Which ionisation potential (IP) in the following equations involves the greatest amount of energy

Options

A. `NararrNa^(+)+e^(-)`
B. `K^(+)rarrK^(2+)+e^(-)`
C. `C^(2+)rarrC^(3+)+e^(-)`
D. `Ca^(+)rarrCa^(2+)+e^(-)`

Explanation

To determine which ionization potential (IP) involves the greatest amount of energy, we need to analyze the given elements and their electronic configurations. Ionization potential refers to the energy required to remove an electron from an atom or ion in its gaseous state.

### Step-by-Step Solution:

1. **Identify the Elements and Their Configurations**:
- For Sodium (Na): The electronic configuration is \(1s^2, 2s^2, 2p^6, 3s^1\).
- For Potassium (K): The electronic configuration is \(1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 4s^1\).
- For Calcium (Ca): The electronic configuration is \(1s^2, 2s^2, 2p^6, 3s^2, 3p^6\).

2. **Consider the Stability of the Ions**:
- When an electron is removed from an atom, the resulting ion's stability plays a crucial role in determining the ionization energy.
- A completely filled shell is more stable than a partially filled shell. Thus, removing an electron from a stable configuration requires more energy.

3. **Analyze the Ionization Potentials**:
- The first ionization energy (IE1) of an element is generally lower than the second ionization energy (IE2) because removing an electron from a neutral atom is easier than removing a second electron from a positively charged ion.
- For potassium (K), after losing one electron, it becomes \(K^+\) which has a stable noble gas configuration (similar to Argon).
- For calcium (Ca), after losing two electrons, it becomes \(Ca^{2+}\) which also achieves a stable configuration (similar to Argon).

4. **Compare the Ionization Energies**:
- The ionization potential of \(K\) to \(K^+\) (first ionization) is relatively low because it is removing an electron from a higher energy level (4s).
- The ionization potential of \(Ca\) to \(Ca^+\) (first ionization) is higher because it involves removing an electron from a filled 3p shell, which is more stable than the 4s of potassium.
- The second ionization potential of calcium (removing another electron to form \(Ca^{2+}\)) is expected to be significantly higher due to the increased stability of the resulting ion.

5. **Conclusion**:
- Among the given options, the second ionization potential of calcium (\(Ca\) to \(Ca^{2+}\)) involves the greatest amount of energy due to the stability of the filled electron shells and the energy required to remove an electron from a stable ion.

### Final Answer:
The ionization potential that involves the greatest amount of energy is the second ionization potential of calcium (Ca to Ca²⁺).