Question

The decreasing order of second ionization cnergy of \(\mathrm{K}, \mathrm{Ca}\) and \(\mathrm{Ba}\) is (1) \(\mathrm{Ca}>\mathrm{Ba}>\mathrm{K}\) (2) \(\mathrm{Ba}>\mathrm{K}>\mathrm{Ca}\) (3) \(\mathrm{K}>\mathrm{Ca}>\mathrm{Ba}\) (4) \(\mathrm{K}>\mathrm{Ba}>\mathrm{Ca}\)

Short answer

Option 3: K > Ca > Ba

Step-by-step solution

Understand the Concept of Second Ionization Energy

The second ionization energy is the energy required to remove the second electron from an atom after the first electron has been removed. It generally increases as the effective nuclear charge increases and decreases as the atomic radius increases.

Consider the Elements Involved

The elements in question are Potassium (K), Calcium (Ca), and Barium (Ba). Locate these elements in the periodic table to understand their positions and their electronic configurations.

Evaluate the Electron Configurations

Potassium (K): [Ar] 4s^1. First ionization removes the 4s electron, making it [Ar].Calcium (Ca): [Ar] 4s^2. First ionization removes one 4s electron making it [Ar] 4s^1.Barium (Ba): [Xe] 6s^2. First ionization removes one 6s electron making it [Xe] 6s^1.

Identify the Order of Second Ionization Energy

After removing one electron:Potassium (K): configuration is like [Ar]. Removing another electron from a noble gas-like configuration is very difficult.Calcium (Ca): second ionization involves removing the second 4s electron from [Ar] 4s^1.Barium (Ba): second ionization involves removing the second 6s electron from [Xe] 6s^1.Comparatively, K will have the highest second ionization energy, Ca the next, and Ba will have the lowest because Ca still has one less shielding electron and a higher effective nuclear charge effect compared to Ba.

Verify and Select the Correct Option

The order matches the decreasing second ionization energy as follows: K > Ca > Ba. Therefore, the correct answer is (3).

Key concepts

Periodic Table

The periodic table is like a map for understanding elements and their properties. It organizes elements in rows and columns based on their atomic number, which is the number of protons in an atom. As you move from left to right across a period, elements gain more protons and electrons, changing their properties. Elements in the same column, also known as groups, have similar chemical properties.

• Potassium (K), Calcium (Ca), and Barium (Ba) are all part of Group 2 elements.
• Their placement on the periodic table helps us predict their reactivity and ionization energies.

Understanding the periodic table allows us to see trends in ionization energy, electron affinity, and atomic radius as we compare different elements.

Electron Configuration

Electron configuration describes how electrons are distributed in an atom's orbitals. Each element has a unique electron configuration, which influences its chemical behavior.

• Potassium (K): [Ar] 4s^1 — 19 electrons
• Calcium (Ca): [Ar] 4s^2 — 20 electrons
• Barium (Ba): [Xe] 6s^2 — 56 electrons

Electron configurations are essential for understanding ionization energy. The outermost electrons are removed first during ionization. The configuration also shows how full the energy levels are. Removing an electron from a stable or 'noble gas' configuration, like Potassium (K) after losing one electron, requires more energy.

Effective Nuclear Charge

Effective nuclear charge (Z_eff) is the net positive charge felt by valence electrons. It is 'effective' because inner electrons shield the outer electrons from the full positive charge of the nucleus.

• Z_eff can be calculated approximately by subtracting the number of shielding electrons from the total number of protons.

For example:

• Potassium: After the first ionization, the electron configuration is similar to Argon (Ar), and the effective nuclear charge experienced by the remaining electron is quite high.
• Calcium: With one electron in the 4s orbital, the shielding effect is less, so the effective nuclear charge is moderate.
• Barium: With electrons farther away in the 6s orbital, the shielding effect is stronger, reducing the effective nuclear charge significantly.

A higher effective nuclear charge generally means higher ionization energy because more force is needed to remove an electron.

Atomic Radius

Atomic radius is the size of an atom, typically measured from the nucleus to the outer edge of the electron cloud.

• It increases as you move down a group in the periodic table because additional electron shells are added.
• It decreases as you move across a period from left to right because protons are added, pulling electrons closer to the nucleus.

Let's look at our elements:

• Potassium (K): Has a smaller atomic radius after losing one electron and resembling a noble gas configuration.
• Calcium (Ca): Has a smaller atomic radius compared to Barium because it has fewer electron shells.
• Barium (Ba): Has the largest atomic radius due to being further down Group 2.

A larger atomic radius usually means lower ionization energy because the outer electrons are further from the nucleus and are less tightly held.