**Explanation:**

The second ionization potential (IP) refers to the energy required to remove the second electron from an atom or ion.

In general, the second ionization potential is higher than the first ionization potential because removing a second electron requires more energy as the remaining electrons experience an increased effective nuclear charge.

To determine the correct order of second ionization potentials for Ca, Ba, and K, we need to compare the elements' electronic configurations and their positions in the periodic table.

**1. Electronic Configurations:**

- Calcium (Ca): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s²

- Barium (Ba): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p⁶ 6s²

- Potassium (K): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹

**2. Effective Nuclear Charge:**

The effective nuclear charge is the net positive charge experienced by an electron in an atom or ion. It increases across a period and decreases down a group in the periodic table.

- Ca and Ba are both in the same group (Group 2) and have the same number of valence electrons. However, Ba has more electron shells, resulting in a larger atomic size and a greater shielding effect from the inner electrons. Therefore, the effective nuclear charge experienced by the valence electrons in Ba is less than that in Ca.

- K is in Group 1 and has one valence electron. It has a smaller atomic size and a higher effective nuclear charge compared to both Ca and Ba.

**3. Order of Second Ionization Potentials:**

Based on the above information, we can determine the correct order of second ionization potentials:

- K has the highest second ionization potential because it has a smaller atomic size and a higher effective nuclear charge compared to Ca and Ba.

- Ca has the second highest second ionization potential because it has a larger atomic size and a lower effective nuclear charge compared to K.

- Ba has the lowest second ionization potential because it has the largest atomic size and the lowest effective nuclear charge among the three elements.

Therefore, the correct order of second ionization potentials for Ca, Ba, and K is **K > Ca > Ba**.

**Explanation:**

The second ionization potential (IP) refers to the energy required to remove a second electron from an atom or ion. It is generally higher than the first ionization potential because it becomes more difficult to remove an electron from an already positively charged ion.

To determine the correct order of second ionization potentials of Ca, Ba, and K, we need to compare the ionization energies of these elements.

**1. Potassium (K):**
- The first ionization potential of potassium is relatively low because it has one valence electron in the outermost energy level.
- However, after the first electron is removed, the remaining ion is positively charged, which increases the attraction between the nucleus and the remaining electrons.
- As a result, it requires more energy to remove a second electron from the potassium ion.
- Therefore, the second ionization potential of potassium is higher than the first ionization potential.

**2. Calcium (Ca):**
- Calcium has two valence electrons in its outermost energy level.
- The first ionization potential of calcium is higher than that of potassium because it requires more energy to remove an electron from a neutral calcium atom compared to potassium.
- After the first electron is removed, the remaining ion is positively charged, increasing the attraction between the nucleus and the remaining electrons.
- However, the second ionization potential of calcium is lower than that of potassium because the removal of a second electron from the calcium ion is not as difficult.

**3. Barium (Ba):**
- Barium has two valence electrons in its outermost energy level, similar to calcium.
- The first ionization potential of barium is higher than that of calcium because it requires more energy to remove an electron from a neutral barium atom compared to calcium.
- After the first electron is removed, the remaining ion is positively charged, increasing the attraction between the nucleus and the remaining electrons.
- The second ionization potential of barium is higher than that of calcium because the removal of a second electron from the barium ion is more difficult due to the increased positive charge on the ion.

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