Which of the following relation is correct with respect to first `(I)` and second `(II)` ionization enthalpies of potassium and calcium?

Options

A. `I_(Ca) gt II_(K)`
B. `I_(K) gt I_(Ca)`
C. `II_(Ca) gt II_(K)`
D. `II_(K) gt II_(Ca)`

Explanation

To determine the correct relation between the first and second ionization enthalpies of potassium (K) and calcium (Ca), we can follow these steps:

### Step 1: Write the electronic configurations
- **Potassium (K)**: The electronic configuration is \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^1\).
- **Calcium (Ca)**: The electronic configuration is \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2\).

### Step 2: Analyze the first ionization enthalpy
- Potassium has one electron in its outermost shell (4s), which it can easily lose to achieve the noble gas configuration of Argon. Therefore, the first ionization enthalpy of potassium is relatively low.
- Calcium has two electrons in its outermost shell (4s), and it requires more energy to remove one of these electrons compared to potassium. Thus, the first ionization enthalpy of calcium is higher than that of potassium.

### Step 3: Analyze the second ionization enthalpy
- For potassium, after losing one electron, it attains the noble gas configuration of Argon. Removing a second electron from a stable noble gas configuration requires a significant amount of energy, making the second ionization enthalpy of potassium very high.
- For calcium, after losing one electron, it will have one electron left in the 4s subshell. The removal of the second electron will lead to a more stable configuration (similar to Argon), but it is less stable than the fully filled 4s subshell. Therefore, the second ionization enthalpy of calcium will be lower than that of potassium.

### Conclusion
From the analysis above, we can conclude:
- The first ionization enthalpy of potassium (K) is lower than that of calcium (Ca).
- The second ionization enthalpy of potassium (K) is higher than that of calcium (Ca).

Thus, the correct relation is:
**Second Ionization Enthalpy of Potassium > Second Ionization Enthalpy of Calcium.**

### Final Answer
The correct answer is **D**: The second ionization enthalpy of potassium is greater than that of calcium.

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