The element having greatest difference between its first and second ionization energies, is:

Options

A. Sc
B. Ca
C. Ba
D. K

Explanation

To determine which element has the greatest difference between its first and second ionization energies, we need to analyze the electronic configurations and the stability of the resulting ions after the removal of electrons. Here’s a step-by-step solution:

### Step 1: Understand Ionization Energy
Ionization energy is the energy required to remove an electron from an atom. The first ionization energy (IE1) is the energy needed to remove the first electron, while the second ionization energy (IE2) is the energy required to remove the second electron.

### Step 2: Analyze the Given Elements
We have four elements to consider:
1. **Scandium (Sc)** - Atomic number 21, electronic configuration: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹
2. **Calcium (Ca)** - Atomic number 20, electronic configuration: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s²
3. **Barium (Ba)** - Atomic number 56, electronic configuration: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p⁶ 6s¹
4. **Potassium (K)** - Atomic number 19, electronic configuration: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹

### Step 3: Determine the Stability After Ionization
- **Scandium (Sc)**: After removing the first electron (IE1), it becomes Sc²⁺ with a configuration of 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ 3d⁰. The second ionization (IE2) will be from a relatively stable configuration.

- **Calcium (Ca)**: After removing the first electron, it becomes Ca⁺ with a configuration of 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹. The second ionization will remove an electron from a stable configuration.

- **Barium (Ba)**: After removing the first electron, it becomes Ba⁺ with a configuration of 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s¹. The second ionization will also be from a relatively stable configuration.

- **Potassium (K)**: After removing the first electron, it becomes K⁺ with a configuration of 1s² 2s² 2p⁶ 3s² 3p⁶. The second ionization will remove an electron from a noble gas configuration (Argon), which is very stable.

### Step 4: Compare the Differences
The difference in ionization energies is generally greater when the first ionization results in a stable noble gas configuration. In the case of potassium, after removing the first electron, it achieves the stable configuration of Argon, making the second ionization energy significantly higher.

### Conclusion
Among the given elements, **Potassium (K)** has the greatest difference between its first and second ionization energies because the removal of the second electron requires significantly more energy due to the stability of the resulting noble gas configuration.

### Final Answer
**Potassium (K)** has the greatest difference between its first and second ionization energies.

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