons) increases because there are now fewer electrons (10) than protons (11).

4. **Second Ionization Process**:
- The second ionization process can be represented as:
\[ \text{Na}^+ \rightarrow \text{Na}^{2+} + e^- \]
- The energy required for this process (IE₂) is significantly higher, approximately 4562 kJ/mol.

5. **Reason for Higher IE₂**:
- The increase in effective nuclear charge (due to the removal of one electron) makes it more difficult to remove the second electron. The remaining electrons are held more tightly by the nucleus because there are now more protons than electrons. This results in a higher energy requirement for the second ionization.

6. **Conclusion**:
- Therefore, the second ionization energy is invariably higher than the first because the effective nuclear charge experienced by the remaining electrons increases after the first electron is removed, making it more difficult to remove subsequent electrons.