Problem 97 - A Complete Resource Book in Chemistry for JEE Main

Question

Which ionization potential in the following equations involves the greatest amount of energy? (a) \(\mathrm{Na} \longrightarrow \mathrm{Na}^{+}+\mathrm{e}\) (b) \(\mathrm{K} \longrightarrow \mathrm{K}^{+} \mathrm{e}^{-}\) (c) \(\mathrm{Cs}^{2+} \longrightarrow \mathrm{Cs}^{3+}+\mathrm{e}^{-}\) (d) \(\mathrm{Ca}^{+} \longrightarrow \mathrm{Ca}^{2+}+\mathrm{e}^{-}\)

Step-by-Step Solution

Answer

(c) Cs²⁺ to Cs³⁺ involves the greatest energy.

Step 1: Understanding Ionization Potential

Ionization potential refers to the energy required to remove an electron from an atom or ion in its gaseous state. It typically increases as electrons are removed from closer energy levels or higher positive charged species.

Step 2: Equation Analysis - First Ionization

In options (a) and (b), first ionization is occurring where a neutral atom loses one electron to form a singly charged ion: - (a) Na to Na⁺ - (b) K to K⁺ The ionization potentials for first ionizations are usually lower than for higher ionizations because they involve removal from less strongly attracted outer electrons.

Step 3: Equation Analysis - Subsequent Ionizations

In options (c) and (d), an electron is removed from ions with existing positive charge: - (c) Cs²⁺ to Cs³⁺ - (d) Ca⁺ to Ca²⁺ These involve greater amounts of energy because it's harder to remove electrons from positively charged ions due to greater attractive forces on the electrons.

Step 4: Comparison of Higher Ionizations

Comparing (c) and (d), removing an electron from a doubly charged cation like Cs²⁺ (c) to form a triply charged ion involves the greatest energy because each additional positive charge significantly increases the electron's attraction to the nucleus. This is more intense than the energy needed to remove an electron from Ca⁺ to form Ca²⁺ in (d).

Step 5: Conclusion

The transfer from Cs²⁺ to Cs³⁺ (c) requires the most energy due to increased positive charge and smaller atomic radius, leading to a stronger attraction of the electron to the nucleus.

Key Concepts

First Ionization Energy

The first ionization energy is the energy needed to remove the first electron from a neutral atom. In simple terms, it's like peeling off the first layer of an onion—the outer electrons are removed first. These outer electrons tend to be less tightly bound than those closer to the atom's center because they are shielded by inner electrons from the full attraction of the nucleus.

For elements such as sodium (Na) and potassium (K) in our example, this involves transforming:

• Sodium (Na) to Sodium ion (Na⁺)
• Potassium (K) to Potassium ion (K⁺)

First ionization energies are generally lower compared to second or third ionizations because breaking the "first bond" is always the easiest. It generally requires less energy to remove the first electron from the outermost shell.

Subsequent Ionization

As we remove more electrons, the process is referred to as subsequent ionization. Each electron removal beyond the first is called a subsequent ionization.

• In our given equations, looking at Cs²⁺ to Cs³⁺ and Ca⁺ to Ca²⁺ showcases second and third ionizations.

This process requires much more energy than removing the first electron because, with each removal, the remaining electrons are held more tightly by the nucleus. The increase in positive charge after each electron is removed increases the attraction between the electrons and the nucleus, requiring more significant energy input for subsequent ionizations.

Energy Levels

Every electron in an atom is located in an energy level or shell. These levels are like rungs on a ladder, where moving up the ladder requires energy.

• Electrons closer to the nucleus are at lower energy levels and are held more tightly.
• Outer electrons, at higher energy levels, are easier to remove.

In the context of ionization, the energy level tells us how much energy is required to remove an electron. The lower the energy level (closer to the nucleus), the more challenging it is to remove the electron, thus requiring a higher ionization energy.

Charge and Electron Removal

When ionizing an atom or ion, electron removal becomes increasingly challenging as the positive charge of the ion increases.

• More positively charged ions attract electrons more strongly.
• Consequently, subsequent ionizations become more energy-consuming.

Considering our step by step problem solution, removing an electron from Cs²⁺ to form Cs³⁺ entails a significant amount of energy due to the increased nuclear charge. In simpler terms, as you remove more electrons, the remaining ones cling more closely to the positively charged nucleus, making each subsequent removal require an even greater amount of energy.